Two companies produce similar items for the same market. Company 1 produces 9₁ items and Company 2 produces q2 items. The costs, C₁ and C₂, incurred by Company 1 and Company 2, respectively, are given by C₁ = aq₁ and C₂ = aq2, and the market price P is given by P = A-9₁-92, where a and A are positive real numbers with a < A. Let ₁ and ₂ denote the profit made by Company 1 and Company 2, respectively. Both companies want to choose their production strategies in order to maximize their respective profits. (i) Find expressions for ₁ and 2 in terms of 9₁, 92, a and A. (ii) Find the solution of this problem using the Cournot model, giving your answers in terms of a and A. (iii) Find the solution of this problem using the Stackelberg model with Company 1 deciding its production strategy first, giving your answers in terms of a and A. (iv) Which of the two solutions would Company 1 prefer? Justify your answer.

Two companies produce similar items for the same market. Company 1 produces 9₁ items and Company 2 produces q2 items. The costs, C₁ and C₂, incurred by Company 1 and Company 2, respectively, are given by C₁ = aq₁ and C₂ = aq2, and the market price P is given by P = A-9₁-92, where a and A are positive real numbers with a < A. Let ₁ and ₂ denote the profit made by Company 1 and Company 2, respectively. Both companies want to choose their production strategies in order to maximize their respective profits. (i) Find expressions for ₁ and 2 in terms of 9₁, 92, a and A. (ii) Find the solution of this problem using the Cournot model, giving your answers in terms of a and A. (iii) Find the solution of this problem using the Stackelberg model with Company 1 deciding its production strategy first, giving your answers in terms of a and A. (iv) Which of the two solutions would Company 1 prefer? Justify your answer.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.10P

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