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 = K^1/2/2L^1/2 , and MPK = L^1/2/2K^1/2 .
a) Suppose the price of labor is w = 24, and the price of capital is r = 6. Derive the firm's total cost function.
b) What is the firm's marginal cost?
c) For this problem, you will sketch the graph of the firm's isoquant for Q = 20 units of output, and on the same graph sketch the firm's isocost line associated with the total cost of producing Q = 20 units of output. To get this total cost, you must use the Total Cost function from part a). Please scale your graph up to 100 units of Labor on the horizontal axis, and 100 units of Capital on the vertical axis (do not go above 100 units on either axis). For the isocost line, clearly identify the vertical and horizontal intercepts. For the isoquant, clearly identify 5 combinations of Labor and Capital that will produce Q = 20 (including the bundle that minimizes the firm's cost of production). Make sure your graph is neatly and accurately drawn and carefully labeled.