Question 4: [25 points] Consider a model with asymmetric information of a used car market (similar to the one covered in the class). Each seller observes the quality of her car, and the buyers do not observe qualities of cars. Assume that the car quality is distributed uniformly on the interval [0, 500]. 1. Assume, first, that each seller of a car of quality r values the car at exactly z dollars, whereas a car of quality z is valued by each buyer at a + 200 dollars. (a) Is there an equilibrium in which all sellers remain in the market (in other words, can all car qualities be traded in an equilibrium)? To answer this question, first, calculate the expected value by a buyer, and argue what is the maximal price that a buyer is willing to pay. Then, argue which sellers (if any) will exit the market. 2 (b) Calculate the equilibrium in the game. Remember the equilibrium condition: the equilibrium price must be such that the seller of the highest quality car will just accept to remain in the market. 2. Now, assume that each seller of a car of quality z values the car at x - 100 dollars (less than the car's quality), and assume - as before that a car of quality z is valued by each buyer at r+200 dollars. Is there an equilibrium in which all sellers remain in the market? Support your arguments with calculations and show carefully all of your steps.