10. Suppose an industry has a duopoly structure. Duopolist 1 has a cost function given by: C₁(y₁) = (y₁)² for output y₁20. Duopolist 2 has a cost function given by: C2(y2) = 12y2 for output y2 20. Denoting total output produced in the industry by y = (y₁ + y₂) the inverse demand function for the good produced in the industry is given by: p = 100 - y (a) Find the reaction function of each duopolist. (b) Using (a), obtain the output levels that will be produced in a Cournot-Nash equilibrium, and the price level in such an equilibrium. Illustrate your solution in (b) above in a diagram.

10. Suppose an industry has a duopoly structure. Duopolist 1 has a cost function given by: C₁(y₁) = (y₁)² for output y₁20. Duopolist 2 has a cost function given by: C2(y2) = 12y2 for output y2 20. Denoting total output produced in the industry by y = (y₁ + y₂) the inverse demand function for the good produced in the industry is given by: p = 100 - y (a) Find the reaction function of each duopolist. (b) Using (a), obtain the output levels that will be produced in a Cournot-Nash equilibrium, and the price level in such an equilibrium. Illustrate your solution in (b) above in a diagram.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.5P

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