# ECON 342 ECON342 Exam 2 with Answers (Penn State University)

ECON 342 ECON342 Exam 2 Answers (Version 1) (Penn State University)

Suppose a typical used car buyer is willing to pay $6000 dollars for a low-quality used car (Lemon), and $16,000 for a high-quality car (Plum). Also, suppose the market supply of Plums is given by Q_{P} = -30 +.005P and the market supply of Lemons is given by Q_{L} = -40 +.01 P. Let the typical buyer’s 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.

(16 points) Suppose a manufacturer is a monopoly. This manufacturer produces a good at MC = 20 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 = 180 –2Q, where Q is t

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 whether or not there is an incentive for the firms to vertically integrate. (You may assume the cost of vertical integration is zero).

a) (4 points) In the Tourist-Trap model that we covered in class, what key result regarding prices is different than when consumers have complete information?

5. (8 points) Suppose a monopolist is able to charge a two-part tariff where T is the flat fee charged to consumers, and P is the price per unit charged to consumers. Suppose the demand for the product is given by P = 10 – Q, and that the Marginal Cost is given by MC = 2. In order to maximize profit, the monopolist should charge

6. (16 points) Suppose there are 8 firms located equidistantly around a circle whose circumference is equal to 1. Each firm can produce its good at constant marginal cost, MC = .25. There are no fixed costs. There are 1200 consumers distributed uniformly around the circle. Each consumer gets utility Ū = 1.75 from buying a unit of the good from a firm which sells their ideal brand (a firm located at the consumer’s location). Also, the consumer’s utility decreases by 2 times the distance that the consumer is located from the firm. So a consumer who buys from firm i gets utility given by U_{i} = 1.75 – 2x_{i} where x_{i} is the distance from the consumer’s location to firm i’s location. The consumer’s surplus from purchasing a unit of the good from firm i is the difference between their utility from purchasing a unit of the good from firm i and the price that firm i charges. So CS = U_{i} – P_{i}. Also, the consumer has no alternatives, so the consumer will buy a unit of the good if maximum surplus gained from purchasing from any firm is greater than 0.

7. (16 points) Suppose there are two types of consumers. The demand for each type of consumer is given by:

• Type A: Q = 70 – 2P

• Type B: Q = 60 – 3P

8. (12 points) Suppose that in order to produce any positive amount of output, a firm must build an operating facility which costs $40. The Variable Cost of production is equal to 6q, where q is the quantity of output. Therefore the Marginal Cost of production is constant at MC = $6. If the firm decides not to produce, it does not build the operating facility, and so it incurs 0 costs. The demand facing the firm is given by P = 20 – 2q.