1. A town has two food stores, Store 1, which sells Italian cheese, and Store 2, whichsells French cheese. The two stores have to set their prices individually and simultaneously.If Store 1's price is P₁ (dollars per pound of cheese) and Store 2's price is P2 (dollars perpound of cheese), their respective sales, Q₁ (thousand pounds of cheese) and Q2 (thousandpounds of cheese), are given by the following equations:Q₁ = 14-P₁+0.5P2; Q2=24+0.5P₁- P₂-It costs $2 to make a pound of cheese. This means that, given the prices of the two stores(P1, P2), Store 1's profit function is(P1, P2) (P-2)(14 - P₁ +0.5P2),and Store 2's profit function is2(P1, P2) (P2-2)(24+0.5P - P₂).(a) If Store 2 charges price P2, which price will Store 1 charge? Find the best replyfunction of Store 1.(b) If Store 1 charges price P₁, which price will Store 2 charge? Find the best replyfunction of Store 2.(c) Plot the best reply functions of each store in one figure.(d) Find the Nash equilibrium.

1. A town has two food stores, Store 1, which sells Italian cheese, and Store 2, which sells French cheese. The two stores have to set their prices individually and simultaneously. If Store I's price is P₁ (dollars per pound of cheese) and Store 2's price is P2 (dollars per pound of cheese), their respective sales, Q₁ (thousand pounds of cheese) and Q2 (thousand pounds of cheese), are given by the following equations: Q-14-P₁+0.5P; Q2-24+0.5P-P2. It costs $2 to make a pound of cheese. This means that, given the prices of the two stores (P, Pa), Store 1's profit function is (PP)-(P-2)(14 - P₁ +0.5P2), and Store 2's profit function is 2(P1, P2) (P-2)(24+0.5P-P2). (a) If Store 2 charges price P2, which price will Store 1 charge? Find the best reply function of Store 1. (b) If Store 1 charges price P₁, which price will Store 2 charge? Find the best reply function of Store 2. (c) Plot the best reply functions of each store in one figure. (d) Find the Nash equilibrium.

1. A town has two food stores, Store 1, which sells Italian cheese, and Store 2, which sells French cheese. The two stores have to set their prices individually and simultaneously. If Store I's price is P₁ (dollars per pound of cheese) and Store 2's price is P2 (dollars per pound of cheese), their respective sales, Q₁ (thousand pounds of cheese) and Q2 (thousand pounds of cheese), are given by the following equations: Q-14-P₁+0.5P; Q2-24+0.5P-P2. It costs $2 to make a pound of cheese. This means that, given the prices of the two stores (P, Pa), Store 1's profit function is (PP)-(P-2)(14 - P₁ +0.5P2), and Store 2's profit function is 2(P1, P2) (P-2)(24+0.5P-P2). (a) If Store 2 charges price P2, which price will Store 1 charge? Find the best reply function of Store 1. (b) If Store 1 charges price P₁, which price will Store 2 charge? Find the best reply function of Store 2. (c) Plot the best reply functions of each store in one figure. (d) Find the Nash equilibrium.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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