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Key to Problem Set _6

# Key to Problem Set _6 - Key to Problem Set#6 1(End of...

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Key to Problem Set #6 1. (End of chapter Exercise 20.2) Q d = 30 – 0.5 P is demand for test prep services. Q s = -30 + 2 P is private supply. MEC = 5 + 1.5 Q is the marginal external cost of prep services. Invert demand and supply: P = 60 – 2 Q d and P = 15 + 0.5 Q s . Competitive equilibrium Q = 18, P = 24. To find marginal social cost, add (vertically) MC and MEC: MSC = 20 + 2 Q Socially optimal quantity would be where MSC = MB: 20 + 2 Q = 60 – 2Q ; Q = 10. Deadweight loss is area of shaded triangle: (1/2)(32)(8)= 128. 2. (End of chapter Exercise 20.8 appears to have a typo and doesn’t make a lot of sense, so I have eliminated it from the homework assignment.) 3. In-text Exercise 21.3. C = 1000 + H 2 is the salesperson’s personal cost of (H) high effort. So marginal cost is 2H. Each hour of high effort results in a 4% chance of a car sale. If a car is sold, the profit to the dealer is \$1500. So each hour of high effort results in a marginal benefit of \$60. Even at zero effort, there is an \$800 benefit, so dealership’s benefit function is B = 800 + 60 H.

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