There is only one least-cost way to make wooden boxes for shipping tomatoes, and

Question

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 TC = 200 + q + .005q^2. The inverse market demand for boxes is given by P = 10 - .005Q. There are multiple forms in the industry, and no one firm can exclude others from using the same technology. Essentially the market structure changes from monopoly to perfect competition. (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? Much Thanks!

Explanation / Answer

MC = 0 1 - 0.01 q= 0 q=100 P = 10 - 0.005 x 100 = 9.5 Profit = TR -TC = PxQ - TC = 950 - (200+100+50) = 600 and P = 0 at Q = 2000 Q =0 at P = 10 a) Output = 100 Price =9.5 b) profit = 600 c)Producer's surplus = 9.5 x 100 x0.5 = 475 d) consumer's surplus = 0.5 x 0.5 x 100 = 25

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