1. (12 points) Suppose a typical used car buyer is willing to pay $6000 dollars for a low-quality used car (Lemon), and $14,000 for a high-quality car (Plum). Also, suppose the market supply of Plums is given by QP = -60 +.01P and the market supply of Lemons is given by QL = -20 +.01 P. Let the typical buyerâs belief that a car of unknown quality is a Plum = z, so (1-z) is the probability that a car of unknown quality is a Lemon.

Assume that buyers are risk-neutral so that the price a buyer will offer for a car of unknown quality is given by:

P = z($14,000) + (1-z)($6000). Therefore **P = $6000 + $8000z.**

a) (8 points) State the equilibrium condition in this market.

**z = Q****P****/(Q****P** **+ Q****L****)**

b) (4 points) Determine the two values of z that lead to a market equilibrium. .

**z = 0**

**z = .25**2. (16 pointsSuppose a manufacturer is a monopoly. This manufacturer produces a good at MC = 8 and sells it to a retailer. The retailer is also a monopoly, and it sells the good bought from the manufacturer to consumers. The retailer has no additional costs other than the price they pay to the manufacturer. The retailer faces a demand curve P = 200 â4Q, where Q is the number of units sold.

a) What price will the manufacturer charge to the retailer?

**P****M** **= 104**

b) What price will the retailer charge to the consumers?

**P****R** **= 152**

c) If the two firms merged, what would be the price charged?

**P = 104**

d) If the two firms merged into a single firm, how much profit would the firm make?

**Î = 2304**

e) How much profit would the two firms make if they do not merge?

**Î ****M** **= 1152**

**Î ****R** **= 576**

**Total Î = 1728**

3. (8 points) Consider the case of a manufacturer (upstream firm) who sells a product to a retailer (downstream firm). For each of the following four possible situations carefully explain under which circumstances there is an incentive for the firms to vertically integrate. (You may assume the cost of vertical integration is zero).

Both firms are perfectly competitive

**NO**

Both firms are monopolies

**YES**

The manufacturer is perfectly competitive and the retailer is a monopoly

**NO**

The manufacturer is a monopoly and the retailer is perfectly competitive.

**YES If the Retailer has a variable proportions production function. Otherwise, NO.**