Please indicate in ()'s which problem you are doing ex. (ii) thank you!!!

4. There are many potential used-car buyers. All are willing to pay $1, 000 for a lemon and $2, 000 for a good used car. There are 1, 000 owners of lemons and 1, 000 owners of good used cars. The reservation price of lemon owners is $750. 600 owners of good used car have reservation price at $1, 250, and 400 have reservation price at $1, 750.

(a) Suppose that by running CARFAX the buyers of used cars can identify which car is a lemon and which car is of good quality. With the sellers having a stronger bargaining power, how much a lemon and a good car will be sold for? And how many of them will be sold?

(b) Suppose that we are back in a time when there is no CARFAX or other car reports; the buyers of used cars cannot identify which car is a lemon and which car is of good quality (and the sellers know the exact quality of their cars.)

i. Although the buyers do not know the exact quality of a car, they know that there are 1, 000 lemons and 1, 000 good cars. They assess that with probability 1 2 a car is a lemon and with probability 1 2 a car is of good quality. Suppose that the buyers are risk neutral. How much they are willing to pay for a car?

ii. At the amount the buyers are willing to pay that you find in (i), how many lemon owners (l) and how many good-car owners (g) are willing to sell their cars?

iii. Given what you find in (ii), what will be the new amount the buyers are willing to pay for a car? (Assume that the buyers, by referring to the l and g you find in (ii), update their probability assessment of a lemon and a good car being on the market.)

iv. At the new amount that the buyers are willing to pay for a car, how many lemon owners and how many good-car owners are willing to sell their cars?

v. Given (iii) and (iv), do we have an equilibrium in this used-car market? In other words, is the new amount that buyers are willing to pay for a car an equilibrium price? Explain by referring to the notion of mutual best responses as equilibrium.

(c) Compare the market outcomes in (a) and (b). Comment on how CARFAX could improve market efficiency