투입 효율성 III

When the isoquants of two producers are tangent, it means they have the same Marginal Rate of Technical Substitution at that point. 

MRTS is the slope of the isoquant, representing how much one input, such as labor, must decrease when another input, like capital, increases, to maintain the same level of output.

Mathematically, MRTS is the absolute value of the ratio of the marginal product of labor to the marginal product of capital.

Efficient input allocation across producers requires their MRTS to be equal. When MRTS is equal, reallocating inputs will not lead to further efficiency gains.

Additionally, cost-minimizing producers set their MRTS equal to the ratio of input prices, specifically wages and rental rates for labor and capital, respectively.

Since input efficiency is achieved when Farmer A’s MRTS equals Farmer B’s MRTS, it can be expressed by the ratio of the marginal product of labor to the marginal product of capital for each farmer, which in turn equals their wage-to-rental price ratio.

This relationship ensures that producers allocate labor and capital in a way that minimizes costs and maximizes productivity.