Let the quality of a second-hand car be denoted by 0 = {1,2,3}, where is the number of tune-ups that the car received in the past. The value of a car of quality to the seller is $8000. Each potential buyer has an initial wealth of $9,025 and the utility of purchasing a car of quality 0 at price P is 9,025-P+1,0000 (while the utility of not buying is 9,025 = 95. Let the proportion of cars of each quality be as follows (where q is a number strictly between 0 and ): 1 2 3 proportion 9 -9 }// Suppose that the price of a second-hand car is P = $1,700. [In the following assume that, if indifferent between selling and not selling, the owner of a car would sell and, if indifferent between buying and not buying, a potential buyer would buy.] (a) Are there values of q such that ALL cars are traded? (b) Are there values of q such that all cars of quality 0=1 and 0=2 are traded? (c) Are there values of q such that only cars of quality 0=1 are traded?