6. A firm operates with a technology that is characterized by a diminishing marg

Question

6. A firm operates with a technology that is characterized by a diminishing marginal rate of technical substitution of labor for capital. It is currently producing 32 units of output using 4 units of capital and 5 units of labor. At that operating point the marginal product of labor is 4 and the marginal product of capital is 2. The rental price of a unit of capital is 2 when the wage rate is 1. Is the firm minimizing its total long-run cost of producing the 32 units of output? If so, how do you know? If not, show why not and indicate whether the firm should be using (i) more capital and less labor, or (ii) less capital and more labor to produce an output of 32.

Explanation / Answer

MRTS = MPl/MPk = 4/2 =2

w/r = 1/2. At cost minimizing level. MRTS = w/r. But here MRTS>w/r therefore firm is not cost minimizing. Since MRTS> w/r implies output from per dollar spent on labor is more than that from capital. Therefore, firm should employ more of labor.

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