(a) Assume that both firms sell to both types of consumers and they each charge a single price to both types of consumers. Specify the demand function that each firm faces. Confirm that each firm's demand function is decreasing in its own price and is increasing in the rival's price. (b) If the firms simultaneously choose prices, what prices are they going to choose in a Nash equilibrium? (c) Now suppose that tp profits. 20 and te 10. Find each firm's market share and its
(a) Assume that both firms sell to both types of consumers and they each charge a single price to both types of consumers. Specify the demand function that each firm faces. Confirm that each firm's demand function is decreasing in its own price and is increasing in the rival's price. (b) If the firms simultaneously choose prices, what prices are they going to choose in a Nash equilibrium? (c) Now suppose that tp profits. 20 and te 10. Find each firm's market share and its
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Consider the standard model of product differentiation where two firms (Firm 0 and
Firm 1) are located at the two endpoints of a line of length 1km. Each firm has a
marginal cost of c. There are two types of consumers who live in this linear city. Both
types of consumers are uniformly distributed on the line and each consumer has unit
demand. There are 100 "picky" consumers who suffer a travel cost of t, for each km of
travel. There are 100 "easygoing" cosumers who face a travel cost of 0 < te < tp for
each km of travel.
(a) Assume that both firms sell to both types of consumers and they each charge a
single price to both types of consumers. Specify the demand function that each
firm faces. Confirm that each firm's demand function is decreasing in its own price
and is increasing in the rival's price.
(b) If the firms simultaneously choose prices, what prices are they going to choose in
a Nash equilibrium?
(c) Now suppose that tp
profits.
20 and te
10. Find each firm's market share and its
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