If the buyer can tell good or ordinary or bad will the good

Question

1 Market for lemons

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 bad second-hand car worths $5 to the seller and $3 to the buyer. Assume that one third of the cars are good, one third are ordinary, and one third are bad.

1. If the buyer can tell good or ordinary or bad, will the good cars sell? Will the ordinary cars sell? Will the bad cars sell?
2. Now assume that the buyer cannot tell good or ordinary or bad but knows that the probabilities of a good, ordinary, and bad car are 1/3, respectively. How much will a risk neutral buyer be ready to pay?
3. Will the seller keep the good cars in the market?
4. 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?
5. How much will the buyer be ready to pay now?
6. Will the seller now keep the ordinary cars in the market?
7. Understanding this, now the buyer sees a car in the market. What is the probability that this car is good, or ordinary, or bad?
8. How much will the buyer be ready to pay now?
9. Will the seller now keep the bad cars in the market?
10. Will any car be sold?