A firm is producing 1,000 units of output with 40 units of labor and 30 units of

Question

A firm is producing 1,000 units of output with 40 units of labor and 30 units of capital. The marginal product of the last units of labor and capital are, respectively, MPL = 69 and MPK = 135. The prices of labor and capital are, respectively,w = 30 and r = 85. What should the firm do in order to minimize the cost of producing 1,000 units of output? Should the firm increase capital and decrease labor or the other way around? When should the firm stop replacing one input for the other? Explain.

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Explanation / Answer

The cost minimizing/profit maximizing bundle is the bundle at which MPL = MPK. Using the current bundle, MPK > MPL. Considering the property of diminishing marginal product - the fact that increasing the use of an input decreases the marginal output associated to that input - you would want to increase the use of capital (which would cause MPK to fall) while simultaneously decreasing the labor force (which would cause MPL to rise) until you reach the cost minimizing condition MPL = MPK.

So, the answer is that the firm could reduce the cost of producing its current output level by employing more capital and less labor.

the firm should stop replacing one input for the other when MPL=MPK

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