Income and Employment Theory
Income and Employment Theory
Income and Employment Theory
The modern theory of income and employment, for which we may thank the genius of J. M. Keynes (1936), is without question the most important advance in economic analysis in the twentieth century. Keynes taught us to understand the nature of depressions and radically changed our thinking about how to deal with them. Keynesian principles have been widely applied in the policies of most industrialized countries, and governmental responsibility for the maintenance of “full employment” is now generally accepted. In the United States the growing influence of the “new economics” led, in 1946, to the passage of the Employment Act, which created the Council of Economic Advisers and committed the federal government “to promote maximum employment, production, and purchasing power.”
In addition to its profound influence on economic policy, the modern theory of income and employment has paved the way for important developments in many areas of economic analysis. The purpose of the present essay is to provide a broad, simple outline of the theory. Many subtleties and extensions have necessarily been glossed over or omitted completely. [The interested reader is urged to consult the separate articles on topics treated only briefly in this article:Consumption Function; Employment AND Unemployment; Fiscal Policy; Inflation AND Deflation; Interest; Investment; Liquidity Preference; Monetary Policy; andMoney.]
Meaning of unemployment. It is important at the outset to be clear about the meaning of unemployment. Full employment implies that all who wish to work at the existing level of wage rates are employed. There are, to be sure, potential workers who choose not to seek employment because wage rates are too low. But such persons are said to be voluntarily unemployed, and the theory of employment is not concerned with them; rather, it is concerned with involuntary unemployment—with a situation in which there are workers who would be willing to take employment at prevailing wages but cannot find it.
Pre-Keynesian economics generally held that involuntary unemployment could persist only as the result of market imperfections. The excess supply of labor implied by involuntary unemployment would cause wages to fall, and the combined effect of an increased demand for labor (owing to the fall in its cost) and the voluntary withdrawal of some workers from the labor market (owing to the lower wage rate) would be to clear the labor market and restore full employment, just as a fall in price in any market would eliminate excess supply. On the other hand, Keynes and his followers argued that a state of involuntary unemployment could persist and that many levels of employment could be thought of as equilibrium levels. The path to full employment, moreover, lay not in the direction of wage rate adjustments but rather in the direction of raising the total level of spending in the economy.
The theory of income and employment is an aggregative theory which lumps all markets for final goods and services into a single product market, all financial markets into a single money market, and all markets for labor services into a single labor market. Customarily the analysis proceeds with a description of the properties of the individual markets and then links them together into an overall picture.
The sum total of the production of final goods and services (defined as output that is not resold in any form during the accounting period) when valued at market prices is the gross national product. The deduction of a capital consumption allowance for the replacement of capital equipment that was used up during the course of producing current output reduces this total to the net national product (NNP). The figure that results when NNP is “deflated” by an index of prices of final products in order to obtain constant dollar values we call real NNP, which for present purposes we refer to simply as income, denoted by the symbol Y.
Income and employment analysis begins by breaking income down into several components. The typical approach is to divide the economy into sectors and to examine the determinants of spending and the income receipts of each sector. A complete analysis would include a household sector, a business sector, a government sector, and a foreign sector [see National Income AND Product Accounts]. However, for present purposes it suffices to confine the analysis to the household and business sectors. The portion of production that is purchased by households is called consumption, C. The remainder of the nation’s output accrues to the business sector in the form of capital goods (new plant and equipment) or of additions to the stocks of finished and unfinished goods. Denoting the product retained by the business sector as net realized investment, Ir, we have the basic definition
Y≡ C + Ir.
Provided that the business sector retains no earnings, each dollar of expenditure will be received by households as income. Since households are free either to consume or to save their incomes, we also have
Y≡ C + S,
where S is the level of saving. When we equate the two expressions we obtain the fundamental accounting identity
Ir = S.
We proceed with the theory of income determination by considering the consumption component first. Although aggregate consumption spending is related to many variables, we confine ourselves to the original proposition of Keynes that consumption is an increasing function of the level of income. In Figure 1 the curve labeled C represents an imaginary aggregate consumption function. Consumption rises as income rises, but not by as much. In the hypothetical situation of Figure 1 a rise in income of 200 from an initial level of 200 is accompanied by an increase in consumption of 150 to a level of 350. The ratio of the rise in consumption to the rise in income, ΔC /ΔY, is the marginal
propensity to consume, which is simply the slope of the consumption function; in this example it has a value of .
Because saving is the difference between income and consumption, the level of saving can be measured as the vertical distance between the 45° line and the consumption function, or the separate S curve of Figure 1. The ratio of the change in saving to the corresponding change in income is the marginal propensity to save. Since an extra dollar of income must be either spent or saved, the sum of the marginal propensity to consume and the marginal propensity to save must be 1.
The consumption function is a schedule of intentions. It indicates what the level of consumption spending will be at different levels of income. We may now introduce a schedule of business intended investment spending, which we may either plot separately or add to the consumption function in order to obtain the aggregate demand, C + I, schedule. The aggregate demand schedule shows the level of total spending that will be forthcoming at different levels of income. In the present example it is assumed that intended investment is 50 at all levels of income.
Care must be taken to distinguish between intended investment, I, and realized investment, Ir. Realized investment consists of all output that is retained by the business sector; intended investment is only that portion of output that the business sector actually intended to retain when production plans were formulated. Realized investment will exceed intended investment if business overestimates the level of potential sales and will fall short of intended investment if potential sales are underestimated. The amount of this discrepancy is unintended investment, Iu, so by definition
Ir ≡ I + In .
The presence of unintended investment implies that sales forecasts have been mistaken. In order to reduce unintended inventory accumulation, output will be cut back; in order to offset unintended inventory depletion (negative unintended investment) due to underestimation of potential sales, production will be increased. Intentions and realizations, then, will be equal only when unintended investment is absent. Since by definition
Ir ≡ I + Iu ≡ S,
and since equilibrium requires Iu to be zero, we infer that equilibrium requires intended investment to equal saving. Although realized investment must always equal saving, intended investment will equal saving only when the product market is in equilibrium.
A glance at Figure 1 confirms that I = S at an income level of 400. This income level must necessarily also be where the aggregate demand schedule cuts the 45° line. Any other income level would be characterized by the presence of unintended investment. For example, if business produces $500 billion worth of output, consumption will be $425 billion and intended investment will be $50 billion. Total demand of $475 billion therefore falls short of production of $500 billion, with the consequence that unintended investment is $25 billion. Realized investment is $75 billion, and this does, to be sure, equal the level of saving, but un-desired inventories will pile up as long as production is maintained at $500 billion and thus business must revise its sales estimates and reduce the level of output.
Multiplier. Any change that raises the aggregate demand schedule will raise the level of income. Moreover, the rise in the level of income will exceed the size of the shift in aggregate demand that brings it about. Referring again to Figure 1, we may suppose for a moment that intended investment is zero and observe that the equilibrium level of income is 200, since that is where saving is zero. Assume next that intended investment rises from zero to 50 and remains there. The equilibrium level of income jumps to 400—an increase not of 50 but of 200. This multiplied increase in income results from the fact that the increase in investment spending raises income, thereby inducing additional consumption spending. It can be seen from Figure 1 that the rise in income from 200 to 400 is composed of the increase in investment of 50 plus an increase in consumption of 150.
The ratio of the change in income to the change in investment, ΔY/ΔI, is the multiplier, .and its numerical value is the reciprocal of the marginal propensity to save. If intended investment rises by one dollar, equilibrium will not be restored until saving has also risen by one dollar. If the marginal propensity to save has a value of x, an income increase of 1/x dollars is required to raise saving by one dollar. In the present example, when income rises by one dollar saving rises by 25 cents. Since saving must rise by one dollar, the required increase in income is four dollars. [For an alternative and more elaborate discussion of the multiplier, seeconsumption function.]
The multiplier permits us to calculate the effect on the level of income of an upward shift in the aggregate demand schedule. The multiplier also tells us how much aggregate demand must be raised to reach an income level which will bring full employment. In Figure 1, if the equilibrium level of income is 400 and the full-employment level of income is 600, the required increase in income is 200. Since the multiplier is 4, a policy that shifts the aggregate demand schedule up by 50 will raise income to the full-employment level. The required shift in aggregate demand can also be found by measuring the deflationary gap, which is defined as the deficiency of aggregate demand measured at the full-employment level of income. Inspection of Figure 1 confirms that the magnitude of this gap is 50.
Before we add to this simplest of all models, it might be instructive to put the model into algebraic form. In linear form the consumption function can be written
C = a + bY = 50 + .75Y,
where a is the level of consumption associated with a zero level of income and b is the marginal propensity to consume. The saving function must be
S = Y - C = -a + (l - b)Y = -50 + .25Y.
where 1—b is the marginal propensity to save. Since the equilibrium condition is
I = S,
I = -a + (1-b)Y,
50 = 150 + 25Y.
Thus, we can solve for Y and obtain
The multiplier is
The next step in constructing the theory of income and employment is to drop the assumption that intended investment is a constant somehow determined by factors outside the economic system. Although many alternative theories of investment behavior have been developed, we take note here only of the fact that ordinarily a business decides to borrow in order to expand its stock of productive capacity or its inventory holdings only when the expected rate of return on the new investment (the marginal efficiency of capital) is in excess of the cost of borrowing funds (the rate of interest). Alternatively, if funds are available without borrowing, the firm must determine whether it is more profitable to invest or to engage in some form of lending—for example, the purchase of government bonds. The higher the cost of borrowing (or the return on lending), the less inclined firms will be to engage in investment spending. For this reason the level of intended investment is usually regarded as a decreasing function of the rate of interest, i.
If the saving function is written in the general form
S = S(Y),
(read: saving is an increasing function of the level of income) and the investment demand function in the form
I = I(i)
(read: intended investment is a decreasing function of the rate of interest), and if we equate intended investment with saving, it becomes apparent that the equilibrium level of income depends upon the rate of interest. To put it differently, we now have two variables, i and Y, but only one equation,
I(i) = S(Y),
and we must therefore find out how the rate of interest is determined.
Money market and the rate of interest
The rate of interest is the return on lending or the cost of borrowing money. It can also be thought of as the return that wealth holders forgo when they hold money balances that could have been lent at interest, and it therefore constitutes the cost of holding money balances. Given the quantity of money held by wealth holders, the equilibrium rate of interest is that rate at which they feel no incentive to convert money into other financial assets or vice versa. Such a situation is denoted as monetary equilibrium; it obtains when the demand for money balances to hold equals the supply of money.
The simple theory of income and employment customarily treats the supply of money, usually defined as the currency and demand deposits held by the nonbank public, as a policy variable—i.e., its size is determined by the central monetary-fiscal authority. Under fractional reserve banking, however, money can, within limits, be created or destroyed by the commercial banking system. Money is created, for example, when banks convert excess reserves into earning assets, since this involves creation of additional deposits. Thus, the size of the money supply depends to some extent upon the degree to which banks are willing to make this conversion. The uncertainty that arises from the possibility of deposit withdrawal makes some holding of excess reserves desirable. However, banks forgo earnings when they hold excess reserves. Since a rise in the rate of interest increases this cost, such a rise is likely to be accompanied by an increase in bank lending and therefore in the money supply. For this reason many modern writers treat the supply of money as an increasing function of the rate of interest. A money supply function might be written in real terms as
M8/p = ϕ(R/p, i),
where R is the quantity of nominal bank reserves (determined by the monetary-fiscal authority), i is the rate of interest, M8 is the nominal stock of money, and p is the level of prices.
Keynes’s theory of the demand for money was one of his most important contributions. He delineated three motives for holding money—the transactions, precautionary, and speculative (liquidity preference) motives. The transactions and precautionary demands were recognized by traditional theory. Keynes’s great insight was to add the liquidity preference motive and to recognize the importance of the rate of interest in determining the demand for money.
The transactions demand for money arises from the necessity for economic units to hold certain levels of money balances because money receipts and disbursements are not perfectly synchronized in time. For example, an individual who receives $1,000 at the beginning of a month, makes disbursements at a uniform rate throughout the month, and ends the month with a zero money balance will have an average cash balance of $500. In the long run the magnitude of such average balances depends upon the nature of institutional payments-practices and upon the growth of income and wealth. In the short run the size of transactions balances depends upon the number and size of the transactions that the individual makes. Keynes and earlier writers therefore regarded the transactions demand for money as proportional to the level of income.
Precautionary balances are held in order to meet unforeseen contingencies and to take advantage of fortuitous opportunities. The magnitude of these balances was also viewed as proportional to the level of income.
Keynes held that the speculative demand for money arises out of fear that interest rates may rise in the future and that wealth holders will therefore suffer a capital loss if they hold bonds instead of money. The lower the rate of interest, the greater is the risk of such a capital loss and the lower is the return on bond holdings (the cost of holding money). Consequently, the quantity of speculative balances held is viewed as a decreasing function of the rate of interest.
The theory of liquidity preference has been attacked on a number of grounds (see Tobin 1958) which we need not go into except to note that money balances can usually be converted into risk-less savings accounts. Nevertheless, empirical research (e.g., Tobin 1947) discloses a strong correlation between the rate of interest and the average length of time that money is held between transactions, a circumstance which seems to indicate that the demand for money is a decreasing function of the interest rate. This suggests that transactions and precautionary balances are also interest-elastic. Individuals who accumulate cash balances in anticipation of a large future outlay may convert these balances into short-term securities, which they liquidate when cash is needed. The greater the return on such securities relative to the transactions costs which their purchase and sale entails, the greater is the incentive to economize on money balances and the lower will be average transactions balance held (Baumol 1952; Tobin 1956).
The distinctions between the three motives for holding money are regarded as arbitrary by contemporary monetary theorists. Nevertheless, it is useful for expository purposes to maintain a distinction between transactions (active) balances and speculative (idle) balances. In any case it is clear that the demand for money is a function of both the rate of interest and the level of income, so we may ignore the separate motives and write quite generally
Md/p = L(i, Y)
as the demand for money to hold in real terms.
Joint equilibrium of the two markets
It was seen earlier that product market equilibrium is established when intended investment equals savings—i.e., when
Similarly, monetary equilibrium is established when the demand for and the supply of money are equal. Accordingly, we have
as the condition for monetary equilibrium. If the real value of the stock of bank reserves is known, the two equations determine the equilibrium level of income and the rate of interest.
In Figure 2 this general equilibrium solution is sketched out in a way originally presented by Hicks (1937). The curve labeled ISo is a diagrammatic representation of equation (1). It represents all combinations of interest rates and income levels that are consistent with equality of intended investment and saving. The curve has a negative slope because a decline in the rate of interest raises the level of investment and therefore also the level of saving and income.
The LMo curve depicts equation (2), representing all combinations of income levels and interest rates that yield monetary equilibrium. The curve ordinarily has a positive slope because a rise in the level of income raises the required quantity of transactions balances so that monetary equilibrium is usually obtainable only if the rate of interest rises. The point of intersection of IS0 and LM0 defines the equilibrium level of income, Y0, and rate of interest, i,0—the values that are compatible with equilibrium in both markets simultaneously.
Monetary versus fiscal policy
An increase in the money supply brought about by a central bank purchase of securities on the open market shifts the LM curve to the right (for example, from LM0 to LM, to LM1 in Figure 2) because for any level of income, it is only at a lower rate of interest that wealth holders can be induced to hold the additional money balances. As can be seen from Figure 2, the size of the increase in income that this shift brings about depends upon the slope of the LM curve in the range in which it intersects the IS curve.
The vertical range of the LM curve represents the classical view that in a state of monetary equilibrium, money balances are never held except for transactions purposes. Thus, a rise in the money supply must cause the interest rate to fall and investment and income to rise until income rises by enough to absorb all of the additional money into transactions balances. If, therefore, the IS curve cuts the LM curve in the classical range, the level of income must rise in direct proportion to the increase in the money supply.
The horizontal portion of the LM curve represents Keynes’s liquidity trap. Once the rate of interest falls to a critically low level (i2, in Figure 2), wealth holders regard bonds and money as perfect substitutes, and banks simply allow excess reserves to pile up. Consequently, if the IS curve cuts the LM curve in the horizontal range, the open market purchase of securities by the central bank fails to lower the rate of interest, since all the added money balances are simply held as speculative balances. As a result the level of investment and the level of income fail to rise at all.
Whereas classical theory supports the effectiveness of monetary policy and Keynesian theory denies it, exactly the opposite views emerge with respect to fiscal policy. An increase in government purchases, for example, can be thought of as an upward shift in the investment demand schedule of Figure 1. The consequence of this increase in aggregate demand is that the IS schedule shifts to the right by an amount equal to the increase in government purchases times the multiplier. However, whether the actual increase in income also equals the multiplier again depends upon the slope of the LM curve.
The reader can visualize that a shift in the IS curve which cuts the LM curve in the liquidity trap range will yield a fully multiplied increase in income whereas an intersection in the classical range will yield no increase in income at all. In the classical case the attempt to increase total spending is frustrated because a rise in the rate of interest cannot bring about an increase in transactions balances. The rise in government purchases cannot generate a multiplier response, since any tendency for income to rise will drive up the demand for money and raise the interest rate until private investment is reduced by exactly the amount of the increase in government purchases. In the liquidity trap range, on the other hand, rising income merely activates idle money balances without affecting the rate of interest, and the level of private investment, therefore, does not decline.
In the classical view fiscal policy is incapable of raising the level of income, and fiscal changes merely have the effect of redistributing national output between the private and the public sectors; reliance is to be placed on monetary policy. In the Keynesian view, on the other hand, fiscal policy is the more certain (and in some cases the only) method of raising the level of income.
Labor market and automatic adjustment
In the Keynesian view the equilibrium level of income that is jointly determined by product market and money market equilibrium need not be the full-employment level. However, if an equilibrium level of income (for example, Y0 in Figure 2) implies the presence of involuntary unemployment, will not competition for jobs among workers cause wage rates to fall, and will this not cause the level of employment and income to increase?
The theory of income and employment is a theory of the behavior of the economic system in the short run. It therefore presupposes that the stock of capital equipment is fixed and views labor as the only variable factor of production. From the theory of the competitive firm it can be deduced that labor will be hired up to the point where the value of its marginal product just equals the wage rate. Expressed in symbols, this condition is
ω = MP X p,
where ω is the money wage rate, MP is the marginal -physical product of labor, and p is the price of output. Dividing through by p, we obtain
ω/p = MP,
where ω/p is the real wage rate. According to the law of diminishing returns, an increase in employment will be accompanied by a decline in the mar ginal physical product of labor. A rise in employment, therefore, cannot take place unless the real wage is reduced. Since the demand for labor is a decreasing function of the real wage, we can write
Nd = D(ω /p)
as the demand for labor function.
In the classical view the quantity of labor supplied is normally an increasing function of the real wage rate; it can be written
Ns = S(ω /p).
If there exists a labor market clearing mechanism such that Nd tends to equality with N8, these two expressions can be equated to yield the equilibrium level of employment. Since involuntary unemployment would be eliminated, this level of employment would be the full-employment level. The full-employment level of income can then be determined by substituting the level of employment into the production function,
Y = X(N),
which specifies the technical relation between factor inputs and the level of output.
Whether the level of income is determined by product market and money market equilibrium (the Keynesian view) or by competition in the labor market (the classical view) depends upon whether a labor market clearing mechanism operates so as to equate the demand for and the supply of labor. If involuntary unemployment exists, the supply of labor exceeds the demand, and the restoration of full employment requires that the real wage be reduced. Job competition among workers will reduce the money wage rate, but whether the real wage rate will also fall depends on what happens to the price level.
A fall in money wage rates leads business to expand the level of output and to increase the level of employment. However, since the marginal propensity to consume is less than unity, only a fraction of the additional output will be bought by consumers; unintended investment in inventories will therefore take place, and output will tend to return to its original level. In Figure 1 it is apparent that a rise in output of 100 from the original equilibrium level of 400 causes consumption to rise by 75, and the remaining additional output of 25 represents unintended investment. Unintended investment will not be eliminated until output falls back to 400. Since the equilibrium level of income will be the same as before the wage cut, the level of employment must also return to its original level, and this implies that the real wage will be restored to its original level as the result of a fall in the price level proportional to the original fall in the money wage rate. It is clear, then, that the equilibrium level of income cannot change unless the fall in money wage rates somehow succeeds in shifting the entire aggregate demand schedule upward.
We have seen that the fall in money wage rates will induce a fall in the price level. This means that the real value of the money supply, M8 /p, will increase, which in turn will cause the rate of interest to fall. As a consequence the level of intended investment will rise, and so also will the levels of income and employment. The argument can be visualized by reference to Figure 2. The increase in the real value of the money supply shifts the LM curve from LMo to LM1, the rate of interest drops from i0 to i1, and the level of income rises from Y0 to Y1,.
Underemployment equilibrium. There were two reasons, in Keynes’s view, why this interest-investment mechanism might fail to work. First, there is the possibility of the liquidity trap, which, if present, would mean that the increase in the real value of the money supply could not lower the rate of interest. Second, there is the strong possibility that under depressed economic conditions investment would be insensitive to changes in the rate of interest. The first possibility can be visualized by further reference to Figure 2. If the IS curve cuts the LM curve in the horizontal (liquidity trap) range, the increase in the real value of the money supply would have no effect on the rate of interest or on the level of income. The second possibility can be visualized if we recognize that the IS curve would be vertical if investment were totally insensitive to changes in the rate of interest. If it is true, as is implied by the Keynesian analysis, that a fall in money wage rates will not raise the level of income, either because of the presence of the liquidity trap or because investment is interest-inelastic, then the labor market clearing mechanism fails to operate, and the existing level of income can be thought of as an equilibrium level.
The most elegant challenge to the Keynesian doctrine of underemployment equilibrium came from Pigou (1943), who suggested that if consumption were a function not only of the level of income but also of the level of wealth, a fall in the price level would increase the real value of the stock of currency and government debt held by the private sector, and this increase in wealth would cause the consumption function to shift upward. As long as the labor market remained uncleared, wages and prices would continue to fall, wealth would continue to increase, and the consumption function would continue to shift upward until the full-employment level of income was reached.
The theoretical issue cannot be said to have been resolved. A fall in wage rates may either raise or lower the level of income. The corrective interest-investment and Pigou effect mechanisms discussed above may, for example, be offset by the generation of adverse expectations. If wage reductions take place in a sluggish, piecemeal manner, entrepreneurs in industries where wages have not yet fallen will anticipate cost reductions by reducing output and employment and by selling from inventory. And if consumers expect the price level to fall, post-ponable consumption expenditures will be reduced. Moreover, a wage reduction will redistribute income in favor of profit earners, whose marginal propensities to consume may be lower than those of wage earners, and this could cause the aggregate consumption function to shift downward.
For practical purposes it is sufficient to recognize that in advanced economies wages and prices tend to be downwardly rigid. It would be difficult to implement a national wage reduction policy, and, as Keynes recognized, there is little that can be accomplished by such a policy that cannot also be accomplished by a relatively painless expansionary monetary policy. Output and employment cannot be raised without an increase in aggregate demand. Such an increase in demand might conceivably be brought about by wage reduction, but a policy of wage reduction would be inefficient and might not work at all. If it did work, the desired effects might take an intolerably long time to materialize. And the policy would certainly be inferior to a policy of direct demand expansion through monetary-fiscal measures.
Money illusion. In recognizing the institutional facts of life, Keynes broke away from the classical theory of labor supply. Instead of assuming that the supply of labor depends on the real wage, he assumed that labor is subject to money illusion—i.e., that the quantity of labor supplied responds to changes in money wage rates but not to changes in the price level and that the supply of labor is therefore a function of the money wage rate rather than of a real wage rate. In Figure 3, ω0 is the historically given money wage rate, and P0 is the ruling price level. At money wage w” workers will offer anywhere from zero toN* units of labor. Thus, at w0/Po the labor supply curve is a horizontal line up to N*. Although the money wage rate cannot be made to fall, it will rise when all who are willing to work at w” are employed and additional workers are desired. Consequently, the labor supply curve bends up sharply once N* is reached. The labor
demand schedule cuts the supply schedule at No, and the distance N*N0 therefore measures involuntary unemployment.
Since the money wage rate is assumed to be rigid downward, full employment can be restored only through a fall in the real wage brought about by an increase in aggregate demand and a rise in the price level. If such a rise in the price level takes place, the entire labor supply schedule shifts downward, and involuntary unemployment is eliminated. Thus, at real wage ω0/Pi the labor demand curve cuts the supply curve at N*, where all who are willing to work at the new real wage are employed. Even though the real wage has fallen, the assumption of money illusion on the part of workers implies that the same quantity of labor will be supplied at the new real wage as at the old.
The Keynesian and classical models may now be sharply delineated. Although these models are static systems in which the equilibrium values of the variables are simultaneously determined, it is nevertheless instructive to think of the determination of the equilibrium values as running in a definite sequence.
In the Keynesian system, product market equilibrium can be written more generally as
I(i, Y) = S(i,Y)
to reflect the traditional view that a rise in the rate of interest induces individuals to increase the level of saving and to incorporate the notion that the level of investment depends upon the levelof income as well as upon the rate of interest. When the monetary equilibrium condition,
ϕ (R/p,i) = L(i,Y),
is added and the level of real bank reserves is assumed to be known, the two relations jointly determine the level of income and the rate of interest, as well as the levels of consumption, saving, and intended investment. The level of income being known, the production function,
Y = X(N),
defines the level of employment. The demand for labor, together with the historically given rigid money wage rate, wo, provides the equation needed to determine the price level,
N = Nd = D(wo/P).
In the classical system the sequence can be thought of as beginning with the labor market, where the real wage and the level of employment are determined by labor market equilibrium,
D(w/p) = S(w/p).
The full-employment level of employment, N*, is now known, and the full-employment level of income follows from the production function; since the level of income is known, the product market equilibrium equation collapses to
I(i) = S(i),
which implies the classical proposition that the investment and saving functions serve only to determine the rate of interest and the way aggregate output is divided between consumption and investment. Finally, since both the level of income and the rate of interest are known, the monetary equilibrium condition can be collapsed to
R/p = constant,
which implies that the price level is entirely determined by the nominal stock of bank reserves. In the absence of fractional reserve banking, the preceding expression can be replaced by the more familiar
M/p = constant,
which reflects the traditional notion that given a fixed level of income, the level of prices must be directly proportional to the quantity of money.
The substantial differences between the ways in which the equilibrium values of the variables are determined rest upon whether the equilibrium level of income can differ from the full-employment level. This is illustrated in Figure 4, where it is assumed that the original LM curve is LMo and the full-employment level of income is Y*. If the IS
curve cuts LM in the horizontal range at less than full employment (curve ISo), the rate of interest is the liquidity trap rate which cannot be changed by a shift in the IS curve within the horizontal range of the LM curve. The IS curve, in turn, determines the equilibrium level of income which cannot be affected by changes in the money market (shifts in the LM curve).
If the IS curve (curve 7S,) cuts the LM curve at less than full employment but in a range where the LM curve has a positive slope, the equilibrium level of income, Y1, and rate of interest, i1, are jointly determined by conditions in the product and money markets, and both can be affected by changes in either market.
Finally, suppose that the IS curve (curve IS2) cuts the LM curve at the full-employment level of income and interest rate i2. Suppose next that the money supply is increased and shifts the LM curve to LM,. Joint product market and money market equilibrium would now obtain at interest rate i3 and income level Yi. But Y3 is in excess of the full-employment level of income and is therefore not attainable. Excess demand for goods and services must now exist. As a consequence, the price level rises, and the real value of the money supply decreases—the LM curve shifts back to the left. Since the LM curve must shift back exactly to its original position if equilibrium is to be restored, the increase in the money supply only produces a proportional increase in the price level and leaves unaffected the other equilibrium values of the variables. The only possible equilibrium interest rate in this classical case is the natural rate of interest, i2. It is found at the point of intersection of the IS curve and the vertical line at the full-employment level of income, and it exactly equates intended investment with the full-employment level of saving.
[See also the biography ofKeynes, John Maynard].
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