# Neoclassical Growth Model

# Neoclassical Growth Model

The neoclassical model of long-run economic growth, introduced by Robert Solow (b. 1924) and Trevor Swan (1918–1989) in 1956, analyzes the convergence of an economy to a growth rate set by exogenous population increase and, as added the following year by Solow (1957), an exogenous rate of technical change. Earlier growth models by R. F. Harrod (1900–1978) in 1939 and Evsey Domar (1914–1997) in 1946 (both reprinted in Stiglitz and Uzawa 1969) had assumed fixed coefficients in products, which the Solow-Swan neoclassical model generalized to allow for substitution between capital and labor. The term *neoclassical* reflected the model’s concern with long-run equilibrium growth of potential output in a fully employed economy, abstracting from short-run Keynesian issues of effective demand.

The neoclassical growth model assumes the existence of an aggregate production function Y = F(K, N), where Y is aggregate output, K is the capital stock, and N is the number of workers. The production function has constant returns to scale (if K and N change in the same proportion, Y will also change in that proportion), with positive but diminishing marginal products of capital and labor. Dividing by the number of workers N, output per capita y = Y/N is a function of the capital/labor ratio k = K/N:

y = f(k)

and y = c + i, where c = C/N is consumption per capita and i = I/N is investment per capita. The per capita consumption function is assumed to be c = (1–s)y, where s is the marginal propensity to save and (1–s) is the marginal propensity to consume. In equilibrium, (desired) investment is equal to saving, i = sy = sf(k).

In the steady-state equilibrium, per capita output (y) and the capital/labor ratio (k) do not change, and total output Y grows at the rate n, the exogenous growth rate of the population and labor force (N). Required gross investment in the steady state will be just enough to cover depreciation (replacement investment) and to equip each new worker with the same amount of capital that existing workers have. Required investment per capita in the steady state is thus (n + d)k, where n is the rate of population growth and d is the depreciation rate. The steady state equilibrium capital/labor ratio k* will be given by sf(k*) = (n + d)k* and steady state output per capita will be y* = f(k*). Because f, the rate of change of output per capita with respect to a change in the capital/labor ratio, is positive but decreasing (an increase in the capital/labor ratio raises output per worker, but not by as much as the previous increase of the same size), if k is initially less than k*, investment and saving will exceed the investment needed to keep k constant, and the capital/labor ratio k will increase until it reaches k*. If k is initially greater than k*, investment and saving will be less than the investment needed to keep k constant, and k will decrease until it is equal to k*.

Solow allowed for neutral technical change by writing the production function as Y = A(t)F(K, N), where A(t) is an index of total factor productivity at time t. By calculating how much growth was due to growth of capital and labor inputs, and subtracting these estimates from the observed growth rate, Solow (1957) obtained a measure of the rate of change of A (the Solow residual), an implicit measure of technical change. Later studies adjusted for improvements in the quality of capital and labor inputs (such as better educated and trained workers), and thus reduced Solow’s high original estimates of how much economic growth was due to technical change.

In the neoclassical growth model, the growth rate is independent of the savings rate, and depends only on population growth and technical change, both taken as determined exogenously outside the model. A higher propensity to save leads to a higher level of output per capita in the steady state, but not a higher steady state growth rate. Faster population growth reduces per capita output and consumption in the steady state.

Neoclassical growth theory was sharply criticized by the Cambridge school, building on works on capital accumulation and income distribution by Joan Robinson (1903–1983) and Nicholas Kaldor (1908–1986), both published in 1956 (see Harcourt 1972 on the Cambridge capital controversies between Post-Keynesians at Cambridge University and neoclassical economists, such as Solow, at Massachusetts Institute of Technology). The Cambridge theorists objected to explaining the return on capital by differentiating an aggregate production function with respect to the capital stock K, measured as so many identical machines. They denied the existence of an aggregate production function, and argued that since capital goods are heterogeneous, there is no physical measure of aggregate capital that is independent of prices and rates of return, hence of income distribution (see papers by Robinson, Kaldor, Richard Kahn, and David Champernowne reprinted in Stiglitz and Uzawa 1969).

Beginning with Kaldor’s and James Mirrlees’s technical progress function and with Kenneth Arrow’s “learning by doing,” which makes total factor productivity depend on cumulative past investment (both reprinted in Stiglitz and Uzawa 1969), economists have tried to dispense with the exogeneity of technical change in neoclassical growth theory. Unlike the neoclassical growth model, endogenous growth theory (“new growth theory”), pioneered by Paul Romer, models improvements in productivity as depending on investment in research and development and, through education and health care, in human capital.

The neoclassical growth model implies that, if the same technology is available to all countries, every country will converge to a growth rate that differs from that of any other country only by the difference in their rates of population growth. Whether such convergence of growth rates has been observed is controversial. Endogenous growth theory, by dropping the assumption of diminishing returns to investment, does not follow the neoclassical growth model in predicting convergence (see the symposium by Romer et al. 1994).

Criticisms of the Solow-Swan neoclassical growth model, whether directed at the aggregate production function with a single capital good or at the exogeneity of technical change, view the model as an oversimplified parable. It was, however, the simplicity of the neoclassical growth model that kept it tractable, and made it so useful and influential as a framework for organizing thinking about economic growth.

**SEE ALSO** *Cambridge Capital Controversy; Golden Rule in Growth Models; Growth Accounting; Immiserizing Growth; Optimal Growth; Saving Rate; Solow Residual, The; Solow, Robert M.; Technological Progress, Economic Growth*

## BIBLIOGRAPHY

Harcourt, Geoffrey C. 1972. *Some Cambridge Controversies in the Theory of Capital*. Cambridge, U.K.: Cambridge University Press.

Romer, Paul M., Gene M. Grossman and Elhanan Helpman, et al. 1994. Symposium: New Growth Theory. *Journal of Economic Perspectives* 8 (1): 3–72.

Solow, Robert M. 1956. A Contribution to the Theory of Economic Growth. *Quarterly Journal of Economics* 70: 65–94 (reprinted in Stiglitz and Uzawa 1969).

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

Solow, Robert M. 2000. *Growth Theory: An Exposition*. 2nd ed. New York: Oxford University Press.

Stiglitz, Joseph E., and Hirofumi Uzawa, eds. 1969. *Readings in the Modern Theory of Economic Growth*. Cambridge, MA: MIT Press.

Swan, Trevor W. 1956. Economic Growth and Capital Accumulation. *Economic Record* 32: 334–361 (reprinted in Stiglitz and Uzawa 1969).

*Robert W. Dimand*

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