COMM

# Answer total cost c 10 q ac 10q 1 mc avc 1 q m p m

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Answer: Total cost, C = 10 + Q; AC = 10/Q + 1; MC = AVC= 1 Q m P m MC=AVC D MR AC \$ DWL profits AC Q 1 7. Can a firm be a natural monopoly if it has a U-shaped average cost curve? Why or why not? Answer: Yes. As explained in footnote 13 of chapter 9, if a firm has a U-shaped average cost curve it may still be able to produce the market quantity more cheaply then the aggregation of separate firms’ production, even if that quantity is on the upward-sloping portion of its average cost curve.

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9. If the inverse demand function is p = 300 – 3Q, what is the marginal revenue function? Draw the demand and marginal revenue curves. At what quantities do the demand and marginal revenue lines hit the quantity axis? Answer: 11. If the inverse demand curve is p = 120 – Q and the marginal cost is constant at 10, how does charging the monopoly a specific tax of 10 per unit affect the monopoly optimum and the welfare of consumers, the monopoly, and society (where society’s total surplus includes the tax revenue)? What is the incidence of the tax on consumers? Answer: We get R = pQ = (120-Q)Q = 120Q – Q 2 . Therefore MR = 120 – 2Q. Initially MC = 10, so setting MR = MC to maximize profit yields 120 – 2Q = 10 or Q = 55. It follows that p = 120 – Q = 65. Profit is R – C = 65(55) – 10(55) = 3025. Consumer surplus is the area under the demand curve and above the price = .5(55)(55) = 1512.5. Total surplus is 3025 + 1512.5 = 4537.5. If there is a tax of \$10 per unit, MC rises to 20. Setting MR = MC yields 120 – 2Q = 20 or Q = 50. In this case p = 120 – 50 = 70. Thus price rises by \$5. Consumers pay half of the tax – the incidence is 50%. Tax revenue is 10(50) = 500. Profit = 70(50) – 20(50) = 2500. Consumer surplus is 0.5(50)(50) = 1250. Total surplus is 500 + 2500 + 1250 = 4250. The tax causes total surplus to fall.
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