1. Write down a firm As 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 , 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 * L^b * K^a

2. Write down firm Bs profit maximization problem. Firm B has N inputs: G₁, G₂, . . . G_N1, G_N . We can denote the ith input as G_i. The cost to rent/hire the ith input is _i. The firm has Cobb-Douglas Production Function, where the power coefficient for each ith input is _i. 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.