Consider a firm producing output q using labor L and capital K as the two inputs where the price of labor is w = 40 and the price of capital is r = 50. The firm's total costs are TC = 10,000. Assume that the production technology to produce the output is given by: Q = 20L + 30K.
(a) What will be the firm's optimal choice of inputs? Referring to marginal product and input prices, explain why this is the optimal point.
Now consider a firm with the following production technology: Q = L^(1/4) * K^(1/4) with the price of labor denoted by w and the price of capital denoted by r.
(b) Set up the firm's long-run profit maximization problem and solve to find an expression for the firm's supply function and its profit function.
(c) A firm's decision to produce, and how much to supply, depends on whether we consider the short run or the long run. Explain how a firm's average costs will be used when it is deciding when and how much to supply in the short and long run.