14.13 : Input Efficiency III

When the isoquants of two producers are tangential, they have the same Marginal Rate of Technical Substitution (MRTS) at that point. The MRTS describes how one input, such as labor, can be substituted for another, such as capital, while maintaining the same level of output. Mathematically, it is given by:

where ‘MP_L’ and ‘MP_K’ are the marginal products of labor and capital, respectively. This ratio indicates the rate at which a firm can trade-off labor for capital without changing total production.

Efficient Input Allocation

For input use to be efficient across different producers, their MRTS must be equal. If one producer has a higher MRTS than another, reallocating labor and capital can improve efficiency by moving resources to where they generate the greatest marginal benefit. When MRTS is equalized, further reallocations will not lead to additional efficiency gains.

For example, suppose an apple farmer and an orange farmer have different MRTS values. If the apple farmer can substitute labor for capital more effectively than the orange farmer, shifting labor toward apple farming and capital toward orange farming would improve overall efficiency. The optimal allocation occurs when their MRTS values are equal.

Cost Minimization and Input Prices

Firms that aim to minimize costs set their MRTS equal to the ratio of input prices, as follows:

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where ‘w’ is the wage rate and ‘r’ is the rental rate of capital. This condition ensures that firms allocate resources efficiently, using labor and capital in proportions that minimize production costs.

Thus, input efficiency is achieved when both the apple and orange farmers have the same MRTS, which also equals the wage-to-rental price ratio. This ensures that labor and capital are used in a way that minimizes costs while maintaining maximum productivity.