This article will guide you to learn about how to calculate marginal productivity of capital.
The main contention of the marginal productivity (MP) theory of factor pricing is that the price of a particular factor should be equal to the value of its marginal product (VMP). The MP theory is also applicable to the determination of rate of interest.
For interest is the price to be paid for the use of the factor called capital. It may be noted here that if there is perfect competition in the product market, then the VMP of capital would be equal to its marginal revenue product (MRP) [VMPK = MRPK].
Again, if there is perfect competition in the capital market, then the firm which is the buyer of the services of capital, may buy any amount of these services, i.e., may borrow any amount of capital, at the prevailing rate of interest (r). That is why both the average and marginal rate of expenses for capital would be a constant (= r), whatever may be the amount of capital used by the firm.
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From the discussion of the MP theory, we know that VMPK depends upon the amount of capital (K) used by the firm, and, under the law of diminishing returns, VMPK decreases (or increases) as K increases (or decreases).
Now, at any K, if we have VMPK = MRPK > r = AEK = MEK, then for the marginal unit used of capital, the revenue product (MRPK) would be greater than the expenses (MEK), i.e., the firm’s marginal profit would be positive.
Therefore, the profit-maximising firm now would go on increasing the amount used of capital till at some K, MRPK diminishes to the level of r, and the marginal profit becomes equal to zero. At this K, the firm’s profit would be maximum. The firm would not increase K after this point, for if it does this, the MRPK would come down below r, and it would have a negative profit on the margin.
On the other hand, if, at some K, the firm has VMPK = MRPK < r = AEK = MEK, then on the margin the firm would have a negative profit, and now to maximise profit, the firm would have to reduce K till at some K, MRPK increases to the level of r.
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At this K, the firm’s marginal profit would become equal to zero and its profit would be maximum. The firm would not reduce K further because if it does that, it would have MRPK > r and its profit would not be maximum possible.
Therefore, from the above discussion, we obtain that the firm would use such an amount of capital at which the VMPK becomes equal to r.
Criticisms of Capital:
All the assumptions of the MP theory are, in general, applicable to the MP theory of capital. These assumptions are unrealistic. In other words, the MP theory in general and the MP theory of capital in particular are based on unrealistic assumptions.
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Apart from this, the MP theory analyses only the demand side of the price determination of a factor. That is why it is not a complete theory of price determination. It actually does not determine the price of a factor of production. The theory helps us to derive only the demand curve of the factor.