Suppose a potential buyer of a used car. The market price for the used car is $5,000. The used car can be in good or bad condition. On average, a proportion p of used cars in this economy are in bad condition. If the car is in good condition, the buyer derives utility worth $10,000. If it is in bad condition, he derives utility worth $0. The buyer cannot observe the quality of the car. However, he can observe if the seller has done a cleaning and polishing treatment of the car for sale. This treatment has no direct impact on the utility the buyer derives from the car. It only serves to signal the quality of the car. This treatment costs $1,000 for the seller of a good quality car. As the treatment aims to camouflage the car's defects, it costs c dollars for the seller of a bad quality car.

In the questions below, I will ask you questions about the welfare losses in dollars related to information asymmetry. Suppose that the "benevolent dictator" evaluating welfare in this economy sums the net gains from trade by assigning a weight of 1 to the buyer's gain, GC, 1p to the gain of the seller of a good quality car, GB, and p to the gain of the seller of a bad quality car, GM. Their social welfare function is therefore W = E[GC] + (1 p) E[GB] + p E[GM].

a) Graphically represent the extensive form of the game. (4 points) b) Suppose c = $6,000 and p = 0.45. What type of equilibrium (separating, pooling, hybrid) do we have in this game? What is this equilibrium? (4 points) c) What is the total welfare loss (in dollars) related to information asymmetry in this economy? (4 points) d) Suppose c = $3,000 and p = 0.45. What type of equilibrium (separating, pooling, hybrid) do we have in this game? What is this equilibrium? (4 points) e) What is the total welfare loss (in dollars) related to information asymmetry in this economy? (4 points) f) Suppose c = $3,000 and p = 0.75. What type of equilibrium (separating, pooling, hybrid) do we have in this game? What is this equilibrium? (4 points) g) What is the total welfare loss (in dollars) related to information asymmetry in this economy? (4 points)