A price taking firm chooses its inputs to maximize long-run profits. Labor and capital are substitutes in production and both exhibit decreasing returns to scale, q(L, K) = L^(1/2) + K^(1/2) . The output price is 100 and the price of each of the inputs is 10.
(a) Set up the firm’s profit function and provide the two conditions for profit maximization. (b) Find the profit maximizing levels of capital and labor. (c) How does a change in labor change the optimal choice of capital?