2.(a) Consider the market for used cars as presented in class and in the course notes. Let X = value of the car. Sellers know the value of the car they sell and their utility is U(X) = X. Buyers only know that car values are uniformly distributed on ($4000, $6000), are risk-neutral, and their utility is 1.1XX. Suppose the posted price for used cars is $5,000. Will consumers buy a car at this price? Explain. (b) Suppose all individuals face a loss distribution that is uniformly distributed on ($0, $15,000). Each individual knows his loss but the insurance company does not. If all individuals are risk neutral will the insurance company make a profit if it sells a complete-cover insurance policy for $10,000 (and faces administration costs of $1,000 per policy)? Explain your answer. (c) Give a definition of adverse selection.