solow growth model

The Neoclassical Growth Theory

Solow, R., “A contribution to the theory of Economic Growth,” QJE, Feb, 1956, vol. 70, pp. 65-94.

“Technical change and the Aggregate Production Function,”RES , August 1957, vol. 39, pp. 312-320.

Meade, J., “A Neo-classical Theory of Economic Growth,” Allen&Unwin, London 1961.

1Introductiondeveloped by R.Solow (1956) and James Meade (1961) in order to correct the instability problem inherent in the H-D by relaxing the H-D assumptions of fixed K/Y and non-substitutability of labor and capital(by the changes in relative resource prices).

SOLOW MODEL OF GROWTHHe builds his model of economic growth as

an alternative to the Harrod Domar line of thought without its crucial assumptions of fixed proportions in production. Solow postulates a continuous production function linking output to the inputs of capital and labour which are substitutable.

ThemeStates that the rate of growth of an economy is influenced by the rate of growth of the factors of production (labor, capital, land , technology) weighted by the elasticity of production of each factor.

alternatively, economic growth rate depends on the rate of growth of labor force, capital stock, technical know how over time weighted by the respective elasticity of each factor.

Y = A f(K, L) =

bbLAK 1

= rate of income growth

= rate of technological change

b= output elasticity of capital 1-b = output elasticity of labor

= rate of growth of labor force

L

L

= rate of growth of capital

3Assumptions the Neoclassical Growth Model-Perfect substitution of factors of production (K/L)-Perfect competition in the resources market facilitates the price adjusting mechanism-Full employment-Flexibility of K/Y unlike the Harrod-Domar case.

Given:ln Y = ln A +b ln K + (1-bb)ln

LTotal differentiation with respect to time(t)

yields:

Note: b= output elasticity of capital

(1-b)= output elasticity of labor

L

L

bbL 1

L

Lbb

1)1(

11

(1) the rate of income growth not only on the rate of capital formation and the rate of labor growth, but also the rate of technological change.

(2)Income per capita growth rate depends on the rate of technological progress and the growth rate of capital per capita

)(L

L

L

L

(3)Technological progress can rescue the economy from the trap of diminishing returns.

(4)Output-capital ratio depends on technology and labor-capital ratioi.e.

1)(L

Some Implications of the Neoclassical Model-Does not reflect the long-run effect of rapid labor force growth on gainful employment and growth -The decision to save is automatically taken as the decision to invest.i.e. S = I (classical view)

-The perfect factor substitution assumption implies that forces of competition are sufficiently strong.-Direct application to LDCs is doubtful.

-There is a limit to income growth through K and L due to the law of diminishing returns (LDR). K and L must be accompanied by technological improvements.

Differences between the H-D and the Neoclassical Growth-K/L can change in the neoclassical model unlike the H-D model-The neoclassical model assumes that population grows independently of income

Unlike the H-D model, the neoclassical model assumes that structural flaws or constraints can be overcome by the operation of free markets-Both capital and labor can be used to produce output unlike the H-D model which is based on the capital theory of value.

The neoclassical growth model does not suffer from the instability problem

3.1=2.1 +.25(2) +.75(.7)

.5 .525Output growth due to capital =Output growth due to labor =Output growth due to tech. = progress

L

L

)1(

16.1.3

5.

16.1.3

525.

68.1.3

1.2

In the model, technological progress is “disembodied” or taken as being independent of L and K. K and L are also assumed to be homogeneous.

In practice, technology is embodied and L , especially in capital. Moreover, K accumulation and improvement of L quality enable technological development and its installation.

Embodied technological change - tech. Change embodied in the form of the capital good itself. For instance, the diesel locomotive replaced the steam locomotive Jet airliners replaced the propeller variety. The electronic calculator has made slide rule obsolete.

Disembodied tech. Change - technological change that takes the form of new procedures or techniques for producing goods & services. Example the use of contour-farming to prevent soil erosion on farms, the development of new management techniques in business, the pasteurization of milk.

the equation r*= sF (r, 1) – nr states that the rate of change of

capital-labour ratio (r*) is the difference of two terms.

One representing the increment of capital sF (r, 1) and the other increment of labour (nr)

The ray through the origin is the function nr. The other curve represents the function sF (r, 1). It is so drawn as to show diminishing marginal productivity of capital. At the point of intersection of the two curves nr is equal to sF (r, 1) so capital labour ratio is constant and the capital stock must expand at the same rate as the labour force.

Once the capital labour ratio is established, it will be maintained, and capital and labour will grow in proportion. Assuming constant returns to scale, real output will also grow at the same relative rate n, and output per head of labour force will be constant. So at nr is equal to sF (r, 1) , there will be the balanced growth equilibrium.

CommentThe major source of growth per worker in developing countries is capital per worker (K/L)

The major source of growth in DCs is increased productivity due to technological progress.

8Evaluation of the Neoclassical Model-Some of the assumptions are more realistic than others

(factor substitution, diminishing returns, output-capital ratio, level of technology)-Some assumptions are less realistic (full employment, S=I at full employment output perfect competition)

-Inclusion of more variables gives better insights into the growth process-Importance of technological progress made clearer, but the importance of savings and investment less clear.-Income distribution can be learned more from the model-share of labor and capital in the national income