Two firms produce a homogeneous product. Let p denote the product’s price. The output levelof firm 1 is denoted by q1, and the output level of firm 2 by q2. The aggregate industry output isdenoted by Q, Q = q1 + q2. The aggregate industry demand curve for this product is given byp = 70 − Q.Assume that the unit cost of firm 1 is c1 = 10 and the unit cost of firm 2 is c2 = 20.a. Suppose the firms move simultaneously and compete on quantities. Derive the firms’ bestresponse functions, and find the Cournot-Nash equilibrium. What are the profits of thefirms?b. Suppose the firms move sequentially with firm 1 setting its level of output before firm 2.Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2?c. Now assume that firm 2 sets its level of output before firm 1. Find the Stackelberg-Cournotequilibrium. What are the profits of firm 1 and firm 2? Is there a difference in your findingsbetween part b and c? Explain why. Two firms produce a homogeneous product. Let p denote the product's price. The output levelof firm 1 is denoted by 9₁, and the output level of firm 2 by q2. The aggregate industry output isdenoted by Q, Q = 91 +92. The aggregate industry demand curve for this product is given byp=70 - Q.Assume that the unit cost of firm 1 is c₁=10 and the unit cost of firm 2 is c₂: 20.a. Suppose the firms move simultaneously and compete on quantities. Derive the firms’ bestresponse functions, and find the Cournot-Nash equilibrium. What are the profits of thefirms?b. Suppose the firms move sequentially with firm 1 setting its level of output before firm 2.Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2?c. Now assume that firm 2 sets its level of output before firm 1. Find the Stackelberg-Cournotequilibrium. What are the profits of firm 1 and firm 2? Is there a difference in your findingsbetween part b and c? Explain why.

Duopoly is an economic term that describes a market structure in which there are only two firms that…

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two firms produce a homogeneous product. Let p denote the product’s price. The output level
of firm 1 is denoted by q1, and the output level of firm 2 by q2. The aggregate industry output is
denoted by Q, Q = q1 + q2. The aggregate industry demand curve for this product is given by
p = 70 − Q.
Assume that the unit cost of firm 1 is c1 = 10 and the unit cost of firm 2 is c2 = 20.
a. Suppose the firms move simultaneously and compete on quantities. Derive the firms’ best
response functions, and find the Cournot-Nash equilibrium. What are the profits of the
firms?
b. Suppose the firms move sequentially with firm 1 setting its level of output before firm 2.
Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2?
c. Now assume that firm 2 sets its level of output before firm 1. Find the Stackelberg-Cournot
equilibrium. What are the profits of firm 1 and firm 2? Is there a difference in your findings
between part b and c? Explain why.

Two firms produce a homogeneous product. Let p denote the product's price. The output level
of firm 1 is denoted by 9₁, and the output level of firm 2 by q2. The aggregate industry output is
denoted by Q, Q = 91 +92. The aggregate industry demand curve for this product is given by
p=70 - Q.
Assume that the unit cost of firm 1 is c₁
=
10 and the unit cost of firm 2 is c₂: 20.
a. Suppose the firms move simultaneously and compete on quantities. Derive the firms’ best
response functions, and find the Cournot-Nash equilibrium. What are the profits of the
firms?
b. Suppose the firms move sequentially with firm 1 setting its level of output before firm 2.
Find the Stackelberg-Cournot equilibrium. What are the profits of firm 1 and firm 2?
c. Now assume that firm 2 sets its level of output before firm 1. Find the Stackelberg-Cournot
equilibrium. What are the profits of firm 1 and firm 2? Is there a difference in your findings
between part b and c? Explain why.

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