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Economic Growth

Economic Growth

I. OverviewRichard A. Easterlin

BIBLIOGRAPHY

II. TheoryGustav Ranis

BIBLIOGRAPHY

III. Mathematical TheoryMichio Morishima

BIBLIOGRAPHY

IV. Noneconomic AspectsBert F. Hoselitz

BIBLIOGRAPHY

The articles under this heading give several views of the process of economic growth as a whole. For the role of specific factors in economic growth, seeCapital; Capital, Human; Capital, social overhead; andInnovation. On the role of productivity in economic growth, seeProductivityandAgriculture, article onProductivity and Technology. Related material may be found underDevelopment Banks; Economy, Dual; Foreign aid, article oneconomic aspects; Industrialization; Industry, small; Modernization; andPlanning, economic, article ondevelopment planning.

I OVERVIEW

As a distinctive epoch in economic organization, modern economic growth, or development, dates from the eighteenth century, when its beginnings in western Europe can first clearly be discerned. It may be defined as a rapid and sustained rise in real output per head and attendant shifts in the technological, economic, and demographic characteristics of a society. Together with the more recent concepts of social development and political development, it forms the phenomenon historians designate “modernization,” which embraces innovation in numerous aspects of individual behavior and social organization. Although not a revolution in the literal sense of the word, modern economic growth merits recognition as a distinctive epoch by virtue of the scope of the changes associated with it, the irreversible nature of many of them, and the unprecedented rate at which they have occurred. It seems safe to say that in those economies now characterized as “developed,” most of the population has experienced in the last one hundred years a greater advance in material well-being and a more sweeping change in way of life than occurred in any previous century of human history.

This transformation encompasses wide-ranging changes in techniques of producing, transporting, and distributing goods, in the scale and organization of productive activities, and in types of outputs and inputs. It embraces major shifts in the industrial, occupational, and spatial distribution of productive resources and in the degree of exchange basis and monetization of the economy. On the social and demographic side it involves significant alterations in fertility, mortality, and migration, in place of residence, in family size and structure, in the educational system, and in provision for public health. Its influence extends into the areas of income distribution, class structure, government organization, and political structure.

Compared with previous epochs, modern economic growth has involved marked acceleration in the rate of social change generally—so great that it frequently creates a significant difference in the experience of only two successive generations. The rate of growth has varied substantially, however, among different economies undergoing development at a given time and within a given economy over time. Attempts to distinguish phases of modern economic growth, to classify types, and to identify sequences between economic and non-economic characteristics or among different economic aspects are still at at an early stage, but some suggestive generalizations have been advanced.

From the viewpoint of the world as a whole, the international spread of modern economic growth has so far been limited, although few parts of the world have remained untouched. While the pattern of diffusion in time and space has yet to be established with quantitative precision and partly depends on how widely the process is conceived, the picture in broad outline is as follows. Elements of the transformation become increasingly apparent when one examines parts of northwestern Europe in the eighteenth century, especially, on a fairly extensive scale, in Great Britain. In the course of the nineteenth century, as the process gathered increasing headway in the area of origin, its gradual diffusion southward and eastward throughout Europe occurred. By the end of the century, aspects of its beginnings could be identified in easternmost Europe, including Russia, and also in Japan. A somewhat similar development had been taking place concurrently in overseas areas settled by Europeans, mirroring to some extent the diffusion pattern within Europe. It was apparent first in areas initially settled chiefly by migrants from northwestern Europe—the United States in the first part of the nineteenth century, followed by Canada, Australia, and New Zealand—and subsequently in parts of Latin America, where migration from southern and eastern Europe was especially important. In the twentieth century, and increasingly since World War ii, the initial signs have become more widespread in parts of Asia and, to a smaller extent, Africa—perhaps most noticeably in areas with the longest and fullest contact with some of the original centers. However, by the middle of the twentieth century, for only about a fourth of the world’s population has the transformation proceeded far enough for them to qualify as “developed” by most of the usual indicators.

The appearance and spread of modern economic development sharply accelerated the trend toward wider international contacts, which had been set in motion several centuries earlier by the great voyages of discovery. The peoples of the world have come increasingly to be linked together in a mutually interdependent system of economic and political relations and through new communications networks furthering the flow of information. At the same time, the piecemeal character of the diffusion process has sharply aggravated international differences in economic, social, and political conditions, has repeatedly disturbed the balance of political power both between developing and underdeveloped areas and within the developing group, and has become a major factor in modern wars. In a fundamental sense, modern economic growth is a creature of the scientific revolution, for it reflects man’s growing knowledge of natural phenomena and the power thereby attained to mold his environment to his needs. Whether it will prove possible to contain the disruptive effects of its spread within a framework of nation-states would seem ultimately to depend on whether progress in social science can match that in natural science.

Characteristics of modern economic growth

It is possible to identify a number of recurrent features of modern economic growth if one draws on both the historical experience of now-developed nations and comparisons of countries at different levels of development at a given time. However, the latter comparisons, which are frequently resorted to in lieu of sufficient historical data or research, are not always trustworthy guides to changes over time. The “nation” is adopted here as the unit of economic growth because although there are significant growth differentials among regions within a nation, they are substantially less than those among nations. Moreover, the central government plays an important role in decisions affecting secular growth. The present summary emphasizes similarities, both between countries with different institutional conditions, such as the degree of central planning, and between the current experience of today’s less-developed nations and the earlier experience of the now-developed countries. It emphasizes further the contrast between pre-modern conditions and those characterizing modern economic growth. Only brief reference will be possible to differences in the experience of individual nations and variations in trends from one period to another within a given country, although such differences are sometimes substantial.

Production

From the viewpoint of the economic system as a whole, the central feature of modern economic growth is an immense and continuous rise in the yield from human economic activity. This is reflected in the long-term growth rates of output per head of the total population shown in Table 1. For most of the countries listed, the rate has averaged from 13 to 19 per cent per decade. Such rates, continued throughout a century, imply an expansion of product per capita between 3.4-fold and 5.7-fold. For Sweden, Japan, and the Soviet Union, which have sustained average rates on the order of 26 to 28 per cent per decade for five decades or more, the multiplication in a century would exceed 10-fold.

Table 1–Average rate of growth of real product per capita in developed countries for long periods up to about 1960
 Period
(in years)*
Percent change in real roduct per capita per decade
* Calculated from midpoints.
Source: Kuznets 1966.
England and Wales (later U.K.)  
1780 to 188110113.4
1855–1859 to 1957–195910114.1
France  
1841–1850 to 1960–1962105.517.9
Germany (later F.R.G.)  
1871–1875 to 1960–19628817.9
Netherlands  
1900–1904 to 1960–19625913.5
Belgium  
1880 to 1960–19628114.8
Switzerland  
1890–1899 to 1957–195963.516.1
Denmark  
1870–1874 to 1960–19628919.4
Norway  
1865–1874 to 1960–196291.519.0
Sweden 1861–1865 to 1960–19629828.3
Italy  
1898–1902 to 1960–19626118.7
United States 1839 to 1960–196212217.2
Canada  
1870–1874 to 1960–19628918.1
Australia  
1861–1865 to 1959/1960–1961/196297.58.0
Japan  
1879–1881 to 1959–19618026.4
European Russia (later U.S.S.R.)  
1860–19135314.4
1913–19584 527.4

It should be recognized that any summary measure, such as real national product per capita, reflects certain value judgments and that, consequently, levels or rates of development cannot be measured with the scientific precision of, say, steel output. For example, centrally planned economies would confine such a measure of aggregate output to material production. The concept of economic growth is itself a subjective one to some extent. However, almost any reasonably comprehensive measure would show comparably immense productivity growth, largely because requirements for such elementary goods as food, clothing, and shelter continue to take up such a large proportion of economic endeavor.

The rates shown are averages for half a century or more. For shorter periods much higher and also much lower rates have prevailed; this reflects a second characteristic of modern economic growth, significant variability in the growth rate over time. Wide fluctuations in output growth also occur in premodern economies, primarily in connection with the vagaries of agricultural conditions. In developing economies, however, the nonagricultural sector becomes increasingly responsible for fluctuations. The movements in centrally planned economies have so far received relatively little study. In non-centrally planned economies the most fully analyzed movement is the “business cycle,” which has typically averaged 3 to 4 years in duration. Longer-term movements for which some regularity is said to exist are “major cycles” (Juglar cycles), of approximately 7 years’ duration; “long swings” (Kuznets cycles), ranging from approximately 10 to 30 years in duration; and “long waves” (Kondratieff cycles), of approximately 50 years in duration. Although these longer-term movements have not found general acceptance among economists, they serve to emphasize the high variability that has been observed in growth rates over periods of a decade or two, making inferences regarding secular trends from data confined to such limited periods quite hazardous.

The trend in output per head cannot be attributed to a corresponding rise in labor input per head of the population. It is generally true that in now-developed nations the proportion of the population in the labor force is higher than in the premodern period, chiefly because the proportion of the population of working age has risen as fertility has declined. But this has been more than offset by a decline in the average hours worked per year, so that, on balance, the man-hour input per head of the total population has usually declined somewhat.

More plausible factors in the rise of output per head are capital input and average education per worker. Certainly the rises in these are among the most striking trends in modern economic growth. Although precise evidence is lacking, the expansion in the per-worker stock of reproducible capital (primarily structures and equipment) has involved orders of magnitude comparable to that of expansion in output per worker. With regard to education, modern economic growth has been accompanied by the virtual elimination of illiteracy, a trend toward universal primary and, subsequently, secondary school education, and a rise in college enrollments. The quality of the labor input has been further enhanced by substantial advances in the nutrition and health of the labor force.

Nevertheless, when one considers the nature of premodern methods of production, it seems doubtful that greater capital, education, and other quality inputs per worker, within the framework of that rudimentary technology, would have yielded the immense and continuing rates of productivity improvement characterizing modern growth.

Technological innovation

The fundamental basis for this productivity growth has been technological innovation on a widespread and continuous scale. Indeed, the concrete nature of the technological developments helps explain the changing nature of the economic inputs, as well as a number of other trends accompanying modern economic growth.

Although the great variety of these innovations makes a summary description difficult, it is possible, nevertheless, to identify a few general features that usually distinguish modern from premodern methods. Specifically, the use of methods involving mechanization and high-energy inputs per worker and the associated shift toward a mineral-based economy especially set off many modern techniques. Large and carefully controlled volumes of energy are applied to productive processes, drawing on mineral sources such as coal, petroleum, and natural gas; in contrast, premodern energy inputs, deriving largely from human, animal, wood, wind, and water sources, are much smaller and more erratic. Intimately associated with the energy changes are the shift from hand tools to machine processes and wider use of physical-structure materials derived from ferrous and nonferrous minerals rather than forests or agriculture. With the resort to machine production, final products become more standardized; labor becomes much more specialized, both by industry and, within enterprises in an industry, by process. A corresponding proliferation of detailed industrial and occupational classifications occurs.

Effective use of modern techniques entails a number of corollaries. Because of technological indivisibilities, optimum scales of production become greater. In manufacturing, this means that production tends to be organized in factory establishments, employing large numbers of workers and producing far in excess of local requirements, rather than in small shops involving few hands and producing largely for local consumption.

Optimal locations too are affected by the more advanced techniques. With regard to raw materials, minerals are substantially less ubiquitously distributed than forest and agricultural materials, and differentials with regard to the efficiency of different locations, particularly with regard to energy materials, are thereby heightened. On the side of markets, because production so greatly exceeds the needs of those immediately engaged, existing population centers offering concentrated markets become increasingly attractive. Transport junctions providing ready access to markets and/or materials also become more advantageous. The resulting differential advantage of certain locations, where one or more such factors is particularly favorable, leads to geographic concentration of production and urbanization. This tendency is reinforced up to a point by external, or “agglomeration,” economies.

Even these limited observations clarify some of the trends in the industrial and occupational characteristics of the labor force during modern economic growth. Associated with the growth in specialization of labor by industry, task, and location in the production of commodities is an increasing need for transportation of these commodities and for internal trade generally—and, in turn, for increasing monetization of the economy to facilitate the manifold growth of transactions. A rise is observed in the proportion of the labor force specialized, not in the direct production of tangible commodities or final services but in ancillary activities, such as moving, storing, and distributing goods. Associated with the growth of scale is a growing need for labor in control functions—in administrative and clerical jobs—as problems of coordination of processes and of plant layout multiply. (Even in direct production itself, the worker’s function increasingly becomes one of control, the tending of a machine.) A premodern economy could not spare such a large proportion of specialized workers for continuous employment outside direct production; a developing economy not only can, but apparently must, at least to a substantial extent. Thus the trends in industrial and occupational structure of a developing economy testify both to the distinctiveness and immense productivity of the underlying technological innovations, for they show that the methods employed both require and permit a substantial proportion of labor to be engaged in activities other than direct production. [SeeIndustrialization.]

The nature of the underlying technological developments also helps explain the previously mentioned trends in economic inputs. The growth of machine production and scale calls for much more capital investment per worker, both in equipment and (particularly) structures to house production. Transportation and power needs have major capital requirements, as does the need for workers’ accommodations where new locations are developed. Similarly, the much greater complexity of production requires a better educated labor force to learn and execute the new techniques. The continuous change characterizing modern economic growth (in techniques, locations, types of goods and jobs) calls for qualities of adaptability and adjustment on the part of labor which education facilitates.

These brief remarks on energy and mechanization as leading technological features of a developed economy do not do justice to the immense number of detailed changes implied by such characteristics or to the variety of other technological advances that have taken place, such as scientific hybridization, chemicals and plastics, electronic communications and controls, scientific management, and the supermarket, to mention only a few. Nevertheless, they do suggest the underlying logic of some of the principal trends in economic organization characterizing modern economic development.

Consumption

The rise in output per man-hour implies a similar trend in real income per member of the population, although in part, as was noted, the benefits of higher productivity are taken in the form of more leisure per worker. The specific implications of this rise in real income for the condition of the population would best be revealed by level of living indicators, if they were available, such as per capita calorie consumption, the starchy-staple ratio, persons per room, per cent of dwellings with piped water and flush toilets, various household electrical appliances per capita, physicians and hospital beds per capita, school enrollment ratios, and newspaper circulation and cinema attendance per capita. Suffice it to say that modern economic development in general has meant an unprecedented advance for most of the population in food, clothing, shelter, household furnishings, and health, education, and recreational services— to the extent that dire conditions such as malnutrition have virtually been eliminated.

The foregoing statement refers to absolute levels. When one turns to relative magnitudes, to the proportionate distribution of the end product of the economy, the trends are less clear-cut. This is partly because variations among countries in the institutional conditions governing resource allocation cause differences in the uses to which the higher productivity accompanying modern economic growth is put. One well-established allocative trend is a rise in the share of the gross national product devoted to gross capital formation, attributable to the capital requirements of modern growth. A second is a decline in the proportion of consumption expenditure devoted to food. This development, rooted in the structure of consumer preferences, plays an important part in the decline in the relative importance of agriculture during economic growth, one of the most characteristic and pervasive trends. A third is a rise in the proportionate importance of new or modern goods relative to that of traditional items of consumption, reflecting the impact of technological progress in the consumption sphere. It is an interesting speculation that whereas much of the substantive increase in the early phases of modern economic growth takes the form of food, clothing, and shelter, at a more advanced phase much of the change is connected with the automobile and the way of life associated with it.

Income distribution

It is obvious that such massive changes in industrial, occupational, and spatial distribution, and in the relative proportions of factor inputs must leave their imprint on the income distribution of a society, for not all segments of the population would be equally motivated or equipped to pursue the new opportunities. Generalizations about trends, however, are frustrated by a serious lack of data and the fact that institutional differences intervene in this area to such an extent that even the concept of income shares sometimes differs among countries. Two statements, based almost entirely on fragmentary data for a few noncentrally planned economies in this century, may be ventured. One is that the return per unit of labor has risen relative to that of capital, off setting a contrary movement in the relative factor quantities. As a result, changes in the relative income shares of labor and property have been confined within fairly small limits. The second is that income inequality has on balance tended to lessen. This is suggested both by direct observations on the size distribution of income and by scattered data on income-per-worker differences by industry, occupation, and/or region. There is some indication that this trend has chiefly involved an increase in the share of middle-income groups at the expense of upper and thus is partly bound up with the growing importance of a “middle class” during modern economic growth. [SeeIncome Distribution.]

External trade

Modern economic growth has brought with it a vast expansion in the absolute volume of a nation’s international trade. Indeed, for most developed nations it has involved a greater relative rise in international trade than of GNP, despite the unprecedented growth rate of the latter (although this trend has been somewhat reversed in the twentieth century). Economies not experiencing a relative rise in international trade are those centrally planned economies which have sharply restricted participation in international trade through autarkic policies and some of the overseas countries settled by Europe where trade played a major role even in the premodern period.

Social and political changes

The movement from relatively high to low levels in mortality and fertility associated with modern economic growth has been so pronounced that it merits the distinctive title “demographic transition.” The mortality decline, which typically precedes that in fertility, has been most marked among (although not confined to) younger age groups, particularly infants. Life expectancy at birth in developed nations is now in the vicinity of seventy years, compared with a premodern figure of thirty to forty years. The major pestilential diseases (smallpox, the plague, cholera, yellow fever, typhoid, and typhus) have largely been eliminated, and, more recently, mortality from infectious and parasitic diseases, such as tuberculosis, pneumonia, and dysentery, has been drastically reduced. The principal causes of death in developed economies today are chronic and degenerative illnesses (heart disease, cancer, accidents, and so on). The mortality movement is bound up in part with the improved living levels of the population, for example, improved nutrition, which strengthens resistance to disease. It is due also and increasingly, however, to important advances in medical knowledge and significant innovations in the sphere of public health.

In a developed economy women usually marry later and bear fewer children—typically those surviving to the end of childbearing age will have averaged two to three births versus four to six for women in the premodern period. The reduction in the birth rate appears partly attributable to the decline in infant mortality, since to achieve a given number of surviving children, a smaller number of births is needed. From the viewpoint of females’ time required in childbearing and care, reproduction, in the significant sense of surviving descendants, becomes, like economic production, a more efficient process during modern economic growth.

The “dependency burden,” the ratio of dependent children and elderly persons to those in prime working ages (say, from 15 to 59 years) usually declines in the course of development. This is due to a reduction in the proportion of children in the population as fertility declines; the proportion of elderly persons actually rises somewhat. The number of persons per household also declines. In part this reflects the lower ratio of children to adults; in part it is due to the progressive decline of two-generation or three-generation family units during economic growth.

As has already been noted, economic growth is marked by a progressive shift of population from rural to urban areas. The basic impetus for this arises from the impact of technological change on the spatial distribution of given industries, but it is significantly reinforced by the shift in final consumption patterns which favors the growth of non-agricultural industry relative to agriculture. The growth of urban centers necessitates a substantial redistribution of population through internal migration. [SeeLabor force, article onmarkets and mobility.]

These changes in population characteristics have, in turn, influenced the trends in final products. The reduction in household size and the aging of the population have altered final demands. The effect of the shift to urban locations is apparent in the upward trend in consumer expenditures on a number of predominantly urban services—transportation, communication, personal services, and recreation.

In addition, the trend toward urbanization, and the consequent need for public municipal services, is one of the factors responsible for an increase in the relative size of government during modern economic growth, even in noncentrally planned economies. More generally, in these economies an expansion tends to occur in public expenditure on “social” purposes (education, health, social security, housing, recreation) and “economic” purposes (agriculture, mineral resources, fuel and power, transport, roads, and so on). The size of the central government usually tends to rise relative to that of local governments, partly because of the growing complexity and integration of the economy. With regard to revenue sources, direct taxes, particularly individual income taxes, usually grow in importance relative to indirect levies, such as excise taxes and foreign trade duties. [SeeTaxation.]

The trends characterizing modern economic growth significantly alter the economic bases of class differences and political power. In noncentrally planned economies, for example, there has been a marked rise in the proportion of employees in the labor force and a diminution of self-employed workers. In part this is associated with the shift in the industrial structure of the labor force toward nonagricultural activity, since the latter is characterized by a substantially higher proportion of employees to self-employed workers than is agri-r, it reflects a trend within the nonagricultural sector in favor of employees, due to the growth of factory relative to handicraft operations. Another pertinent change has been the rise in white-collar employment relative to manual labor, an influence strengthening “middle class” tendencies. Still another has been the drastic decline in the relative economic importance of agriculture, which has weakened the political importance of this sector. Such “noneconomic” repercussions of modern economic growth have, in turn, had feedback effects on the growth process through the types of social attitudes and political measures that have ensued.

Patterns and types of economic growth

The time shape of these various trends is by no means uniform among the different characteristics. Moregover, shorter-run changes through time may show significant departures from the underlying trend over lengthy intervals, because of fluctuations such as those mentioned earlier or other factors.

A number of the changes are, however, subject to a distinct upper or lower limit, such as the rise in urbanization, literacy, and nonagricultural activity. As might be expected, for such characteristics the basic secular trend exhibits a logistic pattern, that is, initially change occurs at a slow rate, then at an accelerating one, and finally, as it approaches the limit more closely, at a decelerating one. Even with regard to narrowly defined categories of commodities or industries, where no comparable logical limit exists, evidence has been advanced to show the existence of a secular pattern of acceleration followed by retardation. Among other factors, the nature of technological change has been accorded an important role in accounting for this—in part because technological progress within a narrowly defined industry appears to slow down after a time, in part because technological developments in new commodities and industries create opportunities competing with the older ones. The latter point helps to reconcile the seemingly contradictory observation that growth in the economy-wide level of output per man-hour does not show retardation.

It has already been suggested that noticeable differences between countries sometimes exist in the pattern for a given variable or in the relationships among two or more variables. This may be illustrated by reference to demographic phenomena, where the currently available documentation is in some respects fullest, especially for the premodern period. A shift from early to late marriage occurred in many western European areas well before the eighteenth century, and in a number of these a mild reversal, a decline in age at marriage, occurred in conjunction with economic advance in the nineteenth and twentieth centuries. In eastern Europe, on the other hand, early marriage persisted in many areas through the 1930s despite other developmental changes. With reference to the demographic transition, it appears that fertility began to decline in some European areas prior to or simultaneously with the mortality decline. Recent declines in mortality appear typically to be sharper and more rapid than earlier ones. An important issue, which can only be noted here, is to what extent differences such as these tend to vary systematically between early comers and late comers to the growth process.

To turn from individual aspects of modern economic growth to the process viewed as a whole, we must examine whether it is possible to distinguish regular phases or periods in the process and whether the experience of various countries can be classified in terms of different growth “types.” For example, one stage-scheme that has been proposed identifies five phases: traditional society, preconditions for take-off, take-off, drive to maturity, and age of high mass consumption (Rostow 1963). Another recent typology, proposed by Hoselitz, employs a threefold classification of growth: (1) expansionist versus intrinsic, depending on the degree to which unused land and other resources are available; (2) dominant versus satellitic, depending on the importance of foreign trade in the economy; and (3) autonomous versus induced, based on the degree of central planning (Conference … 1959). One advantage of the proposed stage conception is that it highlights the fact that modern economic growth is characterized by a substantial acceleration in the pace of social change. Moreover, its emphasis on the take-off as a point of transition to “self-sustaining” growth underscores a fundamental aspect of some of the changes, namely, that they are largely irreversible. Similarly, the suggested typology brings to the fore certain factors— the absolute size of the economy, the nature of the decision-making processes—influencing the growth process. On the other hand, attempts to apply such schemes in their specific form to interpretation of actual experience have encountered important difficulties. Although they are suggestive with regard to some of the causal mechanisms or factors underlying modern economic growth, the use of such concepts as valid generalizations about stages or types of growth seems premature in view of the

Table 2 – Crude death rate per thousand of total population, selected areas, since 1750 or earliest known date thereafter
 England and WalesUnited StatesGermany (later F.R.G.)ItalyRussia (later U.S.S.R)JapanChileIndiaAfrica
a. 1870–1880.
b. 1861–1870.
c. 1937.
d. 1905–1909; probably on underestimate.
Principal sources: Demographic Yearbook; Population Bulletin of the United Nations; Kuznets 1966.
About 175032        
About 18002525       
About 18502323a2731b40 35  
1900–1909151619223021d3243 
1930–19391211111418c18243130-35c
1955–1959129111088142027

limited extent to which the facts of growth have so far been established and runs the danger of tending to strait-jacket thinking on the subject.

International spread of economic growth

Ideally, a description of the world-wide diffusion process would be built on a number of time series of growth characteristics for each of the countries of the world since around 1750. Lacking this, principal reliance is placed here on a few characteristics of what are taken as fairly representative situations in different parts of the world—although availability of data has played a part too in the choice of series and areas. In keeping with the approach adopted here, economic growth is viewed as one facet of modernization more generally conceived. Two indicators of social development are used, the crude death rate and school enrollment rate, and two of economic development, nonagricultural share of the labor force and the growth rate of GNP per capita. Although the measures are crude—for example, variations in the age distribution of population in time and space impair the comparability of death or school enrollment rates— as a whole they produce a reasonably consistent picture.

Typically, economic historians trace the origin of modern economic development to eighteenth-century England, and in particular to the industrial revolution. By the latter is meant, in part, the commercial application of Watt’s steam engine and certain innovations in the iron and textile industries over the period from around 1730 to 1820, especially the latter half. From England, the industrial revolution is viewed as having diffused gradually, first to neighboring European nations and England’s overseas descendants and then to some further nations, although the latter aspect of the picture becomes increasingly blurred. The description presented is qualitative in nature, although approximate periods of an industrial revolution are identified for some of the now-developed nations.

Indicators of modernization provide a broader picture, of which the economic forms a reasonably consistent part. Tables 2, 3, and 4 reflect, respectively, the diffusion of modern mortality conditions, education, and industrialization; each tells a fairly similar story. For this purpose, a useful way of forming impressions is to compare the dates at which countries reach a crude death rate of 30 per thousand, a school enrollment rate of 10 per cent

Table 3 — Estimated percentage of total population of all ages enrolled in school, selected areas, since 1818 or earliest known date thereafter
 England and WalesUnited StatesGermany (later F.R.G.)ItalyRussia (later U.S.S.S.R)JapanChileIndiaAfrica
a. Values for 1954 (and, to some extent, for 1928) for the most-developed countries are biased downward relative to those for other times and places, because of decline in ratio of school age to total population.
b. Not available.
c. Around 1870.
d. 1938.
Source; Easterlin 1965.
18186        
1830915173     
1850121816b24e   
1887162218113742 
1928a16241711121315d4ld
1954a1522131315231875
Table 4 — Percentage of labor force in nonagricultural activity, selected areas, since 1700 or earliest known date thereafter
 England and WalesUnited StatesGermany (later F.R.G.)ItalyRussia (later U.S.S.R)JapanChileIndiaAfrica
a. Share of nonagricultural activity in national product.
b. 1820.
c. Not available.
Principal sources: Kuznets 1957; 1966.
1700–177555-60*        
180165(68*)28b       
18417731       
About 1870–188085505838 17   
About 1900916365412530 28 
About 19259376704829496125 
About193594807252c5463c 
About 1950–1960959177596067702726

of the population, and a percentage of labor force in nonagricultural industry of around 30. England tended to be the leader, with major changes usually discernible in the eighteenth century. Within Europe, Germany, a representative of northern and western Europe, was well on the road by the middle of the nineteenth century, followed with some lag by Italy, a representative of southern Europe, and, somewhat later still, Russia, a representative of eastern Europe.

In the overseas areas settled by Europe, modernization was well under way in the United States in the first half of the nineteenth century. Canada, Australia, and New Zealand, if data were shown, would probably lag somewhat, although not a great deal. The series for Chile show signs of modernization in the early twentieth century. As a representative of Latin America, Chile has been in the vanguard, rather than near the average, and has been at least several decades ahead of Latin American nations with substantial Indian populations. (Also, Chile’s position with regard to the share of the labor force in nonagricultural activity has been disproportionately high compared to most countries in this area.) In general, modernization in overseas countries populated chiefly by settlers from northern and western Europe preceded that in Latin America, whose settlers originated primarily in southern Europe. Thus the New World pattern reflects to some extent the diffusion pattern within Europe itself.

In Asia and Africa, indications of modernization were apparent in Japan in the latter part of the nineteenth century and in the Union of South Africa in the early twentieth; but these are noticeable exceptions, at least as far as indexes of economic development are concerned. Typically, these indexes show relatively little evidence of modern economic growth in these continents. With regard to social development, however, the indicators for India, a country reasonably representative of changes in Asia, do suggest that elements of modernization have been occurring in the course of the twentieth century, and even the fragmentary data for Africa show some signs of this since the 1930s. Nations of northern Africa would probably tend to be somewhat ahead of the sub-Saharan countries and more like India in timing.

A table in a form comparable to the preceding ones, showing levels of real product per capita at various dates, would shed valuable light on trends in the relative standing of nations and the extent

Table 5 — Per cent per decade growth rate of real gross national product per capita, selected areas, since 1700 or earliest known period thereafter
 England and WalesUnited StatesGermany (later F.R.G.)ItalyRussia (later U.S.S.S.R)JapanLatin AmericaIndiae
a. Periods are, in order, 1857–1863 to 1896–1904, 1896–1904 to 1946–1954, and 1937–1940 to 1959–1962.
b. 1851–1855 to 1871–1875.
c. 1862–1868 to 1874–1883.
d. 1860 to 1913.
e. Not available.
Principal sources: Kuznets 1964a; 1966.
1700–17802.0       
1780–184113.5       
1841–188113.316.29.2b-0.8c    
1881–191317.416.918.19.114.4 d24.3 4
1913–196015.518.017.417.427.427.9 5
1927–196014.117.323.722.1e26.018.85

of the gaps between them. Although sufficient data are not presently available for this, enough information can be secured on rates of growth to at least check some of the impressions so far obtained (Table 5 ). For those developed nations where rates are available over a long enough period, a noticeable rise to modern growth-rate levels is usually apparent at a time consistent with the previous tables. On the other hand, for India, the one lessdeveloped area shown here with a reasonably long time series, the growth rate remains at a relatively low level, a picture consistent with that relating to the nonagricultural share of the labor force.

Since the social development indicators do suggest the gradual spread in the twentieth century of elements of modernization to less-developed areas in Asia and Africa, it is of interest to look at their most recent experience. Estimates of the rates of change, converted to a per decade basis, of product per capita in these areas (available only for noncommunist countries) for 1957/1958 to 1963/ 1964 are given in Table 6. There is perhaps a suggestion here of an increase in the rates for these areas compared to experience prior to World War ii, although the earlier observation regarding variability of growth rates over time cautions against placing excessive confidence in interpretation of such rates as secular ones. Some support for this inference, however, is provided by data on capital formation, which show a noticeable rise since the pre-World War ii period in the proportion of re-sources devoted to this purpose in underdeveloped countries.

Table 6
 Per cent
* Not including Algeria, Congo (Leopoldville), and Republic of South Africa.
Source: U.S. Agency for International Development.
All noncommunist countries25
Less-developed areas only23
India21
Africa*11

Effect on international disparities

One consequence of the uneven spread of modernization has been the creation of wide differences in various economic and social conditions among nations at any given time. Tables 2 through 5 shed light on the size and trend of such differences. The pattern for mortality and school enrollment rates is rather similar. In the century or so up to, say, World War I, international differences widened markedly as rapid improvement occurred in Europe, northern America, and Oceania, and relatively little in Asia, Africa, and Latin America. Since then, and particularly after World War ii, as advances in the former group slowed down and those in the latter accelerated, differences have narrowed noticeably, most markedly in mortality conditions.

There is little indication in the economic development indicators, however, of a lessening of differences. On the contrary, Table 4 suggests that the gap in the percentage of labor force in non agricultural activity has continued to widen. With regard to GNP per capita, it can also be inferred, despite the limited data, that relative levels have continued to diverge. Today’s developed countries, considered as a bloc, account for approximately one-quarter of the world’s population; four less-developed nations (mainland China, India, Indonesia, and Pakistan) account for about four-tenths. To judge from the indicators for the latter part of the nineteenth century, the developed group was well ahead of these four less-developed countries at that time. Since then, the developed group grew at a rate on the order of 15 per cent per decade, enough to double income in five decades. On the other hand, the four less-developed countries had such low income levels as of 1950 that to assume a growth rate over this preceding period of even the same magnitude would imply improbably low income levels for them in the late nineteenth century. This is supported by the figures for the only one of the four for which an estimate is available, India, where the estimated growth rate averaged only around 5 per cent per decade.

Table 7 provides a summary view of the current state of international differences in GNP per capita produced by these historical trends. Although defects of the measure tend on balance to exaggerate differences, there is little question that to date the spread of modern economic development has created an unprecedented disparity in economic condition between, on the one hand, a small though sizable segment of the world’s population, chiefly resident in Europe and its overseas descendants, and, on the other, the vast majority, primarily concentrated in Asia and Africa. (Table 7, in which populations are classified according to the national average GNP per capita, may exaggerate somewhat the relative position of the mass of the people in Latin America, since there is some evidence that income inequality there may be disproportionately high.) The disparity portrayed, which reinforces (and in part has arisen from) an already existing cultural division, itself becomes, via its political and other repercussions, a factor bearing on the prospect for continued long-term growth of now-developed nations and the further spread of modern economic growth to less-developed ones.

Table 7 — Per cent of world population distributed by national average GNP per capita and geographic area, about 1958
GNP per capita (1958 U.S. dollars)World totalNorthwestern Europe*Southern and eastern Europe*Northern America and OceaniaLatin AmericaAsiaAfrica
* Northwestern Europe comprises the U.K., France, F.R.G., Eire, the Low Countries, Scandinavia, and Switzerland; southern and eastern Europe, all the rest of Europe including all of Russia.
Sources: Demographic yearbook for 1963; United Nations 1952–1963; Kuznets 1964b.
Total100.06.715.07.17.057.17.1
1,000 and over13.36.207.1000
575-9998.90.48.100.30.10
350-5746.10.13.901.40.10.6
200-34913.302.904.35.70.5
100-1996.600.100.83.81.9
Below 10051.70000.147.44.1

Consequences for world population

The spread of modernization has brought major consequences for the size, distribution, and condition of the population of the world, viewed as a whole. The progressive diffusion of improved mortality conditions has led to a noticeable rise in the rate of increase of the world’s population. Between 1000 and 1750 A.D. growth occurred at a rate that on the average would not quite have doubled population every 500 years. (This is, of course, an average; there were wide variations over time and in space.) In the modern period world population doubled between 1750 and 1900, and in the twentieth century it has almost doubled again in the first 60 years.

The uneven spread of modern mortality conditions has noticeably altered the international distribution of population, particularly between Europe, northern America, and Oceania, on the one hand, and Asia (excluding Asiatic Russia) and Africa, on the other. The lead of the former area in the mortality decline raised population growth rates there relative to Asia and Africa, so that by 1930 its share in the world total had risen from a fifth to a third. Since then, with the spread of reduced mortality conditions to Asia and Africa and with the continued transition to lower fertility in the West, this trend has been some what reversed. The share in the world total of Latin America, although small, has risen, at first gradually and then in the twentieth century with increasing rapidity as mortality declined sharply. The first line of Table 7 shows the approximate distribution of world population by region in the late 1950s.

By 1960 the world population exceeded three billion—more than four times the 1750 level. Despite this great and accelerating growth, it is probably true that if one considers absolute rather than relative levels, most persons throughout the world at that date were better off with regard to health conditions and formal education than was true in the past, although much of this change has been fairly recent. Whether economic conditions, in absolute terms, have generally improved is more debatable. Recent estimates of world per capita food production by region show, in general, fairly little difference for better or worse in the situation of those in less-developed areas between the late 1930s and early 1960s.

Effect on international relations

In 1750 the fortunes of those in any one area of the world were usually but tenuously connected with those of persons in other parts; in many respects individuals and nations were isolated from one another. A major consequence of the appearance and spread of modern economic growth has been a vast expansion in international contacts and an increasing degree of interdependence among the peoples of the world. The obstacles imposed by physical distance have been drastically reduced by technological developments in transport and communication. The speed of international travel has been cut to less than one per cent of what it was at the beginning of the nineteenth century, and the international transmission of messages is virtually instantaneous. At the same time, the uneven spread of economic development has altered the international configuration of economic costs and political power in a way that contributes to the rapid expansion of contacts.

Economic relations. In the area of economic relations, the physical volume of international trade rose almost sixfold from 1750 to 1850 and more than twentyfold in the next hundred years. This meant a growth in trade per capita of almost fourfold in the first period and tenfold in the second. Even though world GNP per capita rose over this period it was in a substantially smaller proportion; hence it is clear that world trade rose greatly relative to world production. Moreover, all major areas of the world participated. A rough estimate for the share in world trade of Asia, Africa, and Latin America would run on the order of a fifth to a quarter both in the early nineteenth century and in the middle of the twentieth century. External indebtedness and international migration rose too at an unprecedented rate. At the peak of their growth, roughly between 1870 and 1914, the constant-price volume of foreign debts outstanding expanded around sevenfold and the volume of intercontinental migration was three times that in the preceding half-century. The international distribution of investment and migration differed noticeably, however. In 1914, Asia and Africa accounted for perhaps one-quarter of the debt outstanding, but almost all intercontinental migration was confined to the European culture area and involved the settlement of overseas areas. The expansion of all three economic flows—trade, investment, and migration—was sharply curtailed in the interwar period, but since World War ii it has resumed, although at a more moderate rate than before World War I.

The international flow of information, partly abetted by development of the international economy, has expanded immensely too. Indications of this would be provided by such data as international mail flows per capita, exports and imports of foreign publications, and the number of international periodicals and scholarly organizations.

Political relations. Measures relating to international political relations are scarce, but again there can be no doubt that the trend has been toward vastly expanded contacts—simple series on the number of personnel in consulates and diplomatic organizations would reflect this.

Since productive capacity is more closely related to military potential than is population, the spread of modern economic development has had major implications for the distribution of political power. The impression created by the population distribution as to the relative power of areas is virtually reversed when one looks at production. Although Asia, Africa, and Latin America outnumber the rest of the world by almost three to one, the rest of the world outproduces the former areas by more than three to one. Such differences are obviously pertinent to understanding why in 1914 Great Britain, France, and Germany, which together accounted for only about one-twelfth of the world’s population, counted as political dependencies areas embracing another one-quarter. But the spread of modern economic development altered the power balance not only between developed and less-developed areas but also among the various developed nations themselves. The hegemony of Great Britain in much of the nineteenth century and the subsequent appearance of rivals such as Germany, the United States, Japan, and the Soviet Union show a timing pattern corresponding closely to the spread of modern economic development. The eruption in the twentieth century of the deadliest wars in the history of mankind, in which the developed nations were the leading antagonists, is also clearly related. Rough estimates of the world-wide total of deaths from all wars involving 500 or more deaths show the following trend: 1820-2013;1863, 1.5 million; 1863-2013;1907, 4.0 million; 1907-2013;1950, 41.0 million.

In the international political realm, then, as in the case of economic relations, the long-term record, broadly conceived, shows an immense expansion of contacts, marred by serious disruption in this century. As this has occurred, so too have efforts at international cooperation on economic and political matters, as might be shown by data on the growing number of international conferences, administrative agencies, and arbitral tribunals. The establishment of world economic and political organizations can itself be conceived in part as a response to the pressing problems caused by the international diffusion of modern economic development within a world political framework of nation-states.

Origins of modern economic development

The reasons for treating modern economic development as a distinctive epoch should be clear. In those nations now most developed there has occurred a radical change in the way of life of the average individual. At the same time, the diffusion of this new form of economic organization throughout the world has drastically altered international relations and created interdependence on an unprecedented scale. Although it is true that the majority of the world’s population has so far only begun to be touched, the rate of diffusion, compared with previous epochs, such as that of settled agriculture, has been very rapid.

How can one account for the appearance on the world scene of this phenomenon? The answer would appear to lie in the virtual explosion in the stock of knowledge, and particularly in scientifically established knowledge, which has occurred in the past three centuries. Efforts to conceptualize this development in quantitative terms are only now in their beginning stages. One indication (but no more than that) is provided by the number of scientific periodicals at various dates: 1 in 1665; 10 in 1750; 1,000 in 1850; and 80,000 in 1950. These figures, which represent only approximate orders of magnitude, suggest around a tenfold expansion in each of the two successive centuries after 1650 and only a slightly lower expansion in the most recent century.

In the developments of the seventeenth century now described as the scientific revolution, the dividing line between “pure” science and technology was vague. As man mastered procedures for establishing the “laws of nature,” it is understandable that among the problems which both stimulated such inquiry and attracted applications of the new knowledge, those of production of commodities and services should rank high. Thus, progress in the scientific comprehension of natural phenomena went hand in hand with the use of such knowledge to direct and control man’s physical environment in line with material needs. [SeeScience, article onthe history of science.]

The scientific revolution helps account not only for the appearance of modern economic development as a distinctive epoch but also for the broad geographic pattern of its spread. Modern economic development makes its appearance in the Western world where the scientific revolution is occurring and spreads most rapidly to those areas where educational development has made the transfer of new knowledge most feasible. The gains to be had from modern technology are not costless, however. As has been shown, major changes are involved which often require painful adjustments on the part of individuals or groups—in family life, economic activity, social status, or political power—and, therefore, call forth resistances to adoption of modern technology and more generally to change. It is understandable that typically the societies having so far found such adjustments most feasible (although nevertheless difficult) are those in which the same intellectual movement that had fomented the scientific revolution was promoting rational examination and discussion of social institutions as well. [SeeTechnology.]

Viewed in these terms, modern economic growth is the manifestation in production of the growth and diffusion of the stock of knowledge stemming from the scientific revolution or, more generally, from the intellectual revolution, which began with the Renaissance. The increasingly urgent problems to which the spread of modern economic development has given rise are, at a remove, a reflection of the uneven development of this knowledge itself. However slow the diffusion of modern economic growth may appear to those interested in the welfare of mankind as a whole, it has been rapid enough to produce serious social disruption within countries and major crises in international affairs. The capacity to cope with these problems has been limited by man’s inadequate grasp of social phenomena—indeed, by the limited awareness that such phenomena are even subject to scientific study and generalization. Moreover, the spread of economic development within a framework of nation-states may itself have impeded the growth of social science by promoting national ideologies that pose as science. If, therefore, one turns from the question of the origins of modern economic development, which lie in the growth of natural science, to that of the future outlook, much would seem to turn on the prospect for comparable progress in social science.

Richard A. Easterlin

BIBLIOGRAPHY

Valuable surveys and bibliographies are provided by Ash-worth 1962; The Cambridge Economic History … 1965; Kuznets 1966; Woytinsky & Woytinsky 1953 and 1955, with the first two emphasizing economic history, the others, quantitative material. For current developments, United Nations … 1952–1963 and United Nations … 1945— are good starting points. Quantitative international comparisons are stressed in Clark 1957; Ginsburg 1961; Kuznets 1966; Woytinsky & Woytinsky 1953 and 1955. Of particular interest for noneconomic aspects are Banks & Textor 1963 and Russett et al. 1964 as well as the annual lists of publications in Social Science Research Council. Dewhurst et al. 1961; Kirk 1946; Maddison 1964; Svennilson 1954 are major sources on particular aspects or periods of Western experience. Recent discussions of typologies and periodization are Conference on the State … 1959 and Rostow 1963.

Ashworth, William 1962 A Short History of the International Economy Since 1850. 2d ed. London: Long-mans. → First published in 1952.

Banks, Arthur; and Textor, Robert 1963 A Cross-polity Survey. Cambridge, Mass.: M.I.T. Press.

The Cambridge Economic History of Europe From the Decline of the Roman Empire. Volume 6: The Industrial Revolutions and After: Incomes, Population and Technological Change. Edited by H. J. Habakkuk and M. Postan. 1965 Cambridge Univ. Press.

Clark, Colin 1957 The Conditions of Economic Progress. 3d ed. London: Macmillan. → First published in 1940.

Conference on the state and economic growth, new york, 1956 1959 The State and Economic Growth. Edited by Hugh G. J. Aitken. New York: Social Science Research Council.

Demographic Yearbook. → Published annually by the United Nations since 1948. Data in tables, copyright United Nations 1963. Reproduced by permission.

Dewhurst, J. Frederic et al. 1961 Europe’s Needs and Resources: Trends and Prospects in Eighteen Countries. New York: Twentieth Century Fund.

Easterlin, Richard A. 1965 A Note on the Evidence of History. Pages 422-2013;429 in C. Arnold Anderson and Mary J. Bowman (editors), Educational and Economic Development. Chicago: Aldine.

Ginsburg, Norton S. (editor) 1961 Atlas of Economic Development. Univ. of Chicago Press.

Kirk, Dudley 1946 Europe’s Population in the Interwar Years. Geneva: League of Nations.

Kuznets, Simon 1957 Quantitative Aspects of the Economic Growth of Nations: 2. Industrial Distribution of National Product and Labor Force. Economic Development and Cultural Change 5, no. 4, part 2.

Kuznets, Simon 1964a Postwar Economic Growth: Four Lectures. Cambridge, Mass.: Belknap.

Kuznets, Simon 1964b Quantitative Aspects of the Economic Growth of Nations. 9. Level and Structure of Foreign Trade: Comparisons for Recent Years. Economic Development and Cultural Change 13, no. 1, part 2.

Kuznets, Simon 1966 Modern Economic Growth: Rate, Structure, and Spread. New Haven: Yale Univ. Press.

Maddison, Angus 1964 Economic Growth in the West: Comparative Experience in Europe and North America. New York: Twentieth Century Fund.

Population Bulletin of the United Nations. [1962] No. 6.

Rostow, Walt W. (editor) 1963 The Economics of Take-off Into Sustained Growth: Proceedings of a Conference Held by the International Economic Association. London: Macmillan; New York: St. Martins.

Russett, Bruce et al. 1964 World Handbook of Political and Social Indicators. New Haven: Yale Univ. Press.

Social Science Research CouncilAnnual Report. → Published by the Council since 1926/1927.

Svennilson, Ingvar 1954 Growth and Stagnation in the European Economy. Geneva: United Nations Economic Commission for Europe.

United Nations, Bureau of Economic Affairs 1945— World Economic Survey. New York: United Nations.

United Nations, Bureau of social affairs 1952–1963 Report on the World Social Situation. New York: United Nations.

U.S. Agency for International Development, Statistics and Reports Division 1966 Estimated Annual Growth Rates of Developed and Less Developed Countries. R. C. W-138. Unpublished manuscript.

Woytinsky, Wladimir S.; and Woytinsky, Emma S. 1953 World Population and Production: Trends and Outlook. New York: Twentieth Century Fund.

Woytinsky, Wladimir S.; and Woytinsky, Emma S. 1955 World Commerce and Governments: Trends and Outlook. New York: Twentieth Century Fund.

II THEORY

Perhaps no subject has more fully engaged the minds and energies of economists from the very beginning than the search for a satisfactory explanation of economic growth. This was, in fact, the main focus of the work of Adam Smith and the classicists endeavoring to explain industrialization in eighteenth- and nineteenth-century England, of Marx and Schumpeter in the long neo-classical eclipse of interest, and, most recently, of the post-World War ii revival by those concerned with growth both in the mature industrial and in the less developed nonindustrial societies.

While there is by no means unanimity on how to define growth, it is convenient to adhere to the convention that real per capita national income or output represents the most reliable indicator of a system’s economic achievement at any point in time and that any change in real per capita income over time connotes economic growth. Statesmen and philosophers have joined economists in recognizing that economic growth defined in this way represents the most objective indicator of a society’s welfare. It reflects changes in its ability to attain any socially agreed-upon set of goals, whether consumption, capital formation, national defense or, for that matter, leisure.

Any viable theory of economic growth must thus be able to explain both the level of per capita income of a given economic system at a point in time and the determinants of changes in that per capita income from one period to the next. With respect to the former task, it is generally agreed that the determination of the level of per capita income at any particular historical moment depends in part on the quantity and quality of the economy’s human resources; in part on the available stock of material resources; in part on how efficiently people organize themselves for productive activity; and, finally, in part on the institutional environment in which the society finds itself. Similarly, changes in income per head from one period to the next must be explained in terms of changes in the above four dimensions. All growth theories must thus take into account, in one fashion or another, at least the following: the initial characteristics of and changes in the stock of material agents, i.e., the capital stock and changes in it; the initial characteristics of and changes in the society’s stock of human agents, i.e., population or labor force and population growth; the initial characteristics of and changes in the quality or efficiency of the production process, i.e., technological change; and, finally, the evolution of the society’s organizational or institutional milieu.

The first of the above dimensions relates to the initial material wealth or capital stock per head and to the size of the economy’s saving, i.e., that portion of output not consumed in the current period. Under the standard full employment assumptions we shall adhere to, all such savings are automatically invested and thus come to represent additions to the economy’s capital stock in the next period. Since the size of the capital stock per head of the population is a principal determinant of output per head (or per capita income), the annual magnitude of the surplus per head is of the greatest importance. The second dimension, population and population growth, must be viewed as a two-edged sword. On the one side it provides the economy with the labor force necessary for pro ductive activity, but on the other it requires consumption for its maintenance, thus diminishing the surplus available to enhance the per capita capital stock in the next period. The third dimension, technological change, really is a shorthand way of referring to changes in the quality of the economy’s human agents, in the quality of the economy’s material agents, and in the over-all efficiency with which these factors are combined to produce output. Finally, changes in the way a society organizes itself with respect to its dominant social and political institutions, e.g., between markets and direct controls as organizational devices, may have a profound impact on the more narrowly conceived economic performance of the society in question.

Virtually all growth theory may thus be viewed as an elaboration of one or another of the above four essential facets, with each particular theory emphasizing what is considered most essential given the inductive evidence under consideration and the deductive reasoning being employed. Keeping this in mind, we shall first present the basic outlines of some of the more relevant growth theories of an earlier day and then examine, again in necessarily broad terms, the status of the presentday theory of growth.

The classical theory. The classicists—though there exist considerable differences as between Smith, Ricardo, Malthus, and Mill—thought in terms of the three factors of production—land, labor, and capital—cooperating to produce national output; and growth, consequently, was seen as determined by what happens to land, labor, and capital over time. While in the classical theory land is viewed as fixed in supply, the population, following Malthusian notions, is seen to be a function of the real wage (more exactly, of the gap between the market wage and a long-run subsistence norm). Capital formation, made possible by the society’s saving, provides the main engine of growth. More precisely, the total output generated at any given time is distributed to the various agents who exercise control over the three factors, i.e., the society’s workers, landlords, and capitalists, according to certain rules. Each class of owners then makes its own decision as to what proportion of income to consume and what proportion to save. To understand what happens to the stock of material wealth available for production in the next period, we must thus first under-stand the underlying classical theory of distribution and the classical theory of saving.

The classical theory of distribution is inextricably intertwined with the concept of diminishing returns to increased dosages of labor (and capital) on the fixed land. As acreage that is less and less productive is brought under cultivation, the incremental output declines and the incremental return on the least productive land determines the return to land, or rent. The portion of total output left after rents have been paid is then distributed between workers and capitalists, with workers paid at or near the institutionally determined subsistence wage level. Over time, as more and more labor (and associated capital) is expended on the land and diminishing returns become more pronounced, the landlord’s return (rent) increases and the capitalist’s return (profit) declines, with the worker’s wage retaining its long-run constancy (as population growth erases any temporary gaps between the market wage and the subsistence wage). Since the classicists assume that workers, being inherently poor, are not able to save and that landlords, being inherently wastrel, do not choose to save, the entire burden of saving and investing falls on capitalists and their profits. With declining profits, capital accumulation is increasingly squeezed, finally culminating in the cessation of further growth. Implicitly, if not explicitly, this prediction is based on the assumption that diminishing returns in the preponderant agricultural sector will swamp constant or possibly even increasing returns in industry—and that improvements in the quality of the factors of production, or in the efficiency with which they can be organized, are unlikely to be sufficiently important to change the outcome. [See the biographies ofMalthus; Mill; Ricardo; Smith, Adam.]

Marx’s theory. Marx, in Capital: A Critique of Political Economy (1867-2013;1879), sees capital and labor combining in fixed proportions to produce output, with the accumulation of new capital resulting from the economy’s surplus over consumption requirements in one period providing the motive force for carrying the system forward to higher levels of per capita output in the next. The size of the saving fund automatically converted into investment is once again determined by a distribution theory and a saving theory. Marx’s distribution theory is based on the inequality of bargaining power between capitalists and laborers in the market place, forcing wages down near subsistence levels. In his world, as in the classical, workers do not save and capitalists do not consume; thus, once again, investment is equal to total profits.

Unlike his predecessors, however, Marx is much concerned with changes in technology altering the proportions in which capital and labor are combined to produce output. It is his view that all innovations are by nature very laborsaving, in the sense that they raise the capital-labor ratio and displace employed labor. It is this, plus exogenously determined population growth (Marx rejected Malthusian population theory), which contributes to the creation of the “reserve army of the unemployed,” which, in turn, deprives workers of all bargaining power. Meanwhile, as the capital stock per employed worker continues to increase, capital begins to lose its scarcity value, and its rate of return begins to fall. Capitalists will try to rescue the profit rate by using their dominant bargaining strength in the labor market to make employees work harder and further to reduce the wage, but the drive for capital accumulation finally reduces the rate of profit to a level which brings the capitalist system to a halt. [See the guide to related articles underMarxism.]

Schumpeter’s theory. Perhaps Marx’s greatest contribution to growth theory was his emphasis on the importance of technological change in the production process. This emphasis was carried for-ward by Joseph Schumpeter in The Theory of Economic Development (1912). Schumpeter expanded the concept of innovation to include not only changes in technique but also changes in quality, in markets, and in supply sources. He was, more-over, the first really to focus on the human agent, the entrepreneur, who was capable of perceiving the potentiality of such changes and of doing something about them.

Schumpeter’s theory attempted to analyze the economy’s long-run progress by way of an explanation of its cyclical behavior as the system continuously departs from various quasi-equilibrium stationary states, only to return to others at ever higher levels of per capita income. A Schumpeterian stationary state is characterized by the fact that only enough net investment is being made to equip additions to the labor force at the capital-labor ratio applying to the already existing labor force. The economy is thus moving sideways: labor, capital, and output are all growing at the same rate and per capita income remains constant. This quasi-equilibrium state is then upset by the appearance—for reasons unclear but related to changes in the “climate”—of numbers of gifted individuals capable of perceiving additional attractive investment opportunities. These entrepreneurs appeal to the banking system for the creation of credit, which forces additional savings out of the public’s hands (through inflation) and into their own. Subsequently, pioneering entrepreneurs are followed by large numbers of less gifted imitators who tend to excess, and the system experiences overproduction and recession. But the new Schumpeterian stationary state is reached at a higher level of material wealth per person and a consequently higher level of per capita income. The growth process thus occurs as the consequence of discontinuous bursts of creative entrepreneurial activity. It finally comes to a halt only because of a change in the institutional setting as the “climate” for entrepreneurship deteriorates secularly with the increasing bureaucratization of corporate enterprise. [See the biography ofSchumpeter.]

Modern theory

Where contemporary growth theory also is concerned with the performance of the mature industrial society, it differs from the earlier attempts in that it is both less ambitious and more precise. Postwar growth theorists have been content to relegate theories of population growth, of changes in the organizational or institutional framework, sometimes even of technological change, to other disciplines or to accept changes in these rather crucial dimensions as given, rather than to be explained within the framework of the growth theory itself. At the same time there is a conscious attempt to be more rigorous, to lean more heavily on modern methods of model construction, i.e., structural relationships supplemented by behavioristic relationships.

Harrod-Domar model

Modern growth theory, moreover, is not content to hypothesize certain reasonable behavioristic relationships based on casual observation but insists increasingly on statistical verification, including the estimation of the key parameters involved. It is thus greatly indebted both to the development of the national income accounting system during the 1930s and to Keynes (1936), who, while himself primarily concerned with other, short-run stability matters, employed this system for more general theory construction and statistical implementation. [SeeNational income and product accounts.] This Can perhaps best be demonstrated by examining a particular view of growth, the so-called Harrod-Domar model (Harrod 1939; Domar 1946), as a prototype of post-Keynesian growth theory. While it represents a rather early and relatively simple formulation of the problem, much of contemporary growth theory which follows can be said to represent departures from the basic theme presented here, e.g., using more realistic behavioristic assumptions.

The basic ingredients of the Harrod-Domar view of long-run growth are as follows:

(1) A production function which relates the generation of total output, Q, to the available capital stock, K, via the capital-output ratio, v, that is, Q = K/v. The theory assumes the constancy of the capital—output ratio, i.e., the number of units of capital it takes to produce a unit of output.

(2) A theory of saving based on the Keynesian propensity to save, which stipulates that total savings, S, in any one period is a given fraction, s, of total income or output, Q, of that period: S = sQ.

(3) Adherence to the full employment of capital hypothesis, i.e., all savings are automatically invested and become additions to the capital stock: S = 1 = Δ K.

Capital is the only factor of production explicitly considered in the Harrod-Domar system. Labor combines with capital in fixed proportions, but there is no attempt to reconcile exogenously determined increases in the population or labor force with changes in the derived demand for labor as a factor input as capital accumulation proceeds.

Table 1Harrod-Domar growth model
tKQS = ICLQ/L
1301028100.1000
23210.672.138.54102.1046
334.1311.382.289.10104.1094
436.4112.142.439.71106.1145
538.8412.952.5910.36108.1199

Table 1 may help give a clearer picture of how the Harrod-Domar system operates. Let us assume that it requires 3 units of capital to produce each unit of output, i.e., the capital–output ratio is 3, and that the economy’s saving propensity is .2, i.e., the various income recipients decide to consume 80 per cent of their income in each period and to put away 20 per cent in the form of savings. If such an economy starts with, say, a capital stock (K) of 30 in period (t) 1, it produces an output (Q) of 10. Out of this income 8 units are consumed (C) and 2 are saved (S = 1), leading to an increase of 2 in the capital stock of the next period. The new capital stock of 32 units is capable of producing 10.67 units of output in period 2. This new and higher level of income is once again allocated in proportions of 80 and 20 between consumption and savings; the latter yields a further increment in the capital stock, and thus the economy continues to grow from one period to the next. The exogenous growth of the population or labor force (L), say at the rate of approximately 2 per cent a year, has no consequence for the productive capacity of the system, but affects its measured performance only in terms of per capita income growth as indicated in the last column of the table (Q/L).

The rate of growth of capital can then be quickly determined by dividing each year’s increment, or the investment during that period, I = S = sQ, by the already existing capital stock: I/K = sQ/K = s/v. In our example with s = .2 and v = 3, capital will be growing at an annual rate of 6.7 per cent. Moreover, since v = K/Q (the capital–output ratio) is a constant, the rate of growth of output or income over time must equal the rate of growth of capital. Whether or not per capita income increases or decreases in the course of the growth process will then depend on the relative speed with which the population is growing. If the rate of growth of population, g, is less than the rate of growth of in-come, s/v, per capita income will be rising at the rate (s/v ) − g, etc. In the example, in other words, with population growing at a rate of approximately 2 per cent, per capita income is rising, i.e., growth is occurring, at a rate of about 4.7 per cent annually.

While we may raise a series of questions about its realism, this Harrod-Domar view of the world serves as a point of departure for much modern growth theory, not only as applied to the developed but also to the less developed world. The departures take the form of a series of modifications—sometimes quite sweeping—of the stipulated rules governing the way in which factors are combined to produce output, of how output is distributed, and of how technological and institutional change occurs. What follows will first trace some of the major modifications in modern growth theory as applied to the mature economy and then summarize the state of contemporary growth theory as applied to the underdeveloped world.

Substitutable inputs models

A first and major modification of the Harrod-Domar world results from the explicit recognition (or better, a return to the recognition) that there exists more than one factor of production and that there is a strong possibility not only of joint inputs of labor and capital but of their substitutability in producing a given output. This is the view typical of the so-called neoclassical growth theory represented by Solow (1956) and Swan (1956). Like Harrod-Domar, Solow accepts a proportional saving function, S = sQ, but unlike his predecessors, he conceives of a production process in which both capital and labor appear as substitutable inputs. The production function meets the usual conditions of constant returns to scale, i.e., if we double the amount of both labor and capital inputs, we double output. With the growth of the capital stock determined by the constant saving propensity and the now variable capital-output ratio [ΔK/X = (I/Q)/(K/Q)— s/v] and with the growth of the other input, labor, determined exogenously at the rate g [ΔL/L = g] we have all the necessary ingredients to trace the performance of the system as a whole from one period to the next.

If, for example, the rate of growth of capital, s/v, exceeds the rate of growth of population or labor, g, the economy’s capital-labor ratio rises, i.e., each worker is equipped with a larger stock of material resources. According to the law of diminishing returns, as each worker cooperates with more and more capital, the extra output due to each unit of capital declines, i.e., the capital-output ratio rises. As the capital—output ratio, v, rises, the rate of growth of capital, s/v, declines, and this process will continue in the long run until the rate of growth of capital falls to the level g, the rate of growth of labor. At this point the rate of growth of human and material resources is the same, and no further increases in the capital–labor ratio result. Consequently, the capital—output ratio also ceases to rise, and so we have arrived at a so-called “steady state” growth, in which capital, labor, and output are all growing at the same rate. Alternatively, if initially the rate of growth of labor, g, exceeds the rate of growth of capital, s/v, as the capital-labor ratio falls, the economy reaps more and more extra output per unit of extra capital: the capital–output ratio falls, and, by an argument entirely symmetrical, the rate of growth of capital rises until it reaches the level of the rate of growth of population. We again achieve a steady state, if now from the opposite “direction.” Output per person, our index of growth, is, of course, constant in the steady state; but it will have reached that particular level by increasing toward it continuously in the case of the increasing capital–labor ratio regime and by falling toward it continuously in the case of the decreasing capital–labor ratio regime. Moreover, the permanently maintainable level of per capita income toward which the economy is tending in this very long run will differ, depending on the production function, the saving rate, and the rate of population growth.

Prevalence of distribution theories

A second major modification of the Harrod-Domar world questions the implied irrelevance for aggregate savings of how income is distributed among the various economic agents. Robinson (1956) and Kaldor (1961), for example, point out that profit recipients and wage earners are likely to save different proportions of their income, and since their relative shares in the total are bound to change over time, they challenge the constancy of the aggregate savings ratio, s, in the course of the growth process. In the extreme case they assume, like Marx and the classicists, that workers do not save and that profit recipients do not consume. In that case the savings rate,s, is equal to the profit share, πK/Q, and the rate of growth of capital, I/K = sQ/K, is equal to the profit rate, π.

In this general context two major types of distribution theory have been advanced. One—often called the neoclassical theory of distribution, since it depends on the possibility of continuous factor substitution—stipulates that market forces ensure that all human and material agents participating in the production process are compensated according to their marginal contribution to output. The smooth neoclassical production function, with constant returns to scale, permits us to “attribute” the total output of the economy, Q, to the quantities of the factors of production, say K and L, weighted by their productive contribution at the margin, i.e., their marginal productivities, MPPK and MPPL, respectively. Thus Q = MPPK + MPPL, with MPPKL/Q representing the portion of total output attributable to capital and MPPJLL/Q the portion of total output attributable to labor. Alternatively put, a given percentage rate of growth of output between any two periods can be decomposed into two portions: (1) a “capital contribution,” which is the percentage increase in the capital stock multiplied by the capital elasticity of output (i.e., the measure of how much output increased due to each percentage point increase in the capital stock), and (2) a “labor contribution,” which is the percentage rate of growth of the labor force multiplied by the labor elasticity of output (i.e., the measure of how much output increased due to each percentage point increase in the labor force). Hence ΔAQ/Q = (ΔK/K)(MPPKK/Q) + (ΔL/L)(MPPLL/Q). The neo-classical theory of income distribution then states that competitive market conditions force the wage rate, w, to equality with the marginal product of labor, MPPL, and the profit rate, π, into equality with the marginal product of capital, MPPK. Consequently labor’s relative share in total income, wL/Q, is equal to its relative contribution to total output, MPPLL/Q; and similarly for the equality between πK/Q and MPPKK/Q.

A second theory, sometimes called the Marxian theory of distribution, insists, on the other hand, on the noncompetitive nature of markets and shifts from a functional or impersonal determination of rates of return to labor and capital to a determination through the interplay of personal forces related to the relative bargaining strengths of contending groups. Since there is no need to assume equality between various factors’ contributions and their income shares, this view is perfectly consistent with a belief in smooth neoclassical production functions. It is, however, true that many of its modern adherents, e.g., Kaldor and Robinson, view production in terms of fixed proportion processes and thus have no choice but to abandon marginal productivity. Unless the extreme case of subsistence wages is accepted, the distribution of income —and thus the aggregate savings ratio—in such models can be determined only in the sense that they must somehow be brought into line with an otherwise determined investment demand. We shall not, however, concern ourselves here with views of growth which abandon the notion that the system is “pushed forward” by the automatic investment of full employment savings and is instead “pulled ahead” by investment opportunities, animal spirits, and the like.

Technological change theories

The discussion of contemporary growth theory has thus far been concerned only with the consequences of larger quantities of inputs participating, perhaps in different combinations, in the production process. As was pointed out earlier, however, it is not merely the stock of material agents per capita but also changes in the efficiency with which they are deployed which may matter a great deal—not to speak of changes in the quality of the inputs or in the institutional framework within which the system is operating. Thus, a third and major modification of the simple Harrod-Domar formulation must be the reintroduction of technological change. Kaldor (1957), for example, has introduced a so-called technical progress function intended to summarize the twin impact of a larger stock of capital per capita (capital deepening) and favorable changes in productive techniques (technological change) on the index of growth, per capita income. In the same year, Solow (1957), using a three-factor production function with constant returns to scale, the third factor being “time” or technological change, found that only 15 per cent of recent per capita output growth in the United States can be explained by increases in the capital stock; 85 per cent must be ascribed to technological change. Whether or not we accept these statistical findings matters less than the growing realization that growth cannot be explained simply in terms of larger quantities of constant quality inputs combining in known ways to produce output. Economists are reaching a real consensus that the as yet unexplained residual which Abramovitz has aptly labeled “a measure of our ignorance” (1956) is large; consequently, much recent growth-theoretic effort has been directed at this problem. This effort has been twofold: on the one hand, to define more rigorously what is really meant by technological change, and, on the other, to work toward meaningful behavioristic relationships which may tell how and why such changes in production functions occur. [SeeAgriculture, article onproductivity and technology; Productivity.]

As has been noted, the growth performance of any system in terms of the rate of increase of its per capita income invariably depends on the amount of material agents that collaborate with labor, i.e., the capital stock per capita, and on the quality of the economic agents and the efficiency with which they are used in the production process. “Technological change” is a semantic umbrella extended over all the latter; that is to say, all increases in output while the quantity of capital and labor is kept constant. At any point in time, then, technological change will raise the productivity of the existing quantities of capital and labor. Just how the introduction of a particular new method affects the productivity of the existing human and material agents provides the basis for Hicks’s attempt to classify innovations (1932). Hicks defines neutral technological change as one which raises the marginal productivity of labor and of capital at the same rate; a labor-saving technological change as one which increases the marginal productivity of capital more than that of labor; and symmetrically for a capital-saving technological change. Harrod (1948) provides a somewhat different definition of technological change. Here there is neutrality if, after the innovation has occurred, the capital-output ratio remains unchanged at a constant rate of profit. If the capital-output ratio rises, it is a labor-saving innovation; if it falls, capital-saving. For reasons that cannot be dwelt on here, a Harrod-neutral innovation is equivalent to a labor-augmenting innovation, i.e., one which converts natural units of labor into better or more efficient units over time. It is the only type of technological change which still permits the system to move toward steady-state growth in the long run. Finally, and quite symmetrically to Harrod, Solow (1963) and Fei and Ranis (1965) propose a third definition of neutrality: constancy of the labor-output ratio, or per capita income, in the presence of a constant wage rate. Such an innovation may also be called capital-augmenting.

An equally important classification of technical change for purposes of advancing growth theory proper is the differentiation between “embodied” and “disembodied” technological change—between innovations which have to be incorporated or embedded in new capital goods or in the labor force and those which do not and can, rather, be viewed as an independent or third factor of production. Another question revolves around whether innovations should be viewed as exogenous and costless, falling in unpredictable quantity, like manna, from heaven, or endogenously related, perhaps to some specific economic activity, e.g., expenditures on education or on research and development, in the past.

The early Solow and Abramovitz view of innovations as an unexplained residual really implies that technological change is disembodied and exogenous. But this must be viewed as only a first step on the road to probing deeper into the nature of the changes which actually occur in the real world and into how they are produced. His prima facie implausible statistical results led Solow him-self, as well as others, to search for a so-called new view of investment (1960), in which technological change is embodied in the latest vintage of capital, i.e., the current year’s investment. One model is essentially neoclassical, with labor allocated to the various heterogeneous qualities of capital stock (the younger the vintage, the more productive) according to the usual competitive assumptions. Other so-called putty-to-clay models (Johansen 1959; Phelps 1963) accept the neoclassical smooth production assumptions for the latest vintage of capital but assume it becomes “frozen” thereafter, i.e., it is transformed into a Harrod-Domar fixed-proportions type of production process. Arrow (1962) uses a somewhat different version of the vintage approach by linking a continuous reduction in the labor requirements per unit of output on new machines to “experience,” which is in turn related to cumulative past investment activity in the economy.

Finally, other models focus attention on changes in the quality of the labor force affecting either all vintages or only the latest entrants. Denison (1962) includes elements of both approaches. Moreover, there remains the question whether technological change, embodied or disembodied, is to be treated exogenously—perhaps as a free good—or endogenously, i.e., springing from some action of the system in the previous period. Improvements in the quality of machinery and of the labor force can, for example, be attributed either to the sheer passage of time or experience, or to previous expenditures, e.g., on research and development and on health and education. Emphasis on the latter type of theory has been growing of late [see, for example,Capital, humanand Schultz 1961].

It should be noted that there exists a large range for choice among the various innovation-theoretic hypotheses sketched in here. It is possible, for example, that all kinds of technological change are occurring simultaneously, from fully embodied (or factor quality-enhancing) innovations to fully disembodied (or organizational efficiency-raising) technological change, in one dimension; and from fully endogenous to fully exogenous, in the other. Unfortunately, the ability to advance reasonable hypotheses has run considerably ahead of the ability to test them rigorously in a statistical or econometric sense. Moreover, even if we could precisely relate improvements in physical capital to research and development expenditures, and improvements in human capital to educational expenditures, a really satisfactory theory of innovations must also be able to incorporate a plausible inducement or motivational mechanism at the level of the individual entrepreneur. In spite of some attempts in this direction (Fellner 1961), we still do not have a satisfactory explanation of just how the profit-maximizing entrepreneur is motivated to select one available type of innovation over another. In summary, the as yet inadequate understanding of the manifold possible interactions between the economy’s surplus over consumption, technological change, and the passage of time provides the biggest obstacle at this time to a really satisfactory theory of economic growth, i.e., one which is not only sufficient to explain the historical record but is also necessary, and thus is ready for the ultimate predictive test.

But if contemporary growth theory as applied to the mature economy has not yet given a completely satisfactory understanding of the sources of economic growth, a consensus seems to be emerging to the effect that conventional growth in the quantity of human and physical resources is of less importance than changes in the quality of the inputs and in the efficiency with which they are combined in the production process. By experimenting with different types of production functions and applying theoretical as well as econometric ingenuity to the problem of “explaining” the residual growth in productivity, we are making steady, if slow, progress in the attempt to recapture some of the magnificence of the explanatory apparatus of an earlier day—while keeping our feet on firm, i.e., empirically testable, ground.

Underdeveloped economies

Thus far we have dealt mainly with the theory of growth in the mature or industrial economy. A second, and no less important, component of the post-World War ii revival of interest in growth is the concern with economic progress, or the absence of such progress, in the so-called underdeveloped or nonindustrial economies. The attempt to formulate a theory of growth applicable to such countries essentially may be viewed as another strand from the same basic framework of inquiry identified here as the post-Keynesian theory of growth. Patently there must exist a large measure of transferability in the way economic progress is viewed among contexts. Everywhere it requires, at a minimum, abstention from consumption, i.e., capital accumulation; and everywhere it is governed by certain technological constraints, i.e., the state of the arts. Thus the basic Harrod-Domar formulation can again be viewed as a point of departure; but now in modifying the simplified view of how the world operates, we must take into account not only more realistic notions of the role of labor, factor substitutability, and technological change but also of the heretofore neglected changes in the institutional milieu within which an economy operates. No longer is it possible to view organizational change as de minimis and to be neglected; in fact, changes in the environment and in the way a society chooses to organize itself in various markets may have a major impact on the growth performance of the system as a whole. For example, an understanding of the changing legal framework required to initiate and sustain growth, of the changing role of markets and administrative controls as allocative devices, and of the transition from extended to nuclear family concepts may be required along with an understanding of the more narrowly conceived interactions between the society’s human and material resources. Any approach to a really useful theory of economic growth is thus likely to require a broadening of the customary analytical framework.

The typical less-developed economy is characterized by an extremely low ratio of material to human resources and a backward technology, together yielding extremely low levels of per capita income, frequently barely above subsistence. Often a substantial proportion of the labor force is openly or disguisedly unemployed. Substantial growth is likely to be ruled out by the low level of saving possible at extremely low levels of per capita income, plus the customary stagnant levels of domestic entrepreneurship and technology. Often even the most elementary preconditions for sustained growth, e.g., geographic or political cohesiveness, absence of internal market barriers, a unified currency and postal system—all essential for welding a conglomeration of resources into a national economy in the first place—are absent. And even where the environment is more conducive, attempts to move such an economy off dead center must overcome the formidable gravitational pull of accelerating population growth.

One difficulty standing in the way of a viable theory of growth for the less developed world is that most of the considerable post-World War ii efforts—by practitioner and academic economist alike—have been directed toward meeting the pressing problems of improved decision making in the immediate present and heavily tinged with the flavor of a country’s, or a region’s, particular economic and institutional characteristics. Few attempts to generalize from such specific country experience have been forthcoming. One of the notable exceptions is Rostow’s stages theory (1960), which moves directly from an interpretation of the history of the now advanced countries to a general theory of growth in terms of sequential stages, including the famous “take-off” into self-sustained growth. While it may provide insights and direct the attention of others to more analytical inquiry, it also does some disservice in terms of its casual marshaling of evidence and its disregard of the need to isolate key behavioristic relationships which determine the path of the system. However, most of the body of what may be called the theory of development evolving over the past several decades is of a more modest character and may, in fact, be characterized as a series of useful theoretical insights, as yet falling short of being fitted together into any more general theoretical framework.

Most of these insights start with the premise that the underdeveloped system initially finds itself in some sort of “trap,” escape from which requires a major effort or considerable structural change. Rosenstein-Rodan (1961), for instance, emphasizes the importance of externalities and economies of scale, and thus the need for a large nonincremental development effort where only a small industrial base exists. Leibenstein (1957) points to the need to overcome the gravitational pull of stagnation, mainly the forces of accelerated population growth, as the system departs from quasi equilibrium. Nurkse (1953) sees the need for balanced growth between industries and sectors to ensure the simultaneous creation of markets and sources of supply for a sufficient number of hesitant entrepreneurs to move forward together. Hirschman (1958), on the other hand, hopes to solve the same decision-making bottleneck via imbalance between direct private and social over-head activity, a strategy which forces expansion on the system.

While such ideas are essentially policy-focused, they patently cannot be divorced from some underlying view of how the typical underdeveloped system behaves. Formulations which recognize, implicitly or explicitly, the prevalence of a struc tural condition called dualism in many of these economies are especially helpful in this respect. Dualism in this context means that the economy is composed of at least two sectors: one relatively small, capitalistic, and mainly industrial, behaving like the mature competitive economy; the other relatively large, traditional, and mainly agricultural, in which the material resources available, land in particular, are insufficient to employ productively the existing supply of labor at prevailing rates of remuneration, i.e., in which there exists substantial overt and disguised unemployment. [SeeEconomy, dual.]

Quite early Rosenstein-Rodan (1943) and Nurkse (1953) recognized that the disguised unemployed in the subsistence or agricultural sector, sharing equally in the extended family’s produce but contributing little or nothing to it, represent a form of “hidden saving’ or surplus, which can be mobilized through its reallocation to productive activity elsewhere. W. Arthur Lewis (1954) advances the notion that growth in this sort of dualistic economy is a function of the rate at which the “unlimited supply” of low (or zero) productivity agricultural workers in one sector can be reallocated to higher productivity, commercialized activities in the other. With real wages in agriculture institutionally anchored, Lewis’ attention is focused largely on the creation of employment opportunities in the industrial sector, which would exercise a demand for the released agricultural workers at the same (or a slightly higher) constant level of real wages. Jorgenson (1961) and Fei and Ranis (1964) follow this up by examining the developmental process in terms of the interaction between the two sectors over time. The latter, for example, emphasize the requirements for balanced intersectoral growth as increases in agricultural labor productivity—a function mainly of technological improvements—release agricultural workers and generate agricultural surpluses. These surpluses, together with the reinvestment of industrial profits, increase the quantity and quality of the industrial sector’s capital stock and thus its demand for the simultaneous absorption of such workers. As long as this balanced reallocation process pulls people out of the noncommercialized and into the commercialized sector at a rate in excess of population growth (population growth may be viewed as simultaneously adding to the pool of the underemployed) the economy is gradually divesting itself of its labor surplus characteristics. Once the twin forces of capital accumulation and technological change, raising productivity in both sectors in a balanced fashion, have achieved this objective, labor, like capital, becomes a scarce factor, bid for by landlords and industrial entrepreneurs alike, and the entire economy has become commercialized. The economic calculus in the familiar one-sector world context then comes into operation, participation of all economic agents in the system’s productive and innovative processes becomes possible, and the transition to the mature economy is achieved.

It should, of course, be recognized that the labor surplus economy, while representing a common species of underdevelopment, is by no means typical of all such systems. Some underdeveloped economies, for instance, still have exploitable free land and experience year-round labor shortages. Others have no large traditional sectors but suffer from a colonial pattern of trade. There can, in short, be little doubt that the search for any really general theory of development has been severely handicapped by the heterogeneity in initial resource endowment, in the rules of behavior, and in the institutional framework among the countries loosely bearing the underdeveloped label. In the face of this, economists presumably will continue to seek elements of transferability in the experience of particular types of economic systems. The evolution of a meaningful typology of less-developed economies may thus constitute a first step in the direction of a more generally applicable theory of development.

Gustav Ranis

BIBLIOGRAPHY

Abramovitz, Moses 1956 Resource and Output Trends in the United States Since 1870. American Economic Review 46, no. 2:5–23.

Arrow, Kenneth J. 1962 The Economic Implications of Learning by Doing. Review of Economic Studies 29:155-173.

Denison, Edward F. 1962 The Sources of Economic Growth in the United States and the Alternatives Before Us. New York: Committee for Economic Development.

Domar, Evsey D. 1946 Capital Expansion, Rate of Growth, and Employment. Econometrica 14:137-147.

Fei, John C. H.; and Ranis, Gustav 1964 Development of the Labor Surplus Economy: Theory and Policy. Homewood, III.: Irwin.

Fei, John C. H.; and Ranis, Gustav 1965 Innovational Intensity and Factor Bias in the Theory of Growth. International Economic Review 6:182-198.

Fellner, William J. 1961 Two Propositions in the Theory of Induced Innovations. Economic Journal 71:305-308.

Harrod, Roy F. 1939 An Essay in Dynamic Theory. Economic Journal 49:14-33.

Harrod, Roy F. (1948) 1960 Towards a Dynamic Economics: Some Recent Developments of Economic Theory and Their Application to Policy. London: Macmillan; New York: St. Martins.

Hicks, John R. (1932) 1964 The Theory of Wages. New York: St. Martins.

Hirschman, Albert O. 1958 The Strategy of Economic Development. Yale Studies in Economics, No. 10. New Haven: Yale Univ. Press.

Johansen, Leif 1959 Substitution Versus Fixed Production Coefficients in the Theory of Economic Growth: A Synthesis. Econometrica 27:157-176.

Jorgenson, Dale W. 1961 The Development of a Dual Economy. Economic Journal 71:309-334.

Kaldor, Nicholas 1957 A Model of Economic Growth. Economic Journal 67:591-624.

Kaldor, Nicholas 1961 Capital Accumulation and Economic Growth. Pages 177-222 in International Economic Association, The Theory of Capital: Proceedings. New York: St. Martins.

Keynes, John Maynard 1936 The General Theory of Employment, Interest and Money. London: Macmillan. → A paperback edition was published in 1965 by Harcourt.

Leibenstein, Harvey (1957) 1963 Economic Backwardness and Economic Growth: Studies in the Theory of Economic Development. New York: Science Editions.

Lewis, W. Arthur 1954 Economic Development With Unlimited Supplies of Labour. Manchester School of Economics and Social Studies 22:139-191.

Marx, Karl (1867–1879) 1925-1926 Capital: A Critique of Political Economy. 3 vols. Chicago: Kerr. → Volume 1: The Process of Capitalist Production. Volume 2: The Process of Circulation of Capital. Volume 3: The Process of Capitalist Production as a Whole. Volume 1 was published in 1867. The manuscripts of Volumes 2 and 3 were written between 1867 and 1879. They were first published posthmously in German in 1885 and 1894.

Nurkse, Ragnar (1953) 1962 Problems of Capital Formation in Under-developed Countries. New York: Oxford Univ. Press.

Phelps, Edmund S. 1963 Substitution, Fixed Proportions, Growth and Distribution. International Economic Review 4:265-288.

Robinson, Joan 1956 The Accumulation of Capital. Homewood, III.: Irwin; London: Macmillan.

Rosenstein-Rodan, Paul N. 1943 Problems of Industrialization of Eastern and Southeastern Europe. Economic Journal 53:202-211.

Rosenstein-Rodan, Paul N. 1961 Notes on the Theory of the “Big Push.” Pages 57-67 in International Economic Association, Economic Development for Latin America: Proceedings of a Conference Held by the International Economic Association. New York: St. Martins.

Rostow, Walt W. (1960) 1963 The Stages of Economic Growth: A Non-Communist Manifesto. Cambridge Univ. Press.

Schultz, Theodore W. 1961 Investment in Human Capital. American Economic Review 51:1-17.

Schumpeter, Joseph A. (1912) 1934 The Theory of Economic Development: An Inquiry Into Profits, Capital, Credit, Interest, and the Business Cycle. Harvard Economic Studies, Vol. 46. Cambridge, Mass.: Harvard Univ. Press. → First published as Theorie der wirtschaftlichen Entwicklung.

Solow, Robert M. 1956 A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics 70:65-94.

Solow, Robert M. 1957 Technical Change and the Aggregate Production Function. Review of Economics and Statistics 39:312-320.

Solow, Robert M. 1960 Investment and Technical Progress. Pages 89-104 in Stanford Symposium on Mathematical Methods in the Social Sciences, Stanford University, 1959, Mathematical Methods in the Social Sciences, 1959: Proceedings. Edited by Kenneth J. Arrow, Samuel Karlin, and Patrick Suppes. Stanford Univ. Press.

Solow, Robert M. 1963 Capital Theory and the Rate of Return. Amsterdam: North-Holland Publishing.

Swan, T. W. 1956 Economic Growth and Capital Accumulation. Economic Record 32:334-361.

III MATHEMATICAL THEORY

Long-run economic growth, like short-run economic equilibrium, is studied from both the micro-economic and macroeconomic points of view. The microeconomic or multisector theory of growth, which can be thought of as a dynamic extension of the general equilibrium theory of exchange and production, has received considerable mathematical attention in recent decades. Golden equilibrium growth (defined below) is the theory’s central concept, and the mathematical analyses deal with the existence, optimality, and stability of golden equilibrium growth paths.

The roles of monetary phenomena, international trade, and technological change have so far received little attention in the analyses. These factors may have important influences on actual processes of economic growth, and neglect of them may be the source of serious shortcomings in the micro-theory. But the microtheory is still in its early stages of development, and the study of these factors must as yet be left to macroeconomic analysis.

The Walrasian model. The prototype of con-temporary growth models was formulated by Walras (1874–1877). A description of the Walrasian model in its simplest form follows.

It is assumed that there are two groups of citizens—workers and capitalists—and two industries —one producing a consumption good and the other producing a capital good. Assume for the moment that the capital good is not subject to depreciation. A number of basic manufacturing processes are available to firms in both industries, and the capital-input and labor-input coefficients of each process are assumed constant. If perfect competition prevails among firms, no firm will gain supernormal profits. Thus, in an equilibrium state,

(1) the price of the consumption good is less than or equal to the cost per unit of output of any process of the consumption good industry,

and

(2) the price of the capital good is less than or equal to the cost per unit of output of any process of the capital good industry.

Cost per unit of output is the sum of the capital-input coefficient multiplied by the price of the capital service and the labor-input coefficient multiplied by the wage rate. Conditions (1) and (2) must hold with equality for some processes, and those processes for which the conditions hold with strict inequality are not used in equilibrium.

Demand for the consumption good is assumed to depend on the price of the consumption good, the price of the capital good, and total money in-come. If prices and money income change by the same proportion, demand is assumed to remain unchanged. Furthermore, the elasticity of demand with respect to total money income is assumed to be unity. In view of the definition of savings as the excess of income over consumption,

(3) total income is identically equal to consumption plus savings.

The amount of capital used in the economy is the sum over all processes of the output produced by each process multiplied by the corresponding capital-input coefficient. The range of summation covers the entire economy, that is, the consumption good industry as well as the capital good industry. Since the amount of capital utilized at any point of time cannot exceed the amount available,

(4) the amount of capital utilized must be less than or equal to the amount of capital in existence.

Similar conditions must hold for labor, the consumption good, and the capital good, namely,

(5) the amount of labor utilized must be less than or equal to the amount of labor available,

(6) demand for the consumption good must be less than or equal to total output of the consumption good,

(7) demand for the capital good must be less than or equal to total output of the capital good.

The rule of free goods prevails in the markets, so that if one of the conditions (4) to (7) holds with strict inequality, then the corresponding price, say the price of the capital service in the case of (4), is set at zero. Conditions (1) to (7) are then found to imply the equality of savings and investment.

Existence of a golden growth equilibrium. We now examine the Walrasian model for the existence of a golden growth equilibrium, defined as a state in which outputs of all goods grow at a rate equal to the rate of growth of the labor force and in which all prices remain unchanged forever. The argument proceeds in terms of the warranted and natural rates of growth, the most fundamental concepts of growth economics originally due to Harrod (1948).

Harrod defined the warranted rate of growth as “that over-all rate of advance which, if executed, will leave entrepreneurs in a state of mind in which they are prepared to carry on a similar advance” (1948, p. 82). Some preliminary analysis is required to establish the warranted rate, for it is a concept that results from a combination of the so-called factor-price frontiers (Morishima 1964, pp. 76-83; Samuelson 1962) and Kahn’s interindus-trial multiplier (Kahn 1931).

Suppose that prices are normalized so that the price of the consumption good is unity. Then the normalized wage rate gives the real wage. Conditions (1) and (2) now contain three variables— the price of the capital good, the price of the capital service, and the real wage rate. Therefore, two of these prices, say the first two, can be expressed as functions of the third. We can then obtain a relation between the rate of return on capital, that is, the ratio of the price of the capital service to the price of the capital good, and the real wage rate. This relation is referred to as the envelope of the factor-price frontiers, or simply the factor-price frontier. The rate of return on capital can be shown to decrease when the real wage rate increases in an interval permitted by technology.

It follows from (1) and (2) that there exist positive prices corresponding to any preassigned nonnegative value of the real wage rate, provided the value of the real wage does not exceed the maximum permitted by technology. This implies that (4), (6), and (7) hold as equalities. Since demand for the consumption good equals total in-come multiplied by the average propensity to consume (denoted by c),

(8) consumption equals c times the sum of consumption and savings.

If ξ denotes the output of the consumption good, x the output of the capital good, and p the price of the capital good in terms of the consumption good, then conditions (6) and (7), together with other equilibrium conditions, imply that consumption equals ξ and that savings equals px. Substituting (6) and (7) into (8), we obtain the Kahn multiplier,

From the factor-price frontier, prices depend on the real wage rate. Since c is assumed to depend only on prices, it is seen that the real wage rate is the ultimate determinant of the relative outputs of the two industries.

The warranted rate of growth can easily be established now. Dividing condition (4) by the output of the capital good, we obtain to the right of the equality the reciprocal of the rate of growth of the capital stock. Since the processes for which (1) or (2) hold with strict inequality are not adopted, and since the choice of other processes is subject to (9), the rate of growth of the capital stock depends on the real wage rate. Hence, there is a relation between the growth rate of the capital stock and the real wage rate in the entire interval permitted by technology. This relation is called the warranted growth rate curve. Suppose w is the real wage rate arbitrarily set in the technologically permitted interval. Entrepreneurs will increase the stock of capital at the rate corresponding to the given value of w, and all the equilibrium conditions except (5) will be fulfilled. Entrepreneurs will wish to maintain this growth rate, and it will persist if the supply of labor adapts itself to the demand for labor.

In the absence of technological change, the natural rate of growth is equal to the rate of growth of the labor force. The rate of growth of the labor force is often assumed to be constant (independent of the values of economic variables) but may more realistically be considered a function of the real wage rate. Suppose that the growth rate of the labor force is positive, zero, or negative depending on whether the real wage is above, equal to, or below the subsistence level. This relation between the natural growth rate (the growth rate of the labor force) and the real wage rate is called the natural growth rate curve.

The warranted and natural growth rate curves will generally have at least one point of intersection, and at that point the stock of capital and the labor force grow at a common rate. Suppose w is a real wage rate at which the stock of capital, K, and the labor force, L, increase at the same rate g. Let the values of the other variables that satisfy the equilibrium conditions (1) to (7) be denoted by corresponding letters with bars above them. A proportional increase in K and L gives rise to an increase of the same proportion in total income, provided prices remain constant. Since the income elasticity of demand for the consumption good is unity, the increase in total income gives rise to an increase of the same proportion in the demand for the consumption good. Therefore, if prices remain constant over time, equilibrium at any point of time t is established when

where subscripts indicate time; that is to say, when the real wage rate w prevails, the stock of capital, the labor force, and the outputs of the two industries grow forever at the common rate g, and prices remain unchanged. Such a state is called a state of golden growth equilibrium (Robinson 1956, p. 9; Morishima 1964, p. 78).

The von Neumann model. The two-sector model examined so far assumes, among other things, (a) that firms can be classified into two industries producing distinct outputs, (b) that factors of production are instantaneously transformed into products, (coma) that the capital good does not suffer wear and tear, and (d) that the capital stock and the supply of labor are freely transferable from one firm to another. All these assumptions are unrealistic, and they crucially affect the analytical properties of the model.

First, it is clear from actual input-output tables of various countries that many goods are both consumed and used as inputs in many industries in the economy; there is no clear demarcation between consumption goods and capital goods. Second, a certain length of time generally must elapse between the original input of factors and the final output of a product. The period of production usually differs from one good to another, but we may justify the assumption of uniform production lags by introducing as many fictitious intermediate products at each point of time as required.

Third, according to the neoclassical treatment of depreciation, capital goods that were produced several years ago and have been subject to wear and tear are considered to be physically equivalent to some smaller amounts of new capital goods of the same kind. But it is generally impossible to find quantitative equivalents, in terms of new capital goods, of capital goods damaged in various degrees from past use. In fact, if an entrepreneur has a certain amount of a capital good that is in its final stage of wear and tear, he will have no capital equipment at the beginning of the next year; while if he has a certain amount, however small, of a new capital good, he may use it for production throughout its whole lifetime. Only by treating capital goods at different stages of depreciation as qualitatively different goods can we adequately deal with the age structure of the capital stock. Von Neumann (1937) suggested that used capital goods appearing simultaneously with products at the end of the production period be treated as by-products of the manufacturing process. A process that uses capital equipment is regarded as a process that converts a bundle of “inputs” into a bundle of “outputs,” where inputs are defined to include capital goods left over from the preceding period and outputs are defined to include qualitatively different capital goods left over at the end of the current period.

This treatment of capital goods enables us to discard the final assumption of perfect transferability of capital equipment. In addition to being more productive, a new capital good is generally more transferable than a used one. A new machine will be sold to any factory that demands it, while a machine that has already been set up in a factory usually will not be transferred to another factory, even if the factory that owns the machine is overequipped and some other factory is under-equipped. This asymmetry in the transfer ability of capital goods can readily be incorporated in the growth model if we permit joint production in the sense von Neumann suggested and treat capital goods at different dates as different goods.

From these considerations, it is clear that the growth model, if it is not to be trivial, must not only be multisectoral but must also be capable of dealing successfully with joint production. A model fulfilling these requirements was first proposed by von Neumann. He assumed the following: (a) there are constant returns to scale in production of all goods; (b) the supply of labor can be expanded indefinitely; (c) the wage rate is fixed at a level at which workers can only purchase the minimum amounts of goods biologically required to subsist; and (d) the whole of capitalists’ income is invested in new capital goods. It is evident that the model ignores the role played by consumers’ choice in the determination of the rate of growth; workers are like farm animals, and capitalists are simply self-service stands of capital.

Consumers’ choice has been introduced into the model by relaxing the classical assumption that workers only consume and capitalists only save. Morishima (1964) studied models where (1) Although workers still consume their entire income, their demand for consumption goods allows substitution in response to price changes, and (2) capitalists spend a portion of their income on consumption goods in such a way that their demand for each good depends not only on relative prices but also on their income—the income elasticity of demand being unity. Morishima also replaced von Neumann’s unrealistic assumption of an indefinitely expandable labor force with a more plausible assumption of a labor force growing at a rate that depends on the real wage rate.

Perfect transferability of capital goods is not a necessary condition for the existence of golden growth equilibrium; but the assumption of unitary income elasticities of demand, which is very stringent and unrealistic, is an indispensable condition. Aside from uneven effects of technological change on various industries, the only obstacle to golden growth is the existence of different income elasticities of demand for different consumption goods.

In an economy where wages are paid at the end of each period, the golden equilibrium growth rate equals the product of the capitalists’ average propensity to save and the rate of profit on fixed capital. On the other hand, if wages are advanced at the beginning of each period, they earn profit during the period, and the golden equilibrium growth rate equals the capitalists’ propensity to save multiplied by the rate of profit on total capital, which is the sum of fixed capital and the wages fund (Morishima 1964, pp. 145-151).

Stability of a golden growth equilibrium. In examining the stability of a golden growth equilibrium, a problem posed is whether the maintenance of full employment of labor and capital along a path starting from arbitrarily or historically given endowments of capital and labor will eventually lead to a state of golden equilibrium growth. Various writers have studied this problem and have found that a large class of two-sector models have a stable golden equilibrium if certain plausible restrictions are imposed on technology or on the consumption function. For example, in the case of the Walrasian two-sector model, stability is ensured if a constant proportion of income is devoted to consumption.

However, in more realistic multisector models, the tendencies toward a golden growth equilibrium may not exist. It has been argued that the stability of outputs in a multisector model implies the instability of prices, and vice versa. Jorgenson (1960) proved that this is the case for a closed dynamic Leontief input-output system. However, for an open system, he showed that stability of outputs implies stability of prices, except under rather implausible circumstances. Since examples of both stability and instability of golden equilibrium growth can be found, the maintenance of full employment of labor and capital is not a sufficient condition for the attainment of a golden growth state.

A growth path is called efficient if there is no other path along which more of some goods can be produced without reducing the output of another good. A growth path is called optimal if there is no other path that can make the society better off. Full employment of labor and capital is a characteristic of an efficient or optimal growth path if labor and capital are always scarce. Whether or not these factors are scarce, however, depends on the amounts of goods to be produced. In a planned economy, a certain amount of the capital stock may not be used at some point of time if the existing capital stock exceeds the amount required by a long-run growth plan designed to attain either efficiency in production or maximum satisfaction of the citizenry. Similarly, a portion of the labor force may not be used. Hence, rather than examining the convergence of a full employment growth path to the golden equilibrium path, we might examine the convergence of efficient growth paths to the golden equilibrium path.

The turnpike theorems. The turnpike growth path (or, more briefly, the turnpike) is defined as the golden equilibrium growth path (there may be many such paths) that gives the maximum rate of growth. The study of convergence of efficient growth paths to the turnpike has produced the so-called turnpike theorems.

Adopting von Neumann’s assumptions presented above, the basic turnpike theorem may be stated as follows: Let the stocks of goods that the economy intends to have at the end of a planning period be specified in their proportions (but not in their absolute values) by the planning authorities. Consider efficient paths in the set of all feasible growth paths. In this instance, a feasible growth path is one leading from the historically given present state to the prescribed end. There is a long-run tendency for such efficient paths to approximate the turnpike as the planning period becomes longer and longer. In other words, the long-run efficient paths run along the turnpike for most of the planning period, although they will have to leave the turnpike in the final part of the planning period in order to reach the objective (Dorfman et al. 1958, pp. 326-345).

This theorem would be especially useful in formulating a seven-year or ten-year growth plan for underdeveloped or socialist economies. Mathematical economists have provided rigorous statements and proofs of the theorem (Radner 1961; McKenzie 1963) and have found that there are exceptions to the theorem. Unless the technology available to the economy satisfies some special conditions, efficient paths will trace out undamped oscillations around the turnpike (Morishim a 1964, pp. 171-173; Hicks 1965, pp. 224-225, 327-331).

The theorem can be modified or extended in several directions. For example, it has been shown that the stocks of goods discounted by one plus the turnpike rate of growth and averaged along efficient paths over the whole planning period are very close to the turnpike stock vector if the length of the planning period is sufficiently long. Such a convergence theorem may be termed the mean turnpike theorem. There is no cyclic exception to the mean turnpike theorem; even though efficient paths may fluctuate around the turnpike regularly or irregularly, the average of the discounted values of deviations from the turnpike always approaches zero in the limit (Morishima 1965).

The turnpike theorems discussed so far are based on the assumption that the labor force can be expanded at any rate. This assumption can be replaced by the more general assumption that the production and reproduction of workers is part of the over-all process of production. Workers cannot choose goods according to their own tastes but are fed by the dictator or planning authorities just as farm animals are. When there is a shortage of workers, they will be fed well to increase the birth rate; in a period of excess supply of workers, they will be underfed. Obviously, the model describes a shameless society such as a slave economy, although this is not very far from the state of affairs in some countries. The turnpike (mean turnpike) theorem for such an economy asserts that all efficient paths converge to the turnpike in the sense that output of each good per worker (the average discounted output per worker) approximates the turnpike output per worker when the planning period is very long.

In the models just described, the planning authorities specified only terminal stocks of goods. Outputs of goods at any intermediate date were simply inputs for the immediately succeeding date, and there was no consumption at intermediate dates. (Feeding the workers was necessary to produce workers; the food they ate was an input for the process that produced workers who, in turn, were inputs for other production processes.) Hence, a growth path was feasible if it merely satisfied the final-state conditions, and the turnpike theorems stated may be called final-state turnpike theorems. They hold when the sole objective is to bequeath certain stocks of goods to a remote future generation, for example, to our great-grandchildren. But if the welfare of children and grandchildren is to be taken into account, their consumption should also be part of the desiderata in the growth plan. Intermediate states as well as the final state must be evaluated according to some measure of welfare.

This can be accomplished by introducing a utility function that depicts the preference orderings (by the workers or by the ministry of welfare) of different streams of consumption and of amounts of work over the planning period. In particular, suppose we discount consumption and the amount of work at each future date by a subjective time-preference factor that does not exceed the turnpike growth rate. It is assumed that utility depends on the averages over all dates in the planning period of these discounted values. An optimal growth path is one that maximizes this utility function.

With the aid of some additional assumptions, we can establish the following consumption turnpike theorem: As the length of the planning period tends to infinity, any optimal path converges to the turnpike. As in the case of the final-state turnpike theorem, there will be cyclic exceptions to this consumption turnpike theorem if technology does not satisfy some restrictive conditions. Optimal paths may oscillate around the turnpike forever. However, a consumption mean turnpike theorem that is similar to the final-state mean turnpike theorem discussed above can be established, and there is no cyclic exception to the mean theorem.

The consumption turnpike theorem, unlike the final-state turnpike theorems, could avoid cyclic exceptions if it were assumed that society has an aversion to fluctuations. Of two consumption streams having the same average discounted values but having different fluctuations over the planning period, society may prefer the stream with the lesser fluctuations. An optimal growth path would then be one that maximizes a utility function that depends upon the average discounted values of consumption and of amounts of work and upon some measure of the variances of these streams. When the society’s aversion to fluctuations is very strong, its optimal growth path will be a feasible path that has no fluctuations in consumption per capita, so that the convergence of consumption per capita to the turnpike is secured.

Even in this case, however, it is still possible to have fluctuations of outputs around the turnpike; in fact, people would be prepared to accept fluctuations of outputs if fluctuations are required for an optimum steady stream of consumption. Hence, the introduction of very strong aversion to fluctuations will eliminate cycles in the per capita consumption of goods but not in per capita outputs.

Michio Morishima

[See alsoEconomic equilibrium; Interest; Statics and dynamics in economics; and the biographies ofvon Neumann; Walras.]

BIBLIOGRAPHY

Dorfman, Robert; Samuelson, Paul A.; and Solow, Robert M. 1958 Linear Programming and Economic Analysis. New York: McGraw-Hill.

Hahn, F. H.; and Matthews, R. C. O. 1964 The Theory of Economic Growth: A Survey. Economic Journal 74:779-902.

Harrod, Roy F. (1948) 1960 Towards a Dynamic Economics: Some Recent Developments of Economic Theory and Their Application to Policy. London: Macmillan; New York: St. Martins.

Hicks, John R. 1965 Capital and Growth. New York: Oxford Univ. Press; Oxford: Clarendon.

Jorgenson, Dale W. 1960 A Dual Stability Theorem. Econometrica 28:892-899.

Kahn, R. F. 1931 The Relation of Home Investment to Unemployment. Economic Journal 41:173-198.

Mckenzie, Lionel W. 1963 Turnpike Theorems for a Generalized Leontief Model. Econometrica 31:165-180.

Morishima, Michio 1964 Equilibrium, Stability and Growth: A Multi-sectoral Analysis. Oxford: Clarendon.

Morishima, Michio 1965 On the Two Theorems of Growth Economics: A Mathematical Exercise. Econometrica 33:829-840.

Radner, Roy 1961 Paths of Economic Growth That Are Optimal With Regard Only to Final States: A Turnpike Theorem. Review of Economic Studies 28:98-104.

Robinson, Joan 1956 The Accumulation of Capital. Homewood, III.: Irwin; London: Macmillan.

Samuelson, Paul A. 1962 Parable and Realism in Capital Theory: The Surrogate Production Function. Review of Economic Studies 29:193-206.

von Neumann, John (1937) 1945 A Model of General Economic Equilibrium. Review of Economic Studies 13:1-9. → First published in German in Volume 8 of Ergebnisse eines mathematischen Kolloquiums.

Walras, LÉon (1874–1877) 1954 Elements of Pure Economics: Or, the Theory of Social Wealth. Translated by William Jaffe. Homewood, III.: Irwin; London: Allen & Unwin. → First published in French as Elements d’economie politique pure.

IV NONECONOMIC ASPECTS

The concept of underdevelopment which has become quite popular since the end of World War ii applies primarily to societies which are inferior to the principal Western nations in terms of economic performance and technological sophistication. In previous periods these societies were customarily referred to as “backward” or “arrested,” but these terms have fallen into disuse, and in their stead “underdeveloped” or “developing” is used. In even more recent times, and with special regard to countries emerging from colonialism, the concept of “new nations” is being employed.

Although the condition of “underdevelopment” therefore is primarily an economic and technological feature of certain societies, it appears to have important sociological concomitants, and it is these social and cultural aspects of the condition of underdevelopment, as well as the variables which appear important in analyzing the gradual emergence of these societies from a condition of economic and technological underdevelopment to a level of higher economic and technical performance, which will be stressed in the subsequent paragraphs.

The description of underdevelopment and the identification of processes and policies which will lead out of it to higher levels of performance is primarily undertaken by economists. But economists realize that in performing this task they have to take account of noneconomic, i.e., primarily social and cultural, factors which strongly influence patterns of development. In fact, it may be argued that on the purely analytical level the economic problems of economic development are relatively simple, whereas the social and political aspects of the process are much more complex and elusive.

It is generally acknowledged that the main path to higher levels of economic performance is through the rational organization of production, and this rational organization in turn depends primarily on the introduction of industry. Thus, in terms of occupational structure, underdevelopment is characterized by the absolute prevalence of agriculture as the main source of livelihood; and economically more advanced societies usually show an increasing proportion of their labor force in secondary (manufacturing and mining) and tertiary (service) occupations. All societies which are in a state of underdevelopment, therefore, are non-industrialized or little industrialized, and the process of economic development may in a rough way be equated with the progress of industry and associated forms of economic activity.

Classical approaches. We do not lack descriptions of nonindustrial societies, beginning with the ethnographic reports of “savages,” “barbarians,” or “exotic peoples.” But these accounts are of little analytical value. The first useful attempts to come to grips with the analysis of the social system of nonindustrial societies begin with the work of scholars who sought to describe entire social systems associated with different levels of economic performance. Among the most famous attempts at holistic descriptions of differentiated social systems are the well-known dichotomies of Ferdinand Tönnies (1887) between Gemeinschaft and Gesellschaft, of Robert Redfield (1941; 1950) between folk and urban society, and of authors following Max Weber (1919–1920) between traditional and rational patterns of social action. This last contrast has received a great deal of attention, and we find not infrequently that action and behavior patterns in technologically and economically little developed societies are described as “traditional” and that this concept implies that these action patterns are in-efficient, technologically noncomplex, and strongly resistant to innovation.

Redfield’s “folk society’ Before entering into a more detailed analysis of the concept of tradition-oriented behavior, it would be useful to draw attention to two features of nonindustrialized societies which have received extensive treatment in the work of Redfield and Tonnies and their followers. One point often reiterated by Redfield is the fact that social acts in a folk society typically are not “single-interest” but “multiple-interest” actions. Productive activity, for example, not only has an economic purpose but also is conceived by the members of folk societies as containing ritual elements, elements pertaining to social cohesion or structure, “political goals,” and others. This very “multidimensionality” of all social behavior in folk societies is at the bottom of some of the difficulties in bringing about changes in behavior. If social behavior were unidimensional, change would be relatively easy. Since in addition to meeting one specific objective, a given action is conceived of as simultaneously meeting other objectives, change is possible only if the new way of acting can be interpreted as comprising all these associated objectives also. In brief, some such behavior as planting, or harvesting, or engaging in exchange is conceived of not merely as productive activity but also as behavior maintaining the stability and relational adequacy of a person’s position in his culture. Hence, if different forms of productive activity are proposed, they will prove acceptable (without strong external compulsion) only if they also meet in some form or another all or most of the other objectives which were met by the activity to be replaced.

Tönnies’ “small community” The emphasis placed by Tonnies and his disciples on the significance of community also has played an important role in the study of conditions surrounding technological change and economic innovation. The point to be emphasized in this context is that for many nonindustrialized societies, the small group is the relevant unit of social cohesion. This small community often has its origin in tribal or kinship relations, but what is important about it is that its membership is usually strictly circumscribed, limited to persons who have either long-standing faceto-face relationships or some other form of close common identification. All outsiders, i.e., all persons who do not belong to the small community, are strangers and are often regarded with suspicion.

In many underdeveloped societies these highly particularistic groups still exist, and in some instances they have considerable strength. They often appear as tribal groups, but also may constitute village communities, castes, or other associations based on kinship or quasi-kinship ties or joint occupancy of a small area. Usually the group lives in a compact area. Geography and familiarity thus rein-force one another, and the small community may be considered in some cultural contexts as a hard-shelled unit whose main forms of social interaction occur only within the community and whose relations to the outside are tenuous and often associated with suspicion and fear. In the development process, strong tendencies are set in motion to break up this isolation of the community and to enmesh its members in different forms of social relations with the outside. Moreover, it is often those persons who have low status within the community who most easily penetrate the wall built around it and who tend to interact most frequently with the remainder of the society.

Thus the significance of the small community is its resistance against absorption into the “great society” and the conflicts which arise on the social and personal level in the absorption process, in which primary loyalties to the small group gradually tend to be replaced by loyalties to the larger society. Moreover, many of the institutions which have meaning within the context of the small community lose this meaning in the framework of the larger society. The family as a productive unit that yields economic security loses its place in a society in which industrialization has occurred and in which the economic ties are with persons outside the kinship group and economic security is obtained through governmental or other insurance schemes. Similarly, the intimate relation with tribal or village deities loses its full significance for those who enter the larger society, and the patterns of deference and authority within the small community have no force outside it. All this tends to produce conflicts within and beyond the small community. One may notice them in India, where they manifest themselves in conflicts within and between castes; in Africa, where they appear as struggles between centralized authorities and tribal chieftains; and elsewhere, where they take on still different forms.

The strong nationalism which permeates many industrializing countries is the chief ideological underpinning for a process of social change which leads from the ubiquity of small, particularistic communities to a more uniform, structurally diversified but more highly interdependent society. Other processes associated with industrial development and less subject to manipulation by agitators and intellectuals support this trend. Among these are urbanization and bureaucratization of govern-mental and productive procedures. The onslaught on the small community thus comes from all sides, and it is not likely that it can withstand the combined impact of these forces.

From the description of the small community and the folk society, with its multifaceted features of social interaction, we can see that these two concepts are mainly different descriptions of the same social type. A third, and on the whole more popular, way of describing this type of society is to point to its traditionalism or, perhaps more correctly, to describe it as a society in which traditional forms of action predominate. As we have seen, the concept of traditional social action ultimately goes back to Max Weber (1922), who juxtaposed it to different forms of rational action. Since the concept of traditional or tradition-oriented action has gained such wide popularity, it must be considered in somewhat more detail.

Weber’s “traditional behavior” Although Max Weber did not explicitly make the important distinction between traditional action and traditionalistic action, it is implicit in his work. Traditional or tradition-oriented social action is found in all societies. Weber described it as action based upon the psychic attitude set for the habitual workaday and the belief in the everyday routine as an inviolable norm of conduct (1922). But beyond this, the concept of traditional action may be widened by including forms of social behavior which have been taken over from ancestors and forebears, because all populations have a sense of their historical past and a need for continuity of behavioral norms and because these forms of social action can appropriately be fitted into the action schema of a society. This does not mean that traditional action excludes change. Many practices in modern, highly industrial societies are based on tradition and traditional norms. This is true of such everyday behavior patterns as forms of greeting and rules of personal conduct, but it is also true of more complex behavior in the political and economic spheres. It would be difficult to separate societies at different levels of economic performance by the relative “quantity” of tradition-oriented behavior that their members show.

Traditionalistic action, on the other hand, may be defined as action based upon the self-conscious, deliberate affirmation of traditional norms in full awareness of their traditional nature and alleging that their merit derives from that traditional transmission from a sacred orientation (Weber 1919-1920). In other words, traditionalistic action is a conscious revival of a past glorious age or past sacred lore, an ideology which looks to the past as providing a set of norms whose revival would again lead to splendor and greatness. In the nationalisms of many industrializing countries, especially those whose roots go deep into a great past—such as India and the Islamic countries—we can find strong traditionalistic admixtures. These ideologies consist not merely in the rejection of Western values; the revival and revitalization of old values, often long dead, is demanded, and external behavior is ap-proved which is thought to be in conformance with these norms.

Traditional action, though it may sometimes conflict with the demands of modernization and technological change, usually is an important reinforcing element in the preservation of stability in a period of rapid change. On the whole, the permanence of manifold traditions in social behavior may be an important factor mitigating the many dislocations and disorganizations which tend to accompany rapid industrialization and technical change. Traditionalistic action, on the other hand, since it tries to elevate outdated practices and values to the level of current behavioral norms, usually has a reactionary character and tends to retard economic change. [See the biographies ofRedfield; TÖnnies; and Weber, Max.]

Parsons’ pattern variables approach. One attempt to elaborate further the characteristics of tradition-oriented societies and, in fact, to break into its components the rationalism-tradition dichotomy, is the description of societies at different levels of economic performance by means of the pattern variables developed by Talcott Parsons (1951).

Of the five pairs of pattern alternatives stated by Parsons, three are immediately applicable: the choice between modalities of the social object (achievement versus ascription), the choice between types of value orientation (universalism versus particularism), and the definition of scope of interest in the object (specificity versus diffuseness). In applying these three pattern variables to the distinctions between industrialized and predominantly nonindustrial societies, we find that industrialized societies are characterized by the predominance of achievement standards in the distribution of economic roles and objects, that they employ universalistic criteria in this distribution process, and that economic roles in these societies are typically functionally specific. Underdeveloped societies, on the other hand, predominantly exhibit features of ascription, particularism, and functional diffuseness in the corresponding fields of social action. It should be emphasized that we are considering norms of social behavior. In other words, the complex of pattern variables present in any society constitutes an ideal type.

Achievement—ascription. The achievement—ascription dichotomy is closely related to, though not identical with, the contrast between status-oriented and contract-oriented societies first stressed by Henry Sumner Maine (1861). If we apply this dichotomy to economic objects, we find that in a society in which ascription is the norm, economic roles are distributed ideally on the basis of who a person is rather than what he can do. A practical example of a society based on ascription would be an “ideal” caste system, in which each caste is associated with a certain occupation and in which only members of a given caste are admitted to that occupation. The caste system, however, although it may have come close to this ideal in some localities at certain times, never, as a whole, exhibited fully ascriptive features [seeCaste]. But it is quite clear, from the example given, that in a society in which economic roles are assigned on the basis of status or ascription, social mobility is made difficult and social change, to the extent to which it depends upon mobility, is severely impeded.

In contrast, the predominance of an achievement norm with respect to the distribution of economic roles means that the primary criterion for attaining a certain occupation is based on a person’s capacity to perform the required tasks. In practice, an actual test may be involved in the process of allocating economic roles, or, lacking this, certain objective criteria, such as successful completion of a certain number of years of school, or the obtaining of a degree, may be prescribed. Again, it is well known that pure performance criteria are not applied everywhere in industrialized countries, but the ideal of an achievement norm is strong enough so that even where economic roles are actually allocated on the basis of ascription, the pretense is made that the performance requirement has been met.

Universalism-particularism. The next pair of pattern alternatives, universalism-particularism, is related to the first pair. They do not prescribe norms concerning who is to perform a given role but stipulate whether the same rules apply to everyone. A good example of the application of particularistic norms with respect to economic action is the case of European medieval society, in which specific rules applied to peasants and burghers, to nobles and commoners. In many underdeveloped societies, certain markets and certain transactions are reserved to certain groups, and only the admission of an outsider to an otherwise closed group permits him to perform the functions reserved for this group. The principle of universalism, on the contrary, makes no such distinctions. The same rules apply to all, the principle of formal equality being elevated to a general norm of social behavior.

Speciftcity–diffuseness. It almost follows logically that in a society in which economic roles are distributed on the basis of universalistic performance criteria, the roles themselves are functionally highly specific. This requirement is an outflow of the rigorous application of the principle of achievement, which is of little value unless a role can be clearly defined and circumscribed. Functional specificity is, moreover, an outflow of the increasing division of labor. Adam Smith, in his famous example of the manufacture of pins, clearly demonstrates its economic advantage. For, as he points out, “the improvement of the dexterity of the workman necessarily increases the quantity of work he can perform; and the division of labour, by reducing every man’s business to some one simple operation, and by making this operation the sole employment of his life, necessarily increases very much the dexterity of the workman” (Smith [1776] 1937, p. 7). There are other advantages, in Adam Smith’s view, to the division of labor, but he quite accurately places the development of a high degree of functional specificity first.

Functional diffuseness stands in direct contrast with specificity. The simple peasant in a nonindustrial society is a characteristic representative of the functionally diffuse. He not only performs all work connected with producing a crop but he also builds his house, makes his implements, and often produces his own clothes and other final consumption goods. As in the cases of the ascription-achievement duality and the particularism-universalism duality, we find noncharacteristic cases which seem to contradict the generalization that diffuseness is normally associated with underdeveloped societies. For example, in India the system of social division of labor under the predominance of caste has led, even in a nonindustrial society, to a high degree of functional specificity. On the other hand, certain occupations, especially on the highest managerial level, are functionally diffuse, even in highly industrialized societies. In general, functional specificity has been instituted more widely for the simpler and less complex tasks, but the progressive specialization in business management, and even in scientific pursuits, is a sign that this process of occupational differentiation is ubiquitous and strong in modern advanced societies.

The use of pattern variables has the advantage of bringing into sharper focus some of the strategic mechanisms of social change associated with industrialization and technical progress. Although universalistic norms need not generally replace particularistic ones, the transition from a system of ascription to one based on achievement in the allocation of economic roles and the replacement of functionally diffuse by functionally specific norms for the definition of economic tasks appear to have taken place in all cases of successful economic development. It is, therefore, useful to relate the description of industrial and nonindustrial societies which uses the pattern variables to the earlier descriptions which used the folk-urban continuum and the community-society dichotomy.

Integration of approaches. We have seen earlier that the folk society is characterized by a multi-dimensional meaning of economic acts, i.e., their relevance not merely as acts of production or exchange but also as acts of ritual, assertion of associative values, and so on. Alternatively, this fact can be described by pointing to the high degree of functional diffuseness of economic acts in the folk society. If a particular form of social behavior has meaning in several spheres of social action, it must, by necessity, be diffuse. It has many meanings, and although the actual manipulations demanded in its performance may be rigidly prescribed, its “multidimensionality” gives it the character of functional diffuseness, which, incidentally, also makes it so resistant to change.

Similarly, we may conceive of the small community as a set of institutionalized interpersonal relationships based primarily on ascriptive characteristics. The cohesion and compactness of the small community are enhanced because economic roles are tied to ascriptive status and because even where there is a considerable degree of specificity in different economic roles, as in the Indian village, ascriptive norms provide a stability and internal rigidity which makes change from within exceedingly difficult. It is only the breakup of the small community or its infiltration from the outside which tends to reduce the significance of ascription in the distribution of economic (and other, e.g., political or deference) roles.

The gradual destruction of the traditional folk-like small community thus is accompanied in the economic and technological spheres by a process of differentiation of economic roles and a relaxation of the rules assigning those roles to particular actors. But the process is not a smooth one; it proceeds in spurts and jolts. In this process new institutions develop, and as each new institution becomes established, it provides a pivotal point around which further changes gather momentum. If the juxtaposition of societies on different levels of economic modernization provides a classic case of the comparative analysis of social institutions, the analysis of the transformation from one to the next level of economic performance may be regarded as a study of the dynamics of institutional change.

Social deviance. This is not the place to discuss in an exhaustive manner the process of institutional change, which is a much broader process than merely overcoming a state of economic underdevelopment. But it may be useful to discuss the phenomena of social deviance and social marginality, because they have been applied quite commonly in the analysis of the social concomitants of industrialization and economic development.

Deviance. Let us first turn to a brief consideration of social deviance. As already stated, we are concerned here primarily with those forms of deviant behavior which are relevant for economic activity and organization. If the concept of deviance is to have operational meaning, it cannot be interpreted simply as signifying behavior which is new; it must imply that this set of innovating acts is opposed in some way to existing social norms or approved forms of behavior. In other words, a deviant always engages in behavior which constitutes a breach of the existing order and which is either contrary to, or at least not positively weighted in, the hierarchy of existing social values. If we apply this concept to the behavior displayed by businessmen and merchants in the course of the economic history of western Europe, we find that we can speak of genuine deviance in those periods and societies in which entrepreneurial behavior did not belong to the category of social actions which were considered as constituting the “good life.” As late as the fifteenth century, this was true of certain kinds of financial entrepreneurship, which was always tainted by the official opposition of the church against usury. And later, when financial entrepreneurship became fully respectable, industrial entrepreneurship came to be regarded with some disdain because it “dirtied one’s hands.” These sentiments toward business or industrial activity as not quite proper for a gentleman are familiar in many underdeveloped countries today.

If deviance implies some breach with existing social norms, it is interesting to investigate further from what social classes or groups persons come who engage in various forms of deviant behavior. Clearly, the expected rewards of this behavior must be attractive, and persons engaged in this behavior are likely to feel a strong urge to rise in the social scale (perhaps a strong motivation for achievement) or to have resentments against some aspects of the existing order. It is in these terms that the rise of the western European bourgeoisie or even of the lower samurai groups in Japan have been explained. In the view of some, this reshuffling of social positions is the result of class struggles; in the view of others, it is a gradual evolutionary process.

Marginality. An alternative hypothesis is that persons engaging in deviant behavior are at the margin of a given culture or are in a social or cultural position in which they straddle more than one culture. We may identify cases in which deviance coincides with social marginality. For example, in medieval Europe the earliest money-lenders were often foreigners. In Italy at the time of Gothic and Langobard rule, they were Syrians, Byzantines, and Jews. Later, when Italians turned to financial entrepreneurship on a large scale, the Genoese and Pisans, Sienese and Florentines, who were all lumped together under the name “Lombards,” became the financial entrepreneurs north of the Alps.

The role of marginal individuals in various economic pursuits in many economically under-developed countries is eminently manifest today. One could cite the Chinese in various southeast Asian countries, the Indians in east Africa, and the widely scattered Lebanese and Syrians who make their appearance as businessmen in west Africa, Latin America, and elsewhere in poor societies.

What is the mechanism which allows marginal individuals to perform the roles they apparently have so widely accepted? As Robert E. Park (1913–1944), the inventor of the concept and of the significance of social marginality, has stressed, marginal men are—precisely because of their ambiguous position from a cultural, ethnic, linguistic, or sociostructural standpoint—strongly motivated to make creative adjustments in situations of change and, in the course of this adjustment process, to develop innovations in social behavior. Although many of Park’s very general propositions have been refined by subsequent researchers, the theory of social marginality has not advanced sufficiently to supply convincing evidence for the role marginal individuals may play in all episodes of social change. Even if it is admitted that marginal persons tend to make creative adjustments more often than to relapse into old orthodoxies or to embrace new ones, the record is not at all clear, and there are some students who warn us that marginal individuals may be more prone than others to succumb to anomie and thus to become carriers of trends leading toward social disorganization rather than to creative innovations. [See the biography ofPark.]

Institutionalization of deviance. In circumstances in which a certain amount of deviant behavior has been displayed, the anchoring of this behavior in a new institution is of strategic significance. Originally a form of deviance, it becomes routinized and may display all the characteristics of some highly approved form of social behavior. Thus the institutions in which deviant action is anchored form an advance post from which further deviance becomes possible. For example, the institutions which arose in western Europe before the industrial revolution and in Japan before the Meiji period were already the end products of a process of social change which had begun with deviant behavior; these institutions, in turn, by their very existence made possible further economic and technological change.

Sanctions. Whether or not any given form of deviance will lead to the elaboration of new social institutions and ultimate routinization of this pattern of social action will depend upon several factors, among which the system of sanctions existing in a society may be the most important. These sanctions may be internalized, i.e., they may reside in the values and beliefs of a population; or they may be externalized, i.e., they may be imposed by persons in power, by the elite, against actual or would-be deviants. It appears that in some societies, e.g., imperial China, both these types of sanctions were very strong. In pre-Meiji Japan, internal sanctions had partially broken down, and the power of the shogunate had become increasingly weak, so as to soften external sanctions to a point at which they were inadequate to prevent the formation of new institutions, or at least the beginnings of these innovations.

Strategic groups. Thus the analysis of social change may be couched largely in terms of considering the impact of deviance, whether exercised by marginal men or not, the gradual institutionalization and routinization of deviance, and the range of sanctions opposed to deviant behavior. This analysis may be carried out, initially, on the “aggregate level,” i.e., it may take into account an entire society at once. But our insights into social change may be sharpened if we disaggregate the variables in our analysis, i.e., if in a complex society, we take account not of changes affecting the society as a whole but of those affecting specialized sections or classes in the society. For deviance, sanctions, and the process of institutionalization have a different place and impact among different groups. Take sanctions as an example. Clearly, in societies in which ascriptive norms are strong, different individuals, depending upon their status positions, will be subject to different internalized sanctions; and in a society with extensive particularism, even external sanctions will be imposed and enforced to a very different degree on persons belonging to different groups or classes.

Elites. Thus, we are likely to discover in any society certain strategic groups which become the carriers of innovations. In some instances these groups may be composed of marginal individuals, especially if the innovations are transmitted from the outside. The role of marginal individuals in the acculturation or culture contact process has as yet been insufficiently explored, but their prominent participation in this process follows almost as a matter of definition. Another group which often plays a strategic role is the elite of a society. Although considerable attention has been given to the role of the elite in preserving a status quo, its impact on the introduction of organizational and technological innovations has perhaps been under-estimated. In general, social change has been seen as being accompanied by a “circulation of elites,” rather than as a process in which existing elites are capable of reorienting the systemic goals which they attempt to implement. Yet in the present economically underdeveloped countries, in which so much economic change is managed by the holders of political power, the role of the existing elites as innovators must be acknowledged. The entrepreneurial functions, which in Western countries were displayed predominantly by independent businessmen often belonging to a not fully enfranchised and politically impotent bourgeoisie, have been taken over by bureaucrats who operate with the blessing and under the protection of the political power apparatus. [SeeElites; entrepreneurship.]

Role of the state. In part, the intervention of the state in the industrialization process is certainly an outcome of the greater pressures, of the greater distance between reality and aspirations, which exist in the present. We may list several general factors which tend to enhance the role of the state in the process of economic growth. The urge for massive state intervention in the process of economic and industrial growth will be the stronger: (1) the greater the range of ends and the higher the level of attainment sought; (2) the shorter the time horizon within which the ends are to be attained, that is, the more rapid the rate of economic growth desired; (3) the more unfavorable the factor and resource endowments; (4) the greater the institutional barriers to economic change and industrialization; and (5) the more backward the economy in relative terms. As time progresses without development, the fifth condition is bound to obtain, simply because the later the onset of industrialization, the more backward a country will be in relative terms. But if this condition holds, it is also likely that the first, second, and fourth conditions will obtain, and thus we may conclude from this empirically derived set of conditions that in the course of time incentives and urges for state intervention in the industrialization process are constantly on the increase. But this means that industrialization as a goal progressively becomes an objective of over-all social policy and that existing elites, whatever their primary ends may have been in the past, have reoriented the hierarchy of the systemic goals by assigning an increasingly important place to economic development. But the increased interest of governments in economic growth and industrialization means not merely that they are capable of exercising control over the total resources of a society to be applied to its economic buildup, but also that, more effectively than any other agency, they can influence the forms of social behavior by altering patterns of rewards and sanctions and otherwise intervening in the social structure. This shows again that, in spite of the strong impact of ideological considerations in present-day developing nations, the conditions of social structure and the state of relative retardation and underdevelopment exert, in turn, an important influence upon the ideological forms as well as the socioeconomic relations under which the development process takes place.

Bert F. Hoselitz

BIBLIOGRAPHY

Almond, Gabriel A.; and Coleman, James S. (editors) 1960 The Politics of the Developing Areas. Princeton Univ. Press.

Banfield, Edward C. 1958 The Moral Basis of a Back-ward Society. Glencoe, III.: Free Press.

Boeke, Julius H. 1953 Economics and Economic Policy of Dual Societies as Exemplified by Indonesia. New York: Institute of Pacific Relations. →; Revision of the author’s two earlier studies: The Structure of the Netherlands Indian Economy, 1942, and The Evolution of the Netherlands Indies Economy, 1946.

Hagen, Everett E. 1962 On the Theory of Social Change. Homewood, III.: Dorsey.

Hoselitz, Bert F. (editor) 1952 The Progress of Underdeveloped Areas. Univ. of Chicago Press.

Hoselitz, Bert F. 1960 Sociological Aspects of Economic Growth. Glencoe, III.: Free Press.

Kuznets, Simon S. 1959 Six Lectures on Economic Growth. New York: Free Press.

Maine, Henry J. S. (1861) 1960 Ancient Law: Its Connection With the Early History of Society, and Its Relations to Modern Ideas. Rev. ed. New York: Dutton; London and Toronto: Dent. → A paperback edition was published in 1963 by Beacon.

Meier, Richard L. 1956 Science and Economic Development: New Patterns of Living. Cambridge, Mass.: M.I.T. Press.

North American Conference on the Social Implications of Industrialization and Technological Change, Chicago, 1960 1963 Industrialization and Society: Proceedings. Edited by Bert F. Hoselitz and Wilbert E. Moore. Paris: UNESCO.

Park, Robert E. (1913–1944) 1950 Collected Papers of Robert Ezra Park. Volume 1: Race and Culture. Glencoe, III.: Free Press.

Parsons, Talcott 1951 The Social System. Glencoe, III.: Free Press.

Redfield, Robert 1941 The Folk Culture of Yucatan. Univ. of Chicago Press.

Redfield, Robert 1950 A Village That Chose Progress: Chan Kom Revisited. Univ. of Chicago Press. → A paperback edition was published in 1962.

Rostow, Walt W. (1952) 1960 The Process of Economic Growth. 2d ed. Oxford: Clarendon.

Shannon, Lyle W. 1957 Underdeveloped Areas. New York: Harper.

Slotkin, James S. 1960 From Fields to Factory: New Industrial Employees. New York: Free Press.

Smith, Adam (1776) 1937 An Inquiry Into the Nature and Causes of the Wealth of Nations. New York: Modern Library.

TÖnnies, Ferdinand (1887) 1957 Community and Society (Gemeinschaft und Gesellschaft). Translated and edited by Charles P. Loomis. East Lansing: Michigan State Univ. Press. → First published in German. A paperback edition was published in 1963 by Harper.

Weber, Max (1919–1920) 1961 General Economic History. Translated by Frank H. Knight. New York: Collier. → Lectures delivered 1919–1920.

Weber, Max (1922) 1957 The Theory of Social and Economic Organization. Edited by Talcott Parsons. Glencoe, III.: Free Press. → First published as Part 1 of Wirtschaft und Gesellschaft.

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Economic Growth

Economic Growth

MEASURING ECONOMIC GROWTH

THE SIGNIFICANCE OF INCOME PER PERSON AS A MEASURE OF WELFARE

THE GROWTH PROCESS

OPTIMAL GROWTH

THE FUNDAMENTAL FACTORS OF ECONOMIC GROWTH

CONCLUSION

BIBLIOGRAPHY

The improvement of a societys living conditions is a complex process whose study has been at the very origins of economics. This process is called economic growth. In Western civilization, the first attempts to comprehend the mechanism of growth are recent, dating back to the end of the Renaissance only. We owe them to Giovanni Botero (15401617), Maximilien de Béthune, Duc de Sully (15601641), and Josiah Child (16301699). Why not earlier? Because the Middle Ages were doomed by endless conflicts and plagues; in the fourteenth century alone, more than one-third of the European population was wiped out by the great plague. It would have taken a bold thinker to even entertain the idea of development. As the French historian Pierre Gaxotte (18951982) wrote: The man of the Middle Ages does not know of time and numbers (1951, p. 237).

It is not surprising therefore that we owe to Arab civilization the first known comprehensive explanation of the fundamental causes of economic growth. They were given in a masterly way by Ibn Khaldūn (13321406) in his Muqaddimah: An Introduction to History (1377). Ibn Khaldūns objectives went beyond explaining economic growth; he gave himself the formidable task to unveil the causes of the rise and decline of civilizations. The British historian Arnold Toynbee (18891975) commented about Ibn Khaldūns magnum opus that in the Prolegomena to his Universal History he has conceived and formulated a philosophy of history which is undoubtedly the greatest work of its kind that has even been created by any mind in any time or place (Toynbee 1935, Vol. III, p. 322).

Western civilization would have to wait four centuries to see the independent blossoming of very similar ideas in Adam Smiths (17231790) Inquiry into the Nature and Causes of the Wealth of Nations (1776). Today, economic theory has vindicated the conjectures made by these major thinkers, as will be discussed in the last section of this entry. Before that, the entry will explain how growth is measured, what the process of economic growth is, and how optimal growth can be achieved.

MEASURING ECONOMIC GROWTH

The standard, international measure of economic growth is the increase in real income per person (the increase is a percentage rate per year). By income is meant national income ; this concept is derived from the gross domestic product (GDP), which is closely related to the measure of economic activity.

There are three conceivable approaches to measuring societys economic activity. The result of this activity can be considered in terms of the amount of goods and services that society manages to put at its disposal within a given time span (e.g., one year). Broadly speaking, it is customary to distinguish consumption goods and services (produced for their own sake, these will not be transformed at a later stage, and are not used for manufacturing other goods or services) from investment goods. Examples of the latter are equipment, factories, and transportation infrastructure, which will be used for production in coming years. The investment goods will be added to the capital stock in existence; along with technological progress, they will play a major role in the growth process. Exports are added to consumption and investment, since they also reflect societys activity. Naturally, consumption, investment, and even some exports include various amounts of imports; these are finally deducted in order to achieve a first measure of GDP from an expenditure point of view.

A second, equivalent, way to measure economic activity is to count the contribution of each sector of the economy (e.g., agriculture, industry, and services). Since the production of one sector (e.g., aluminum) may be used in another sector (automobiles), double counting must be avoided. For that purpose, only the net production of each sector is taken into consideration, in the form of its added value, equal to its total production less all purchases to other sectors. The sum of the added values of all sectors is then equal to GDP viewed from the production perspective.

Finally, it is clear that the only source that can be used to remunerate the production factors (labor and capital) is the value-added of each sector. In the third approach to measuring GDP, all categories of income are counted: labor income, capital income (interest and rentals paid by firms), and profits. Income used in measuring the growth of an economy is real net national income, determined as follows. First, the yearly depreciation of capital is deducted from the gross domestic product to obtain the net domestic product. We then add all capital and labor income received from abroad by residents, and deduce payments of capital and labor income made abroad to nonresidents. We thus obtain the net national product.

Two further corrections are needed to obtain the income distributed to society: First, we deduct all indirect taxes (paid by firms) and add subsidies (received by individuals and firms). The result is called national income. Finally, we are less interested in national income than in its purchasing power. To that effect, statisticians attempt to measure the average relative price increase of the various pieces of GDP from the expenditure side, and they deflate the yearly national income by that amount. For instance, supposing they estimate that prices have increased from year t to t + 1 by 10 percent; they will divide the years (t + 1) national income by 1.1 to obtain real national income with reference to year t as a base.

THE SIGNIFICANCE OF INCOME PER PERSON AS A MEASURE OF WELFARE

How much can we rely on income per person to gauge a societys standard of living and its progress? This type of measure shows defects that may be detrimental to its significance. Indeed, many expenses are counted in GDP (as well as in national income), although they should not be if we are interested in measuring societys welfare. For example, all expenditures forced upon individuals should be excluded from the measure. These include all public expenses made by authoritarian regimes that would not have received the populations approval through parliamentarian representation. Also included in this category are public expenditures made in countries where democracy is weak. In such countries, for example, the level of military expenditure is often far above what the country would require for pure defense purposes. These unwanted public expenses replace those that the population would have chosen, namely, expenditure for health and education.

We also count in GDP and national income a number of expenses that individuals may choose of their own free will, but which are also sometimes forced upon them by unwanted circumstances. Security expenses security taken in its largest meaningis an example. Those expenses are considerably higher today than they were decades ago, and of course have nothing to do with well-being. Think also of expenses resulting from accidents, disease, or epidemics. Each of the above has two negative effects upon societys welfare. First, society suffers directly from these circumstances and events. Second, those expenditures replace the goods and services that society could have enjoyed instead. No account is taken of working conditions in the measurement of national income. In particular, no account is taken of forced labor, particularly the labor forced upon women and children.

Furthermore, no equity measure appears in national accounts. This entry defines equity as the ability for society to reward each individual according to his or her own qualities and effort, and at the same time protect those hurt by fate.

Finally, national income does not account for damage done to the environment, and more generally to the biosphere. Inasmuch as depreciation of capital is deducted from GDP to obtain, after other adjustments, national income, we should also deduct the cost of the damage to the biosphere due to economic activity.

Despite these reservations, income per person remains a reliable gauge of societys welfare. If not an absolute measure, it is an adequate relative measure, since one can still make international comparisons based upon it. The fundamental reason is that the level of income in any country is intimately linked to its level of democracy. If one establishes a list of countries ranked according to their level of democracy, and set it beside another list on the basis of real income per person, there would be a great similarity in both lists. Economic growth has steadily accompanied societies that havehowever slowlymanaged to protect the individual and have abided by the principle of equality of opportunity. A third ranking of countries according to their welfare would be very similar because democracy is highly correlated to welfare. This is the reason why it is reasonable to measure welfare by income per person, imperfect as that index may be.

THE GROWTH PROCESS

The growth process has been well understood for at least two centuries, and can be described as follows. At the beginning of some time periodfor instance, year t any given country has a capital stock Kt at its disposal, and a workforce Lt, which may be proportional to the population. This workforce enjoys a degree of technological knowledge inherited from the past, just as the stock of capital has been accumulated in the past. During year t, society makes use of those resources to turn out a product referred to earlier as the GDP. Part of the GDP is used to replace the capital stock Kt, inherited at time t, which has depreciated during that year. Subtracting depreciation gives the net domestic product, which can be divided into two parts: By far the largest is consumption (perhaps 85%); the rest is net investment, which is equipment that will be added to increase the capital stock at the beginning of year t + 1. In the same time span, the labor force may have increased from Lt to Lt+1, and technological advances may have been made, carrying the technological capabilities to a new level. This enables society to acquire a higher net domestic product in period t + 1.

It is clear that the resulting increase in income will depend both on the size of net investment made in year t and on the possible technological advances that the labor force may have made. Two fundamental questions now may be asked. Under what conditions will income per person increase? In other words, under what conditions will the economy grow? And if growth is to be observed, can we expect growth to continue indefinitely? The answers to these questions require a quantitative description of the economy and the building of a model of the growth process. This requires making hypotheses on the functioning of the economy, on societys behavior, and on population growth.

First, the functioning is described by a production function linking capital Kt, labor Lt, and technological progress to production Yt (which is considered equal to income) at any time t. This relationship can be written as the three-variable production function Y = F(K, L, t), where F is homogeneous of degree one in K and L. This hypothesis means that if at any point in time t, K and L are multiplied by λ, then Y is also multiplied by λ : We have λY = F (λK, λL, t ). For instance, if λ = 1.1, it means that if K and L both increase by 10 percent, then Y also increases by 10 percent. A common, simple example of such a function is the Wicksell-Cobb-Douglas function proposed by the Swedish economist Knut Wicksell (1851-1926) at the turn of the nineteenth century: Y = KαL1 α egt. The function is homogenous of degree one, and technological progress is taken into account in the exponential term egt, where g is (1/Y)Y/t, the rate of growth of income when K and L are constant (e.g., g= 1.5 percent per year).

A second hypothesis reflects the behavior of society with regard to saving and investment; one possibility is to posit that society saves and invests a fraction s of its income (e.g., s = 0.1 or 10 percent). Investment I being the rate of increase of capital, we then have I = dK/dt= sY = sF(K, L, t).

Finally, the last hypothesis is about the growth of the population (considered as the labor force). The growth rate of the population is supposed to be constant and equal to n (e.g., n = 1% per year). Equivalently, it means that Lt = L0ent.

With these three hypotheses, we have a complete, albeit simple, model of the growth process. Observe that the rate of increase of capital, I = dK/dt, is a linear function of income, Yt = F (Kt, Lt, t), and the stock of capital Kt is driven by the differential equation,

In the example above, we would have

Equation (2) is a Bernoulli equation that can be easily solved, leading to a trajectory of capital K(K 0 , t) which depends on the initial value of capital K 0 at some point of time t = t 0. In turn, this capital time path can be plugged into the production function Y = F(K, L, t) to yield the time path of Y, as well as the evolution of income per person, y = Y/L, our variable of foremost importance.

In fact, a general, qualitative picture of the evolution of the economy can be drawn by making clever use of a fundamental property of the production function, as Robert Solow did in A Contribution to the Theory of Economic Growth (1956). Observe that if λ is replaced by 1/L in λY = F(λK, λL, t), then y = Y/L = F(K/L, 1, t), which depends now solely upon the capital-labor ratio r and time. Suppose for the time being that there is no technological progress; then y = f(r), and income per person is simply a function of r. This function is always increasing, if Y = F(K, L) and Y/L = f(r), Y= Lf(r) = Lf (K/L), Y/K= Lf'(r) (1/L) = f'(r). Assuming that the marginal productivity of capital Y/K is positive leads to f'(r) > 0. This result is of central importance, because it means that the evolution of income per person is driven by the evolution of the capital labor ratio. Thus, the qualitative evolution of r = K/L will enable us to reach conclusions as to the evolution of income per person, and to answer the second question we asked at the beginning of this section. This can be achieved for very broad families of the production functions, without resolving the differential equation (1), nor knowing the exact mathematical specification of F(K, L, t).

Consider the rate of increase of r(t). Denoting K̇=dK/dt and L̇=dL/dt, it is

Since K̇ = I = sY, we have finally,

which is the fundamental equation of positive economic growth. It has an immediate economic interpretation: The rate of increase of the capital-labor ratio is the difference between investment per person (sY/L = sy) and the investment per person that is necessary to maintain the capital-labor ratio constant (nr); indeed, if L grows at rate n, and if K is to grow at the same rate K̇/K = n, then K̇ (= I ) must be nK, and investment per person K/L must be nK̇/L = nr. It is obvious that r will increase (ṙ> 0) if and only if investment per person (sy) is higher than the investment per person necessary to maintain r constant (nr). Now equation (3) is a differential equation in r, but it does not need to be solved in order to infer the evolution of the economy and its ultimate outcome. Only a picturea phase diagramis required. We can simply draw the curve sy = sf(r) and the ray nr, and consider the difference, ṙ = sy nr, which will be the rate of increase of ṙ. This is done in Figure 1.

Suppose that, initially, the capital-labor ratio is r0. We can immediately see that ṙ is positive at that point; therefore r will increase, and income per person will increase as well. This process will drive r toward its equilibrium value r* where ṙ = 0, and therefore r stays constant. (Whether r* will be reached or not cannot be inferred from the simple reading of the phase diagram. Solving the corresponding differential equation is required; it can then be shown that r * is reached asymptotically onlythat is, when t tends to infinity.) On the other hand, if the initial value r0 is above r*, then ṙ < 0; r will decrease toward r*. If the marginal productivity of capital F/F = f'(r) diminishes in such a way that the curve sf(r) intersects the ray nr, then the economy will tend toward a fixed, equilibrium point (r*, f(r*)) = (r* y* ). Therefore, income per person is bound to tend toward the limit y*.

Two circumstances, however, may arise in which this phenomenon will not occur and income per person is not bounded. The first possibility is that the curve sf(r), concave as it may be, will not intersect the ray nr. Such a possibility may arise if the elasticity of substitution between capital and labor is sufficiently high (the elasticity of substitution measures the ease by which capital may be substituted with labor to achieve a given level of output when the price of labor increases relative to the rental rate of capital (on this concept, see La Grandville 2007b). Then, the curve sf(r) tends asymptotically toward a ray with a slope equal to or larger than n. If that is so, there will be no intersection between sf(r) and nr; ḟ will always be positive, and r will always grow.

The second circumstance that may lead to permanent growth is the very existence of technological progress. Indeed, suppose that f (r ) is multiplied, as in our previous example, by egt. It means that in Figure 1 the curve f (r ) is constantly shifted upward by the mere force of technological progress. It implies that even if, in a first phase, capital labor is decreasing, it will ultimately increase, carrying with it an increase in income per person.

From a methodological point of view, economic growth is first described by a dynamic model that captures the motion of the economy; such models typically generate one, or a set, of differential equation(s). The next fundamental questions are: If we are confident in the validity of such models, can we determine a trajectory of the economy that would be optimal compared to other possible time paths? And how is optimality to be defined?

OPTIMAL GROWTH

Suppose that we are able to infer the future trajectory of an economy from the solution of the model described above. An infinity of choices are offered to society, in the sense that society can choose an infinitely large number of savings investment ratios s, and to each of those corresponds a given future time path for the economy. Which is to be chosen? What would be an optimality criterion for society? A natural answer could come from what was discussed above: Society does not accumulate capital for its own sake, but it does care for the consumption goods and services that capital can provide in the future. So a logical aim for society would be to determine a time path K that would maximize the sum of consumption flows to be received in the future, with an important proviso: A consumption flow received in thirty years is to be valued less than the same flow received much sooner. Accordingly, such future consumption flows have to be discounted, and a discount rate that would reflect societys rate of preference for the present must be defined. Furthermore, following Frank Ramseys (19031930) opening treatment of the subject in 1928, it was proposed that consumption flows Ct should be transformed into utility flows through some concave, increasing, utility function U(Ct). Thus, for about three-quarters of a century, the problem of optimal growth was defined as follows: find a trajectory Kt that would maximize the integral

subject to the constraint

Ct = F(Kt, Lt, t ) K̇t

which is equivalent to maximize

This fundamental problem of optimal growth belongs to the calculus of variations, an extension of differential and integral calculus. Differential calculus deals, among many other things, with the optimization of functions, that is, relations between one or several variables and a number. The integral in (4) does not have that characteristic; rather, (4) is a relation between a whole function (Kt, for t between 0 and ) and a number (I ). Such a relationship has been given a special name: a functional. The calculus dealing with functionals is the calculus of variations because the increase of a variable in differential calculus is now replaced by the variation of a whole function. This branch of mathematics was born when Johan Bernoulli (16671748) submitted in 1698 to his fellow mathematicians the problem of finding the curve joining points A to B such that a bead sliding along the curve would reach Bin minimum time. The problem was solved by Bernoulli himself, his brother Jacob (16541705), and also by Gottfried Wilhelm Leibniz (16461716), Isaac Newton (16421727), and Guillaume de lHôspital (16611704), each using different methods. A general method of solving variational problems however had to wait for the genius of Leonhard Euler (17071783), who in 1744 showed that if a functional dt is to be maximized, a first-order condition is that it satisfies the differential equation

Equation (5) is generally a second-order, nonlinear differential equation. Its second-order character comes from the fact that the second term on the left-hand side of (5) is the total derivative of Gk̇(K, K̇, t) with respect to t, which will generate a term depending on K, K̇, and t, GK̇K̇, multiplying K̈t.

Applied to the problem of optimal growth, the Euler equation yields,

The Euler equation (6) unfortunately is seldom solvable analytically, and this is precisely the case here. Only numerical analysis is available to determine the optimal trajectory K*t, from which optimal investment I*t = K*t, income Y* = F(K*t, Lt, t), and finally savings rate s*t = I*t/Y*t can be deduced. The difficulty of solving the problem numerically led economists to keep it in the realm of theory. The problem with this situation is that short shrift was given to the fact that each time some numbers were obtained, the strangest results appeared in the form of an exceedingly high optimal initial savings rate, often on the order of 40 percent.

With the invention of efficient computing software, it became possible to undertake a much more systematic examination of the problem of optimal growth. It was found that the culprit was the introduction of an arbitrary utility function, U(C) (La Grandville 2007a). When the objective functional is more simply the sum (the integral) of the discounted consumption flows, then two remarkable consequences emerge: First, the Euler equation is no longer a differential equation solvable only by numerical methods, but an algebraic equation from which the optimal trajectories K*t, I*t, and s*t can be derived in analytic form. Secondand more importantlythe optimal savings rate now has reasonable, reachable values.

THE FUNDAMENTAL FACTORS OF ECONOMIC GROWTH

As mentioned above, Ibn Khaldūn provided the fundamental factors of economic growth. These are not set at random, but follow a logical order, one implying the other.

Demographic Growth and Technological Progress Ibn Khaldūns idea is that a larger population enhances the division of labor. This view of demographic growth was rediscovered four centuries later by Adam Smith in his Wealth of Nations. In addition, the enhancement of division of labor that accompanies technological progress improves the chances that an individual, by concentrating on a specific task, will find ways to innovate.

The Search for Individual Profit The search for individual profit is a factor of growth that is far from obvious. According to Ibn Khaldún: Civilization and its well-being as well as business prosperity depend on productivity and peoples efforts in all direction in their own interest and profit (Ibn Khaldūn [1377] 1958, p. 104). Those words were later echoed by Smith:

Every individual is continually exerting himself to find out the most advantageous employment for whatever capital he can command. It is his own advantage, indeed, and not that of the society, which he has in view. But the study of his own advantage naturally, or rather necessarily, leads him to prefer that employment which is most advantageous to the society. He generally, indeed, neither intends to promote the public interest, nor knows how much he is promoting it. He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. (Smith [1776] 1977, pp. 398400)

It is of fundamental importance that neither Ibn Khaldūn nor Smith defended the idea of using any means to make a profit. Quite on the contrary, both sternly condemned the abuse of dominant positions and monopoly power. But if profits can be made by inventing new processes or new products, how is it possible that such profits might be to the advantage of society as a whole? In addition, a further step was taken by Smith, for whom the optimum employment of capital by an individual would result in a maximum advantage for society.

Ibn Khaldūns and Smiths conjecture can be illustrated and formally demonstrated. A first illustration is based upon the outcome of introducing technological progress. It can be shown that if innovations reduce marginal production costs, societys surplus will always increase, although ultimately some firms may see their profit diminish. Enhanced productivity (to quote Ibn Khaldūn) will induce firms to produce more, thereby increasing competition among them and forcing prices down. The lower prices and increased quantity will benefit consumers. Consumer surplus will increase in such a way that it will always more than compensate for any reduction in surplus suffered by producers. A striking example is the spectacular growth of China since the late 1970s, a growth process never witnessed at any other place or time. Its origin can be pinpointed to the suppression of the popular communes by Deng Xiaoping (19041997) in 1978. When farmers were allowed to increase production on private lots beyond the quota they were required to remit to cooperatives, they generated enormous surpluses for consumers and for themselves alike. Savings and investments increased on a large scale, setting in motion the growth process described in the beginning of this article. Clearly, the aim of farmers was to make a profit, but this benefited the entire Chinese economy, even though such a result had not been their intention (on this and for a formal proof of Smiths conjecture, see La Grandville 2007b).

Private Property The fourth factor of economic growth enunciated by Ibn Khaldūn is the principle of private property. Ibn Khaldūn lists three major transgressions to that principle. The first is slavery, condemned by Ibn Khaldūn who, to the best of our knowledge, was the first thinker to denounce what he considered one of the greatest injustices and one which contributes most to the destruction of civilization (Ibn Khaldūn [1377] 1958, pp. 108109).

The second transgression against private property is private and public monopolies and, more generally, the infringement of competitive markets. (It is striking that Ibn Khaldūn also described the very system that would be implemented in many countries in the coming centuries, whereby farmers would be compelled to sell their product to a central authority that would market it at monopoly prices.)

The third transgression is excessive taxation, which destroys the desire to set up firms, and ultimately the very income that is supposed to be taxed.

The Soundness of Political and Legal Institutions In his Introduction to History, Ibn Khaldūn stressed the fundamental, necessary role that institutions play in the growth process. One of his aims was to warn his contemporaries of the dangers that lurked for their civilization if they did not manage to maintain a political system that would protect the individual. He tells us that he was not able to elaborate a better system of government than that embodied in a famous letter sent in 822 by Tahir, one of the generals of the king of Egypt, to his son Abdallah, which Ibn Khaldūn quotes in full. Here is one of its most significant messages:

Consider it your most important task to take personal charge of the affairs of [your] officials and to protect your subjects by looking after their needs and providing for their requirements. Do not be greedy. Let the treasures and riches you gather and hoard up be piety, the fear of God, justice, the improvement of your subjects, the cultivation of their country, the supervision of their affairs, the protection of the mass of them, and support of the unfortunates. You should know that property, once it is gathered and stored in treasuries, does not bear fruit, but if it is invested in the welfare of the subjects and used for giving them what is due to them and to prevent them from need, then it grows and thrives. The common people prosper. Devote yourself to looking after the affairs of the poor and indigent, those who are not able to bring before you complaints about injustices they have suffered, and other lowly persons who do not know that they may ask for their rights. Inquire about these people in all secrecy, and put good men from among your subjects in charge of them. Command them to report to you their needs and conditions, so that you will be able to look into the measures through which God might improve their affairs. Have regard also for people who have suffered accidents, and for their widows and orphans. Give them stipends from the treasury, following the example of the Commander of the Faithful. Set up houses for muslims who are ill, shelter them, [appoint] attendants in these houses who will handle them kindly, and [appoint] physicians who will treat their diseases. Comply with their desires so long as it does not lead to waste in the treasury. (Ibn Khaldūn [1377] 1958, pp. 143153)

Prosperity, for Ibn KhaldŪn, thus implies as a necessary condition the protection of the individual and at the same time a social policy that corresponds very closely to the equity principle defined above.

CONCLUSION

William Letwin, in his introduction to the Wealth of Nations, described Adam Smiths message thus: Far from being a hymn in praise of anarchic greed, the Wealth of Nations is a reasoned argument for justice, order, liberty and prudent plenty (Smith [1776] 1977, p. xxii). One could not better characterize the Muqaddimah by Ibn Khaldūn. The similarity of those two messages, from different civilizations and four centuries apart, prompts us to beg the question of the convergence of ideas and values among civilizations. Economic growth does require the factors enunciated by Ibn Khaldūn; it also requires peace. Ibn Khaldūn spent a good part of his life trying to negotiate peace treaties on all shores of the Mediterranean. For his part, Smith denounced wars and the financing of wars as the greatest deterrent of economic growth. In Western civilization, one of the most fundamental values is the principle of defensive war, which probably originated in the writings of Augustine of Hippo (354430 CE). Shared by Ibn Khaldūn and Smith, did this idea appear elsewhere? Indeed, they were preceded by the Chinese philosopher Mo-Tzu (c. 470-391 BCE) (Watson 1967).

Mo-Tzu triedin vainto advocate this idea, which he based upon another fundamental principle: that of equality of individuals and states. This latter principle would take more than two thousand years to be slowly implemented in state constitutions, and even longer in social behavior.

Nevertheless, the last millennia definitely witnessed a convergence of ideas and values among civilizations, and such is the reason why we may hope that societies will ultimately achieve economic growth for all.

SEE ALSO Business Cycles, Real; Business Cycles, Theories; Democratization; Development; Development Economics; Golden Rule in Growth Models; Ibn KhaldŪn; Immiserizing Growth; Neoclassical Growth Model; Optimal Growth; Productivity; Property, Private; Saving Rate; Slavery; Smith, Adam; Solow Residual, The; Solow, Robert M.

BIBLIOGRAPHY

Botero, Giovanni. [1589] 1956. The Reason of State. Trans. P. J. and D. P. Waley. London: Routledge and Kegan Paul.

Botero, Giovanni. [1598] 1956. The Greatness of Cities. Trans. Robert Peterson. London: Routledge and Kegan Paul.

Child, Josiah. 1668. Brief Observations Concerning Trade, and Interests of Money. London: Calvert.

Economic Growth Resources. Maintained by Jonathan Temple; hosted by the University of Bristol. http://www.bris.ac.uk/Depts/Economics/Growth/.

Elsgolc, Lev E. 1961. Calculus of Variations. London: Pergamon.

Gaxotte, Pierre. 1951. Histoire des Français. Paris: Flammarion.

Ibn Khaldūn. [1377] 1958. The Muqaddimah: An Introduction to History. Trans. Franz Rosenthal. London: Routledge and Kegan Paul.

La Grandville, Olivier de. 2007a. The 1956 Contribution to Economic Growth Theory by Robert Solow: a Major Landmark and Some of its Undiscovered Riches. Oxford Review of Economic Policy 23 (Spring 2007): 1524.

La Grandville, Olivier de. 2007b. Economic Growth: A Unified Approach. With two special contributions by Robert M. Solow. Cambridge University Press, forthcoming.

Serra, Antonio. 1613. Breve trattato delle cause che possono far abbondare li regni doso e argento dove non sono miniere. Naples, Italy: Lazzaro Scorriggio.

Smith, Adam. [1776] 1977. An Inquiry into the Nature and Causes of the Wealth of Nations. New York: Dent.

Solow, Robert M. 1956. A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics 70 (1): 6594.

Sully, Maximilien de Béthune, Duc de. 1634. Mémoires des sages et royales économies. Paris: Courbé.

Toynbee, Arnold J. 1935. A Study of History. Vol. III. 2nd ed. London and New York: Oxford University Press.

Watson, Burton, trans. and ed. 1967. Basic Writings of Mo Tzu, Hsün Tzu, and Han Fei Tzu. New York: Columbia University Press.

Olivier de La Grandville

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Economic Growth

ECONOMIC GROWTH


Economic growth is the increase in an economy's output of goods and services over an extended period of time. The term economic growth refers to a much broader period of prosperity than the narrow expansion phase of the traditional business cycle since an economy can still be in a period of long-term economic growth while undergoing a recession. Periods of economic growth are marked by rising standards of living, increases in the variety and number of goods and services, and improving rates of productivity. The first analysis of economic growth was provided by the Scottish economist Adam Smith (17231790). In The Wealth of Nations Smith argued that an economy's growth depended on its ability to engage in large-scale production, which depended in turn on the adoption of refined manufacturing methods and the division of labor into highly specialized craftsmen. Perhaps the greatest economist of economic growth in the twentieth century was Joseph Schumpeter (18831950), who argued that the real sources of growth are the technological innovations of entrepreneurs. In his theory of "creative destruction," successful entrepreneurs create an economy of copycats who strive to duplicate the entrepreneurs' success but eventually wind up causing a depression by overinvesting. Economic growth continues again after these depressions, however, when the entrepreneurs' new technologies make possible new phases of ever higher productivity.

Several factors combined to make the economic history of the United States perhaps the greatest historical example of economic growth. From the start, U.S. businesses benefited from the English work ethic, technological ingenuity, and principles of economic and political freedom. Fueled by a steady stream of enterprising immigrants, the U.S. labor force grew faster than in most other developed countries. Americans benefited from a large geographical territory with superior natural resources, and the country's founding fathers put in place a system that encouraged the development of public infrastructure, education, technological innovation, and capital accumulation. Within half a century of its independence, the United States had already one of the richest and biggest economies in the world, and between 1840 and 1960 the United States maintained a 3.6 percent annual growth rate, which economist Robert E. Gallman has described as "extraordinarily high" by historical standards. More recently, between 1950 and 1990 the United States remained a model of strong economic growth, with its gross national product (GNP ) growing at a very healthy 3.1 percent annual rate.

See also: Joseph Schumpeter, Adam Smith, Work Ethic

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economic growth

economic growth The growth of national income, or the output of goods and services per head of population, with output conventionally measured by the Gross National Product (GNP). The alternative term economic development is often used in relation to Third World societies. Economic growth does not necessarily lead to growth in consumption and improved distribution of wealth and public welfare; it depends on how the increased output is used, and by whom.

Economists have devoted much effort to producing theories of economic growth which might guide policy-making in developing countries and in industrial societies. Theories place varying degrees of emphasis on capital investment, the economic infrastructure, manpower planning and education, and the relative roles of government and the private sector. See also ENTREPRENEUR; SUSTAINABLE DEVELOPMENT.

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