Econ100C-Fall2010-Final-sols

Econ100C-Fall2010-Final-sols - Economics 100C:...

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Economics 100C: Microeconomics C Final Exam Solutions: Fall 2010 1. (5 pts) A monopolist faces a linear, market inverse demand curve, P D ( Q ) = a bQ , where a , b > 0. Find the equation for the monopolist’s marginal revenue curve. In words, describe the relationship between a linear market inverse demand curve and the corresponding monopolist’s marginal revenue curve.    2 TR Q a bQ Q MRQ a bQ  It’s a line with the same P -intercept that’s twice as steep.
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2. (9 pts) The graphs for a monopolist’s inverse market demand curve and its marginal cost curve are given below. This is a short run problem. a. Carefully sketch the graph of the monopolist’s marginal revenue curve. Your graph needs to be pretty accurate. (Your results from problem #1 may be helpful. Marginal revenue should intersect marginal cost twice.) b. Indicate the monopolist’s profit maximizing quantity ( Q M ) and price ( P M ) on the graph. Q M is found from the intersection of MR and MC. P M is the corresponding price taken off the inverse demand curve. c. Indicate the monopolist’s producer surplus (PS) on the graph. Producer surplus is the area below price and above marginal cost. It’s the green area minus the red area. P Q MC P D ( Q ) Q M P M MR
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3. (15 pts) A monopolist sells a product in a market with exactly two consumers. The low demand individual has an inverse demand of P 1 D = 12 – 3 q 1 . The high demand individual has an inverse demand of P 2 D = 12 – q 2 . The monopolist’s long run cost function is C ( Q ) = 2 Q . The monopolist offers menus of two-part tariffs. Each menu consists of a fixed fee, F and a per-unit price, p . The first menu, T 1 has a fixed fee, F 1 of 13.5 and a per-unit price, p 1 of 3. The second menu, T 2 has a fixed fee, F 2 of 21 and a per-unit price, p 2 of 0. a. Which menu (if either) will the low demand individual choose? Show your work! Your calculations/logic are much more important than the choice of a plan. NCS L (menu 1) = 0.5(3)(12 – 3) – 13.5 = 0 NCS L (menu 2) = 0.5(4)(12 – 0) – 21 = 3 He’ll choose menu 2. b. Which menu (if either) will the high demand individual choose? Show your work! Your calculations/logic are much more important than the choice of a plan.
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Econ100C-Fall2010-Final-sols - Economics 100C:...

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