3. Consider a market for second-hand cars. Assume that there are 100 sellers with good quality cars and 200 sellers with bad quality cars. Assume also that there are 300 of potential buyers (each buyer is willing to purchase at most one car). A good quality car is worth $10400 to the seller, while a bad quality one is worth only $8000 to the seller. A buyer is willing to pay $13000 for a good car, and $10000 for a bad one. All agents are price takers and they are risk-neutral. Suppose that each seller knows the quality of his car but buyers are not able to distinguish a good car from a bad one. Assume that each seller can sell the car together with a guarantee that costs $0,5 thousand per year to the good quality sellers, and costs $1 thousand per year to the bad ones. Suppose that sellers can choose the duration of the guarantee (i.e. number of years is any nonnegative number). Assume that the sellers get the entire surplus from trade. (a) Find all separating equilibria both graphically and algebraically. Illustrate the best (Pareto superior) equilibrium graphically. Is it efficient? If not, find the value of deadweight loss. (b) Find all pooling equilibria both graphically and algebraically.

3. Consider a market for second-hand cars. Assume that there are 100 sellers with good quality cars and 200 sellers with bad quality cars. Assume also that there are 300 of potential buyers (each buyer is willing to purchase at most one car). A good quality car is worth $10400 to the seller, while a bad quality one is worth only $8000 to the seller. A buyer is willing to pay $13000 for a good car, and $10000 for a bad one. All agents are price takers and they are risk-neutral. Suppose that each seller knows the quality of his car but buyers are not able to distinguish a good car from a bad one. Assume that each seller can sell the car together with a guarantee that costs $0,5 thousand per year to the good quality sellers, and costs $1 thousand per year to the bad ones. Suppose that sellers can choose the duration of the guarantee (i.e. number of years is any nonnegative number). Assume that the sellers get the entire surplus from trade. (a) Find all separating equilibria both graphically and algebraically. Illustrate the best (Pareto superior) equilibrium graphically. Is it efficient? If not, find the value of deadweight loss. (b) Find all pooling equilibria both graphically and algebraically.

Microeconomics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506893

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter10: Price-searcher Markets With Low Entry Barriers

Section: Chapter Questions

Problem 3CQ

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