4. (8 total points) a) (4 points) In the Tourist-Trap model that we covered in c

Question

4. (8 total points)

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?

With incomplete information, many firms can result in higher prices, whereas with complete information, many firms will result in lower prices.

b) (4 points) What key assumption is changed as we go from the Tourist-Trap model to the Tourist-Native Model?

In the Tourist-Trap model, all consumers are uninformed (have incomplete information). In the Tourist-Native model, some of the 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

T equal to ____32________________________________________________________________

P equal to ____2_________________________________________________________________

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 = 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 Ui = 1.75 – 2xi where xi 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 = Ui – Pi. 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.

Consider a firm, Firm 2. This firm’s nearest competitors are Firm 1 located to its left, and Firm 3 located to its right. Suppose Firm 1 charges a price of .40 for each unit of output, and Firm 3 charges a price of .20 for each unit of output.

a) Derive an expression for Firm 2’s demand curve. Be sure to show your work, indicating clearly the steps that you take.

Q = 330 – 600P    or    P = .55 – Q/600

b) What price should firm 2 charge if it wants to maximize its profit?

MR = .55 – Q/300 = .25 = MC Q = 90 P = .4

For parts c – d, assume that Firm 2 is the only firm located on the circle.

c) Write an expression for the demand for Firm 2.

Q = 2100 – 1200P    or    P = 1.75 – Q/1200

d) What price should the firm charge in order to maximize its profit?

MR = 1.75 – Q/600 = .25 = MC Q = 900 P = 1

Explanation / Answer

a)With incomplete information, many firms can result in higher prices, whereas with complete information, many firms will result in lower prices.

b)

In the Tourist-Trap model, all consumers are uninformed (have incomplete information). In the Tourist-Native model, some of the consumers have complete information.

5) 32,2

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