question below please answer

I'\"\"""\""'"'""' V\""""__ \"V "V'V-"'_-"' "W" \"' ' V'J ""W" "" _--"'""-J' ) Consider a game between a buyer and a seller. The seller has a car to sell, which is either a \"peach\" or a \"lemon\". The seller knows whether the car is a peach or a lemon, while buyers know that the car is a peach with probability q, and a lemon with probability 1 q. Peach sellers value their car at 400 dollars, and lemon sellers value their car at 100 dollars. Buyers value a peach at 1000 dollars, and a lemon at 0 dollars. The buyer and the seller simultaneously decide whether to trade or not trade. If both agree to trade, the buyer pays the seller a price p, and the car is traded. The market is for buying cars is competitive, so the price, p, is the conditional expectation of the value of the car to the buyer given the seller's strategy. (E.g. if the seller's strategy is that lemon owners trade and peach owners do not, the conditional expectation of the car's value to the buyer is 0) Recall that this is a game with private information, and a strategy prole species an action for each \"type\" of seller, and an action for the buyer. (a) Suppose q = 0.5. There are two (Bayesian) Nash equilibria. If and when the car is traded, what price is it sold for? Find both, and explain why each is an equilibrium. (10 POINTS) (b) Suppose q = 0.3. There is only one (Bayesian) Nash equilibrium. Find it, explain why it is an equilibrium, and why no others exist. If and when the car is traded, what price is it sold for? (20 POINTS)