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There are two sandwich shops, shop 1 and shop 2, that are 4 miles apart. All consumers of sandwiches live on the straight line connecting the stores. There are 10,000 consumers uniformly distributed on this line between the two stores. A consumer at point x on the line between store 1 and 2 is located x miles from store 1 and 4-x miles from store 2. Suppose each consumer has a transportation cost of $2 per mile. The cost including transportation cost for a consumer located at x to purchase from shop 1 is p₁+2x and the analogous price to purchase from shop 2 is p₂+2(4-x). Each consumer purchases one sandwhich from the shop with the lowest cost including transportation cost. Suppose both shops have the same marginal cost of each sandwhich equal to $3. When shop 1 picks p₁it takes as given p₂ Analogously, when shop 2 picks p₂ it takes p; as given. Suppose shop 1 thinks that shop 2 is going to set p₂-$13. What is the optimal price for shop 1 in this this case? 12 Suppose shop 1 thinks that shop 2 is going to set p₂-$12. What is the optimal price for shop 1 in this this case? Thank through why neither of these is an equilibrium of price competition between the two shops. In the Nash equilibrium of this game, both firms set price equal to 11

There are two sandwich shops, shop 1 and shop 2, that are 4 miles apart. All consumers of sandwiches live on the straight line connecting the stores. There are 10,000 consumers uniformly distributed on this line between the two stores. A consumer at point x on the line between store 1 and 2 is located x miles from store 1 and 4-x miles from store 2. Suppose each consumer has a transportation cost of $2 per mile. The cost including transportation cost for a consumer located at x to purchase from shop 1 is p₁+2x and the analogous price to purchase from shop 2 is p₂+2(4-x). Each consumer purchases one sandwhich from the shop with the lowest cost including transportation cost. Suppose both shops have the same marginal cost of each sandwhich equal to $3. When shop 1 picks p₁it takes as given p₂ Analogously, when shop 2 picks p₂ it takes p; as given. Suppose shop 1 thinks that shop 2 is going to set p₂-$13. What is the optimal price for shop 1 in this this case? 12 Suppose shop 1 thinks that shop 2 is going to set p₂-$12. What is the optimal price for shop 1 in this this case? Thank through why neither of these is an equilibrium of price competition between the two shops. In the Nash equilibrium of this game, both firms set price equal to 11

Principles of Microeconomics
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 6PA
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There are two sandwich shops, shop 1 and shop 2, that are 4 miles apart. All consumers of sandwiches live on the straight line connecting the stores. There are 10,000 consumers uniformly distributed on this line between the two stores. A consumer at point x on the line between store 1 and 2 is located x miles from store 1 and 4-x miles from store 2. Suppose each consumer has a transportation cost of $2 per mile. The cost including transportation cost for a consumer located at x to purchase from shop 1 is p₁+2x and the analogous price to purchase from shop 2 is p₂+2(4-x). Each consumer purchases one sandwhich from the shop with the lowest cost including transportation cost. Suppose both shops have the same marginal cost of each sandwhich equal to $3. When shop 1 picks p₁it takes as given p₂ Analogously, when shop 2 picks p₂ it takes p; as given. Suppose shop 1 thinks that shop 2 is going to set p₂-$13. What is the optimal price for shop 1 in this this case? 12 Suppose shop 1 thinks that shop 2 is going to set p₂-$12. What is the optimal price for shop 1 in this this case? Thank through why neither of these is an equilibrium of price competition between the two shops. In the Nash equilibrium of this game, both firms set price equal to 11
Transcribed Image Text:There are two sandwich shops, shop 1 and shop 2, that are 4 miles apart. All consumers of sandwiches live on the straight line connecting the stores. There are 10,000 consumers uniformly distributed on this line between the two stores. A consumer at point x on the line between store 1 and 2 is located x miles from store 1 and 4-x miles from store 2. Suppose each consumer has a transportation cost of $2 per mile. The cost including transportation cost for a consumer located at x to purchase from shop 1 is p₁+2x and the analogous price to purchase from shop 2 is p₂+2(4-x). Each consumer purchases one sandwhich from the shop with the lowest cost including transportation cost. Suppose both shops have the same marginal cost of each sandwhich equal to $3. When shop 1 picks p₁it takes as given p₂ Analogously, when shop 2 picks p₂ it takes p; as given. Suppose shop 1 thinks that shop 2 is going to set p₂-$13. What is the optimal price for shop 1 in this this case? 12 Suppose shop 1 thinks that shop 2 is going to set p₂-$12. What is the optimal price for shop 1 in this this case? Thank through why neither of these is an equilibrium of price competition between the two shops. In the Nash equilibrium of this game, both firms set price equal to 11
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