# Kaldor’s Growth Model

Prof. Kalder in his model “A model of economic growth” follows the Harrodian dynamism and analysed the Keynesian techniques of analysis. But his model is quite different form Harrodian and other models.

As per Kaldor his model is a piece of economics which tries to show that the ultimate casual effect factor is not saving and capital accumulation but the “technical dynamism”.

Assumptions :

1. There are only two factors of production i.e., L and K, so $$Y = W \;+ \;P$$. All the profits are saved and the wages are consumed.
2. Total savings consist of savings out of wages and savings out of profit so $$S = S_w + S_p$$ and also $$MPS_w$$ < $$MPS_k$$.
3. Profit in the economy is the function of investment.
4. Technical progress depends on the the rate of capital accumulation but Kaldor postulates the technical progress function with a joint product of two tendencies i.e. Growth of Capital and Growth of productivity.
5. Prices are assumed to be constant.
6. The choice of techniques also may alter with the rate of capital accumulation and progress of techniques in the capital good market.

Working of Model :

This Model operates under two stages :

1. Constant Population
2. Expanding Population

Constant Working Population

In this case the promotional growth rate of total real income will be equal to the promotional growth rate of output per head. For operation of his model Kaldor uses three equations.

A. Savings Functions

$$\ S _{t}\; =\; \alpha P_{t}\; +\; \beta \left( Y_{t}\; -\; P_{t} \right)$$,

$$S_{t}\; =\; Saving\; in\; time\; period\; t$$,

$$P_{t}\; =\; Profit\; in\; time\; period\; t$$,

$$Y_{t}\; =\; Income\; in\; time\; period\; t$$,

$$\alpha \; ,\; \beta \; =$$ $$MPS_w$$ and $$MPS_k$$ is such a way that 1 >$$\; \alpha\;$$>$$\; \beta\;$$$$\geq$$ 0 and $$MPS_w$$ < $$MPS_k$$.

B. Investment function

$$K_{t}\; =\; \alpha’ \; Y_{t}\; +\; \beta’ \; \left( \frac{P_{t-1}}{K_{t-1}} \right)\; Y_{t-1}$$,

$$I_{t}\; =\; K_{t+1}\; -\; K_{t}$$,

$$K_{t}\; =$$ Stock of capital in time period t,

$$Y_{t} =$$ Output in previous period,

$$\frac{P_{t-1}}{K_{t-1}}\; =\;$$ Rate of profit on capital,

$$\alpha’ \; ,\; \beta’ \; =$$ Co-efficient of rate of output and rate of profit on capital in such a way that $$\alpha’\;>0 , \; \;\beta’\; > 0$$,

C. Technical Progress Function

$$\frac{\left( Y_{t-1}\; -\; Y_{t} \right)}{Y_{t}}\; =\; \alpha ”\; +\; \beta ”\; \frac{I_{t}}{K_{t}}$$,

Where $$\frac{\left( Y_{t-1}\; -\; Y_{t} \right)}{Y_{t}}\; =\;$$ rate of growth in income,

$$\frac{I_{t}}{K_{t}}\; =\;$$ rate of net investment,

$$\alpha” and\; \beta” =$$ Co – efficient of technical progress and $$\frac{C}{L}$$,

Here $$\alpha” >0$$ and $$1 > \beta” > 0$$,

Giving these three functions the rate of growth of income i.e. $$\frac{I_{t}}{K_{t}}$$ is equal to the rate growth in the economy of constant working  population. It can been shown with the help of following diagram where proportionate growth of capital $$\left[ \; \frac{\left( K_{t+1}\; -\; K_{t} \right)}{Kt} \right]$$ is measured horizontally and the proportionate growth of income $$\left[ \; \frac{\left( Y_{t+1}\; -\; Y_{t} \right)}{Yt} \right]$$ vertically. Point G as determined by the technical progress function TT’ and the 45 degree line is one of the steady growth points where proportionate growth of income equals proportionate growth of capital, starting from period $$t_{1}$$ where the growth of output $$G_{1}$$ is greater than growth of capital, i.e., C/O is less so investment will increase in the subsequent period so as to make capital equal to $$G_{1}$$ at A. This will, in turn, raise the growth of output in period $$t_{2}$$ to $$G_{2}$$. The rate of investment will increase further to A, in period $$t_{3}$$. So as to make A, equal to $$G_{2}$$ at point B. Similarly, the growth of output in subsequent periods will raise till point G is reached. This process will be reinforced by change to the rate of profit on capital.

Expanding Population

In this case the population change in total real income in the sum of proportional change in output per head and the proportional change in the total working population.

$$I_{t} = g_{t} (g_{t} \geq \lambda)$$,

and $$I_{t} = \lambda$$ [By relaxing the assumption of constant population]

By relaxing the assumption of constant population Kaldor connected the growth of population to the growth of income. It is expressed above.

$$I_{t}$$ is the percentage of population growth

$$g_{t}$$ is the percentage of growth in income

$$\lambda$$ is the maximum rate of population

If $$g_{t} > \lambda$$ then $$I_{t} > \lambda$$ then the rate of growth of income and population will continue to raise till the growth rate of population is equal to $$\lambda$$ .

This relation can be shown with the help of diagram : The relation between population growth and income growth is represented in the diagram where proportionate rate of growth of income is measured horizontally and proportionate rate of growth of population is measured vertically. Growth path of income is shown by OY . PL$$\lambda$$ is the curve of the growth rate of population. As the growth rate of income increases the growth rate of population also rises till PL$$\lambda$$ curve becomes horizontal to a level where the rate of growth of income exceeds the former as at point E. In the long run population would grow at its maximum rate indicated by L$$\lambda$$ portion of the dotted population growth rate curve. This assumes that the shape and position of the technical progress function as given by the coefficient $$\alpha”$$ and $$\beta”$$ in the above equations are not affected by the changes in population.

But in developing economy with a low capacity to absorb technical changes due to the scarcity of land and capital, the technical progress function will be lowered with the increase in growth rate of population. In this situation the technical progress function will cut the x-axis positively as in the figure below. This implies that in order to maintain output per head at a constant level, a certain percentage growth in capital per head will be required. We have therefore two points of intersection P and P’ of the technical progress function. Point P’ is unstable equilibrium and point P of stable long run equilibrium. If the rates of growth of income and capital continuously diminish in the economy, both the output per head and capital per head may cease to grow. This may happen if the economy is to the left of point P’. If this situation persists, the technical progress function TT’ may slip down as the dotted curve in any long run equilibrium. Rather, there may be stagnation in the economy.

The conclusion emerges from this 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 :

1. Maximum rate of population is less then $$\lambda$$.
2. Rate of technology which causes a certain percentage increases in productivity, $$\alpha”$$ in the equation above, when both population and capital per head are held constant.

Critical Appraisal

Kaldor’s model is based on the Keynesian tools of analysis and follows Harrod’s dynamic approach regarding the rates of change in income and capital as the dependent variable of the system. But his model is quite different from the Harrodian and other models. In Kaldor’s own word, “the ultimate casual factor was not saving or capital accumulation but,’technical dynamism’ – the flow of new ideas and the readiness of the system to absorb them”.

1. It explains the steady-path of the growth rather than steady state.
2. The division of the model into two stages-constant population and expanding population- is an attempt to reconcile the Harrodian warranted and natural rates of growth by demonstrating the effect of population growth of income in developing countries.
3. Kaldor’s technical progress function is an improvement over the usual production function. As the former relates the technical progress to growth of productivity and capital accumulation while letter relates output per head to capital per head.

Despite these virtues of the Kaldor Model, it is not free from certain weakness.

1. Kaldor’s Model does not explain the determination of the rate of growth of the economy, as has been explained in the Harrod-Domar Models in terms of the volume of investment, saving income ratio and the capital-output ratio.
2. Unlike the Harrod – Domar Model , this model does not give the reason for stability or instability in the economic system. Rather it analyses, certain features of the growth process which emphasise convergence stability.

These drawbacks, however, do not detract one from the advances made by Kaldorian in growth theory through this model.