Kaldor - Mirrlees Model of Economic Growth:

Kaldor presented his first model of economic growth in 1957 and second model in 1962. But here we will present that model which he presented in 1962 along with collaboration of Mirrlees.

Features of the Model:

The salient features of Kaldor - Mirrlees Model of Economic Growth are as:

(i) By making the saving rate flexible a constant growth rate of the economy can be attained.

(ii) Contrary to neo-classical economists, the capital - output ratio remains fixed and constant.

(iii) This model rejects the production function approach. Rather, it introduced the function of technical progress.

(iv) In neo-classical model the investment function has not been introduced. But this model also presents the investment function which depends upon that investment which is linked with one laborer.

(v) In this model the assumptions of full employment and perfect competition have been dropped.

This model starts with this hypothesis that national income (Y) is the sum of wages (w) and profits (p). It is as:

Y = W + P

The total savings (S) consist of savings made out of wages (Sw) and the savings made out of profits (Sp). It is as:

S = Sw + Sp

Where Sw = SwW and Sp = spP, then putting them in the above equation:

S = swW + SpP

Where sw = marginal propensity to save of wage earners, and sp = marginal propensity to save of profit earners. The sw and sp are assumed constant. It means that their average and marginal values will remain the same. Thus, as:

Y = W + P or Y - P = W and S = swW + spP

Then putting the value of W:

S = sw (Y - P) + spP

S = swY - swP + spP

S = spP - swP + swY

S = (sp - sw) P + swY

As at Equilibrium S = I, then putting the value of S:

I = S

I = (sp - sw)P + swY

Dividing both sides by Y:

  I   = (sp - sw) (P) + swY

                                                                Y          Y                Y

  I   - swY = (sp - sw)   (P)

                                                                Y      Y                      Y

 I   - sw = (sp - sw)   (P)

                                                                 Y                            Y

Solving for P/Y:

The last equation shows the ratio between profits (P) and the level of income (Y). The stability of the model requires that:

The flexibility of savings in Kaldor-Mirrlees model can be obtained with the help of different propensities with respect to wages and profit. If we are having the values of sp and sw (which can be obtained with the help of income distribution in a country) we can tell that what are the determinants of 1/Y and P/Y. If we assume that  sw = 0, then the last equation will assume following shape:

 P =     1     .    I    -       0      

                                                             Y     sp - 0      Y       sp - 0

P =     1     .  I    

                                                                      Y        sp      Y      

If capital-output ratio (K/Y) is considered constant, (as it was assumed in H - D model), then the above equation is multiplied by (Y/K).

  P  (Y/K) =     1     .   I   (Y/K) 

                                                              Y                 sp       Y

P/K = (1/sp) . (I/K)  

If P/K is shown by V which represents profit on capital, and I/K is shown by J which represents capital accumulation the above equation will be as:

V= 1/sp . (J) or (sp) (V) = J

If sp = 1, then V = J

If the natural growth rate is shown by 'n' and it is assumed as given, then the above equation will be as:

V = J = n

The equation shows that the growth rate is associated with the rate of profits, and it is determined by propensity to profit.

Criticism:

(i) According to Prof. Pasinetti there exists a logical defect in Kaldor's arguments as he permits the laboring class to make the savings, but these savings are neither ploughed in capital accumulation, nor they generate income. He further says that if any country lacking the investing class and there are no profits, then how the growth rate will be determined.

(ii) Kaldor assumes that the saving rate remains fixed. But assuming so he ignores the effects of 'Life-Cycle' on savings and work.

(iii) Kaldor model fails to describe that behavioral mechanism which could tell that distribution of income will be such like that the steady growth is automatically attained.

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