There is only one least-cost way to make wooden boxes for shipping tomatoes, and any firm that makes them has a cost function given by 2 TC q q = + + 200 .005 .The inverse market demand for boxes is given by P Q = ? 10 .005 . There is currently only one firm in the industry and it is able to act as a monopolist. (a) What is its output and what price does it charge for boxes? (b) What is the firm's profit at this output level? (c) Does the firm have any producer's surplus? Support your answer by calculating it. (d) What is the magnitude of consumer's surplus in this situation? 3. Suppose now that the firm in problem 2 can no longer exclude others from using the same technology and producing boxes, so the market structure changes from monopoly to perfect competition. (That is, assume that all firms produce at minimum average cost in equilibrium.) (a) What will the market price and quantity be? (b) What is the magnitude of consumer's surplus under this market structure? (c) What are the magnitudes of aggregate producer profits and producer's surplus? (d) Comparing the two market structures for this industry, which has a larger social surplus (sum of producer's and consumer's surplus)?