Assume that a firm produces a good using labor (L) and capital (K). It has a production function Q(L,K) = LK. The marginal productivity functions are MPL = K and MPK = L. Assume the firm has $50 to spend on inputs where the wage is $10 and the interest rate is $25. What is the maximum efficient level of output, and how much labor and capital does this output require?
Added by Brett B.
Step 1
Given the wage and interest rate, the firm can afford 5 units of labor (50/10) or 2 units of capital (50/25). Second, we need to find out the combination of labor and capital that maximizes the production function. The firm's problem is to maximize LK subject to Show more…
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