A firm has the following production function for smoke detectors: q = 4KL, where K is the amount of capital employed and L is the amount of labor employed. The price of capital is r = $8 and the price of labor is w = $2.
a. Does the firm’s production function exhibit constant, increasing, or decreasing returns to scale? Briefly explain
. b. Find and graph the expansion path.
c. Suppose that an order of 1600 units of smoke detectors has been placed. How much labor and capital should the firm employ in order to minimize the (long run) cost of production? How much will it cost to produce the 1600 units?
d. Find the long-run total cost curve (LRTC) as a function of q, and derive the long-run average cost curve (LRAC), and the marginal cost curve (LRMC) for this firm.
e. For the following statement, please answer True or False (and shortly explain): This firm is experiencing economies of scale at every level of output.