Posted by **matherik** on Monday, September 8, 2008 at 1:59am.

A firm offers two differentiated products, X and Y and faces two types of consumers, types A and B. There are equal numbers of each type of consumers ¡V so, for simplicity, assume there is just one of each type. The valuations of the two types of customers of the two products are summarized in the table below. Assume (for simplicity) that the marginal cost of manufacture of X and Y is identical, constant and equal to zero:

Customers

& Products X-cheapticket Y-VIPticket

Type A 10 15

Type B 12 25

(a)If the firm offers good X for a price of 11 and good Y for a price of 26, which (if any) product will each consumer type buy (if she only wants to buy one)?

(b)If the firm offers good X for a price of 9 and good Y for a price of 24, which (if any) product will each consumer type buy (if she only wants to buy one)?

(c)Calculate the profits earned by the firm on each of the set of prices in parts (a) ¡V (b). Can you propose prices for X and Y to achieve higher profits?

(d)How does the consumer surplus for Type B on good X limit the price that can be set for good Y (to get Type B to select good Y)? Is there a positive or negative relationship between the price on good X and the price that can be charged on good Y? Why (if we want both consumers to purchase a good) does this imply that the price on good X should be set leaving Type A with zero consumer surplus?

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