For a profit maximizing firm, the problem of determination of optimal combination of factors of production can arise in the short-run as well as in the long-run. When out of two factors of production (say, labour and capital), one is variable (say, labour) while the level of other input remains fixed (say, capital), and determination of optimal quantity of the variable input is required, it becomes a short run problem. In case of long run, both the inputs become variable and thus, it is required to determine the optimal quantities of both the variables.
For determining optimal allocation of labour (amount of capital being fixed) in the short-run, the required condition to be satisfied is equality between Marginal Revenue Product of the variable factor (i.e., MRPL) and Marginal Cost (MCL) of that factor.
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MRPL is defined as the incremental revenue that the firm can obtain by employing one additional unit of that variable factor. MRPL is the product of marginal productivity of the variable factor (say, labour) and marginal revenue earned by selling one additional of the unit of the product. That is,
MRQ is the price of the output, since this amount can be fetched by the firm by selling an additional unit of output.
MCL is defined as the additional cost incurred by the firm to hire the last unit of labour. If the firm operates in a situation where the labour market is perfectly competitive, MCL will be fixed and equal to wage rate.
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Thus, short-run optimality of a profit-maximising firm requires the following condition to be satisfied:
MRPL = MCL
Or, MPL. P = w
Worked out Numerical Problem:
