A firm produces output with capital and labor. Suppose currently the marginal product of labor is 20 and the marginal product of capital is 2. Each unity of labor costs $8 and each unity of capital costs $1. Is the firm minimizing the cost of production? Explain.



Let MPK be the marginal product of capital, MPL be the marginal product of labor, r be the proce of capital, w be the cost of labor, and MRTS be the marginal rate of technical substitution.



The firm is:



A. Not minimizing the cost of production because MRTS>MPK/MPL


B. Not minimizing the cost of production because MPK/r

C. Minimizing the cost of production because MRTS = MPK/MPL


D. Minimizing the cost of production because MPK/r = MPL/w


E. Minimizing the cost of production because MPK/r