Problem 1 (28 points) Consider a potential buyer of a used automobile. The market price for the us car age is $5,000. The used automobile can be in good or poor condition. On average, a proportion p of used automobiles in this economy are in poor condition. If the automobile is in good condition, the buyer derives utility equivalent to $10,000. If she is in poor condition, he derives utility equivalent to $0. The buyer cannot observe the automotive quality. On the other hand, he can observe whether the seller has carried out treatment of automobile cleaning and polishing for sale. This treatment has no impact directly on the utility that the buyer derives from the automobile. It only serves to signal the quality of the automobile. This treatment costs $1,000 to the seller of a good quality automobile. As the treatment aims to camouflage the defects of the car, it costs c dollars at least seller of poor quality cars. In the questions below, I will ask you about welfare losses in dollars linked to information asymmetry. Suppose that the "benevolent dictator" evaluating well-being in this economy sums the net gains from exchange giving a weight of 1 to the gain of the buyer, GC, of 1 p to the gain of the seller of good quality automobile, GB of p to the gain of the seller of poor quality automobiles, GM. Its evaluation function social 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 quec = $6,000 and quep = 0.45. What type of balance (separator, mixing, hybrid) do we have in this game? What is this balance? (4 points) c) What is the total welfare loss (in dollars) linked to information asymmetry in this economy? (4 points) d) Suppose c = $3,000 and quep = 0.45. What type of balance (separator, mixing, hybrid) do we have in this game? What is this balance? (4 points) e) What is the total welfare loss (in dollars) linked to information asymmetry in this economy? (4 points) f) Suppose quec = $3,000 and quep = 0.75. What type of balance (separator, mixing, hybrid) do we have in this game? What is this balance? (4 points) g) What is the total welfare loss (in dollars) linked to information asymmetry in this economy? (4 points)