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Criticism, Clark's Product Exhaustion Theorem

 Criticism, Clark's Product Exhaustion Theorem

Criticism

In reality, constant returns to scale are incompatible with competitive equilibrium. For if long cost curve of the firm is horizontal and coincides with the piece line the size of the firm is indeterminate, if it below the price line the firm will become a monopoly concern and if it is above the price line, the firm will cease to exist.

            The entire study is based on the postulation that factors are fully divisible. Since the entrepreneur cannot be varied, we have not taken him as a separate factor. In fact, entrepreneurship disappears in the stationary economy. When there is full equilibrium at the minimum point of the LRAC curve, there is no uncertainty and profits disappear altogether.

            So hypothesis of an entrepreneur-less economy is justified for the solution of the adding up problem. But once uncertainty appears, the entrepreneur becomes a residual claimant and the exhaustion of the production problem disappears.

                                   

            Under imperfect or monopolistic competition, the total product adds up to more than the share paid to each factor, that is P is greater than C and L. taking an imperfect labour market, the average and marginal wage curve (AW and MW) incline upward and the average and marginal revenue product curves (ARP and MRP) are inverted U shaped as represented in the diagram 3.

            Equilibrium is established at point E where the MRP curve cuts the MW curve from above. The firm employs OQ units of labour by paying QA wage which is less than the marginal productivity when there is imperfect competition. This argument applies not only to labour but all shares even under constant returns to scale in the industry.

Clark’s Product Exhaustion Theorem
                       

Postulations

  1. There is free competition in both the product markets and factor markets.
  2. Prices and Wages are not manipulated either by government action or collusive agreements.
  3. The quantity of each factor is given.
  4. There are no changes in the tastes and of consumers or techniques of production. It means that the same goods are produced in the same quantities and by the same methods.
  5. The quantity of capital equipment is fixed. But the form of capital equipment can be changed to co-operate with the quantity of labour available. It means that in the long run plants can be adapted and replaced in keeping with the availability of labour.
  6. Workers are interchangeable and of equal efficiency. It means that there is a single wage rate for all occupations for the reason that there is perfect labour mobility.

Explanation

            Based on these hypotheses Clark summarised the working of such an economy in figures as represented below. There are two factors of production: labour, land and capital. Units of labour are shown on the horizontal axis and the MP of labour on the vertical axis in diagram 4 of the representation. The MPL curve is the marginal physical product of labour which falls steadily as more workers are employed with fixed capital.

                                   
OL represents the number of workers available for employment. If all are employed the MP of the last worker is LA who paid LA wage. Since all workers receive the same wage rate, the total wage bill is the number of workers OL multiplied by the wage rate LA (=OB), i.e. the area OLAB.

The triangular area ABM goes to the owners of capital as the residual interest. Thus the total product is the area OMAL which has been distributed as PLAB as wages to workers and ABM is interest to owners of capital i.e. between labour and capital, the two factors in the economy.

                       

If labour is a fixed factor and capital is a variable factor in the economy, it can again be represented that the total product is fully exhausted. Now units of capital are taken on the horizontal axis and the MP of capital on the vertical axis and MPc as the marginal physical product curve of capital in diagram 5.

Given the same quantity of labour, OK of capital is employed with KC as its marginal product so that the rate of interest is OD = KC per unit of capital. This gives the area OKCD as the total interest income on capital. The workers receive wages equal to the area CDM.

Thus the total product of the economy is the area OKCD and workers as wages equal to the area CDM so that OMCK = OKCD + CDM. It must be noted that for the product exhaustion theorem, to be valid in Clark’s view, area OLAB in diagram 4 must equal DCDM in diagram 5 and area OKCD of diagram 5 must equal DABM in diagram 4 of the representation.

Importance of Product Exhaustion Theorem

            Euler’s theorem plays an important role in the theory of distribution. The total product is produced by combining different factors of production. The question that mounts is how the total productivity must be distributed among the factors of production.

If the production function is standardised of degree one, then Euler’s theorem can solve this question. It provides the solution to the producer’s long run problem of allocation of total product to each factor and the distribution of the total outlay among the different inputs.

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