Consider a market in which sellers sell their used car. There are three types of used cars, indexed by q = 10, 20, 30. The monetary value of a car of type q is q to the seller, and (1.1)q to the buyer. The seller knows the type of his car, but the buyer does not. There are 100 sellers of each type (so 300 in total}, and 301 buyers. Buyers are not cash-constrained (each buyer has at least $100 of money). a) Find the competitive equilibrium price and allocation (quantity and types of car transacted). b) 'What would be a Pareto optimal allocation in this market? c) Suppose a \"lemon law\" is enacted that forces sellers to disclose the quality of their car. That is, q is now known to buyers as well as to sellers. Describe the competitive equilibrium price[s) and allocation tmder the lemon law. (1) Compare your answers to questions a), b), and c). What is learned about the opportunity for govennnents to enact this kind of lemon law