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A Model of Economic Growth – by Professor Kaldor

Professor Kaldor in his A Model of Economic Growth follows the Harrodian dynamic approach and the Keynesian techniques of analysis. The other neoclassical models treat the causation of technical progress as completely exogenous, but Kaldor attempts “to provide a framework for relating the genesis of technical progress to capital accumulation.”

**Assumptions**:

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The basic properties or assumptions of Kaldor’s model are as follows: it is based on the Keynesian full employment assumption in which the short-period supply of aggregate goods and services is inelastic and irresponsive to any increase in monetary demand.

Function which is convex upwards but flattens out beyond a certain point, such as P in the figure, when capital per worker starts diminishing. The annual percentage growth in capital per worker at time t is measured horizontally and the annual percentage growth in income per worker at time t is measured vertically.

At point P, the percentage rate of growth of capital and the percentage rate of output (income) are equal. The behaviour of the capital-output ratio will depend upon the flow of new ideas, as represented by the shape and position of the TT curve and the rate of capital accumulation.

If the rate of capital accumulation is less than the point of equality of the growth of capital and the growth of output, the capital-output ratio will be falling and there will be labour-saving inventions, and vice versa.

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If the rate of capital accumulation is less than OK or one happens to be to the left of P, output will be growing faster than capital, the rate of investment will be stepped and the rate of profit on new investment will increase.

This will lead to a movement towards the right till point P is reached. On the contrary, if one happens to be to the right of, capital will be growing faster than output, the rate of investment will decline, so will the profit rate and a backward movement towards P will set in till the equilibrium point is reached.

Income consists of wages and profits where wages comprise salaries and earnings of manual labour, and profits comprise incomes of entrepreneurs as well as property owners.

Total savings consist of savings out of wages and savings out of profits.

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It is assumed that the share of profits in total income is a function of investment, given the propensity to save out of profits.

All macroeconomic concepts of income, wages, profits, capital, saving and investment used in the model are expressed at constant prices.

Kaldor assumes an investment function which makes investment of any period partly a function of the change in output and partly of the change in the rate of profit on capital in the previous period.

Monetary policy plays a passive role in the model in that money wages may be raising faster than productivity or pari passu with productivity or money wages may be constant.

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It is assumed that there are no effects of a change in the share of profits and wages, and of a change in interest rates on the choice of techniques adopted.

The choice of techniques is assumed to alter with the accumulation of capital and the progress of techniques in the capital goods making industries.

Given these assumptions, the model operates under two stages: (a) constant working population, and (b) expanding population. In the former, the proportionate growth rate of total real income will be the same as the proportionate growth rate of output per head.

In the latter, the proportionate change in total real income in the sum of the proportionate change in output per head and the proportionate change in the total working population. We discuss these two versions of the model below:

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**(A) Constant Working Population:**

For the operation of the model, Kaldor postulates three functions: (i) the savings function, (ii) the investment function and (iii) the technical progress function.

**(B) Expanding Population:**

Leaving the assumption of constant working population, Kaldor studies the relation between growth in population and growth in income.

Starting from the Malthusian contention that the growth rate of population is a function of the rate of increase of the means of subsistence, he assumes that: (a) “For any given fertility rate… the percentage rate of growth in population cannot exceed a certain minimum however real income is rising;” and (b) “the rate of population growth will rise moderately as a function of the rate of growth of income over some interval of the latter before that maximum is reached.”.

Given these assumptions, the relation of population growth with the growth in income is expressed by Kaldor algebraically as under:

Where it, is the percentage rate of growth of population, g, is the percentage rate of growth of income, and X is the maximum rate of population growth. If g, < X and so is l_{t} > X, the rate of growth of income and population will continue to rise till the growth rate of population equals X.

This relation between population growth and income growth is represented in Fig. 3, where the proportionate rate of growth of population is measured vertically and proportionate rate of growth of income is measured horizontally. OY is the growth path of income. PLX is the curve of the growth rate of population.

As the growth rate of income increases, the growth rate of population also rises till the X curve becomes horizontal as a level where the rate of growth of income (OY) exceeds the former, as at point E. In the long run, population would grow at its maximum rate indicated by L’k portion of the dotted population- growth rate curve.

This assumes that he shape and position of the technical progress function, as given by the coefficients a” and (3″ in equation (3) are not affected by the changes in population. This implies that there are constant returns to scale, that is, “an increase in numbers, given the amount of capital per head, leaves output per head unaffected.”

The conclusion emerges from the above analysis that the growth in population will lead to long-run equilibrium growth in income depending upon the relative strength of the following two factors: “(i) the maximum rate of population increase X and (ii) the rate of technical progress, which causes a certain percentage increase in productivity, cc” in equation (3) above, when both population and capital per head are held constant.”

The very narrow focus of the neoclassical growth model sets the baseline against which progress in growth theory can be judged. Writing in 1961, Kaldor was already intent on making technological progress an endogenous part of a more complete model of growth.

Growth theorists working today have not only completed this extension but also brought into their models the other endogenous state variables excluded from consideration by the initial neoclassical setup. Ideas, institutions, population, and human capital are now at the centre of growth theory. Physical capital has been pushed to the periphery.

Kaldor had a model in mind when he introduced his facts. So do us. … In the near term, we believe that this model should capture the endogenous accumulation of and interaction between three of our four state variables: ideas, population, and human capital.

For now, we think that progress is likely to be most rapid if we follow the example of the neoclassical model and treat institutions the way the neoclassical model treated technology, as an important force that enters the formalism but which evolves according to a dynamic that is not explicitly modeled.

Out on the horizon, we can expect that current research on the dynamics of institutions and politics will ultimately lead to a simple formal representation of endogenous institutional dynamics as well.