a. Write down a firm As profit maximization problem. Assume that the firm has fixed free labor
Question:
a. Write down a firm A’s profit maximization problem. Assume that the firm has fixed free labor inputs, but must choose capital inputs. At the start of a period, a firm rents capital inputs and combines capital with labor to produce outputs. At the end of the period, the firm sells its outputs and pays interest rates based on how muchcapital it rented (no wage costs). Profits is denoted by π, period interest rate is r, the price of output is p, the firm makes Y units of output, and the production function is Cobb-Douglas: f(L, K) = A * Lb * Ka
b. Write down firm B’s profit maximization problem. Firm B has N inputs: G1, G2, . . . GN−1, GN . We can denote the i’th input as Gi. The cost to rent/hire the i’th input is ρi. The firm has Cobb-Douglas Production Function, where the power coefficient for each i’th input is γi. As before, the price of output is p, and the firm makes Y units of output. The firm has to pay for all inputs, however, all inputs except for G1 are fixed. This means the firm only chooses G1.
