A Lemon Market: There is a dealer, Super Ford, selling used cars in Wayne, Michigan. Assume that the dealer has cars of two types, Type S (Superior) and Type I (Inferior). The Type S is worth $5,000 and the Type I is only worth $4,000 to you, a potential buyer. Assume that 1) you, as a potential buyer, only know that these two types of cars distribute with equal chance; 2) the dealer, on the other hand, has information advantage and knows exact type of each car to be sold; 3) the dealer gets those used cars from a car rental company, Avis, by paying $4,600 to Type S and $3,600 to Type I.

1. If you want to make an offer to buy a car based upon its expected value, what is the maximum price to be offered?

2. (Continuing on 1) Will the dealer, Super Ford, accept your offer? Which type(s) of cars will be sold to you?

3. (Continuing on 2) Are you satisfied with the car you get at the price that you paid as in part 1)?

4. (Continuing on 3) If giving you a second chance to bid, what is the maximum price that you are willing to offer? Will the dealer, Super Ford, accept your new offer? Which type(s) of cars will be sold to you with your new offer?

5. (Continuing on 4) Now further assume that the dealer could offer an extended warranty of 10,000 miles for one free part replacement to each car that it sells. The part costs $2000. The probability of the replacement need is 0.2 for Type S and 1 for Type I. Which type(s) of cars will be sold with warranty? What will be the maximum price for cars with a warranty and the maximum price for cars without a warranty?