Assume that a good second$-$hand car worths $$10$ to the seller and $$12$ to the buyer,an ordinary second$-$hand car worths $$7$ to the seller and $$9$ to the buyer, and a badsecond$-$hand car worths $$5$ to the seller and $$3$ to the buyer. Assume that one third ofthe cars are good, one third are ordinary, and one third are bad. a$.$ If the buyer can tell good or ordinary or bad, will the good cars sell? Will theordinary cars sell? Will the bad cars sell? b$.$ Now assume that the buyer cannot tell good or ordinary or bad but knows that theprobabilities of a good, ordinary, and bad car are $1/3,$ respectively. How much willa risk neutral buyer be ready to pay? c$.$ Will the seller keep the good cars in the market? d$.$ Understanding this, now the buyer sees a car in the market. What are the probabil$-$ities that this car is good, ordinary, and bad, respectively?e$.$ How much will the buyer be ready to pay now?f$.$ Will the seller now keep the ordinary cars in the market?g$.$ Understanding this, now the buyer sees a car in the market. What is the probabilitythat this car is good, or ordinary, or bad?h$.$ How much will the buyer be ready to pay now?