### Meaning and Solution of Product Exhaustion:

The product exhaustion theorem states that since factors of production are rewarded equal to their marginal product, they will exhaust the total product.

The way this proposition is solved has been called the adding-up problem Wick-steed in the Coordination of the Laws of Distribution demonstrated with the help of Euler’s Theorem (developed by Leonhard Euler, a Swiss mathematician of the eighteenth century) that payment in accordance with marginal productivity to each factor exactly exhausts the total product.

The adding-up problem states that in a competitive factor market when every factor employed in the production process is paid a price equal to the value of its marginal product, then payments to the factors exhaust the total value of the product.

It can be shown numerically as under:

Q = (MPL) L + (MPc) C

where Q is total output, MP is marginal product, L is labour and K is capital. To find out the value of output, multiply through P (price). Thus

PxQ = (MPL x P) L + (MPC x P) С

(MPL x p) — VMP, and (MPc x P) = VMPC

PO = VMPL x VMPC

Where VMP, is the value of marginal product of labour and VMPc is the value of marginal product of capital.

### 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 arises is how the total output should be distributed among the factors of production?

If the production function is homogeneous of degree one, then Eular’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.

The theorem also suggests how a firm should employ the various inputs. It tells us that the firm should employ its inputs to that extent at which the reward to the factor equals its marginal revenue product.

However, Prof. Watson questions the existence of constant returns to scale in the economy. According to him, “The rejoinder here is that in the long-run competitive equilibrium price equals minimum average cost, the firm’s cost curve at that point being horizontal. The momentary constancy of unit cost corresponds to a momentary constancy of returns to scale at the point of equilibrium.”