Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by:
MPL = K1/2 / 2L1/2 and MPK = L1/2/ 2K1/2
a) If the price of labor is w = 48, and the price of capital is r = 12, how much labor and capital should the firm hire in order to minimize the cost of production if the firm wants to produce output Q = 18?
b) What is the firm’s Total Cost function TC(Q)?
c) What is the firm’s marginal cost of production?