3. Consider a duopoly market, where two firms sell differentiated prod-ucts, which are imperfect substitutes. The market can be modelledas a static price competition game, similar to a linear city model.The two firms choose prices pi and p2 simultaneously. The deriveddemand functions for the two firms are: D, (P1, P2) = + P2-P1and D2 (P1, P2) =+ 2, where S > 0 and the parameter t > 0measures the degree of product differentiation. Both firms haveconstant marginal cost c > 0 for production.S2tS%3D2 (c) Calculate the limits of the equilibrium prices and profits as t →0. What is P;(qi, P;) as t → 0? Is it downward sloping? Ar-gue that the Bertrand Paradox (i.e., the prediction of the staticBertrand duopoly model, where pi = p% = c) holds only in the%3Dextreme case of t = 0.

The demand function for the firm 1 is given as The demand function for firm 2 is given as The…

(c) Calculate the limits of the equilibrium prices and profits as t→ 0. What is Pi(qi, Pj) as t→ 0? Is it downward sloping? Ar- gue that the Bertrand Paradox (i.e., the prediction of the static Bertrand duopoly model, where p₁ = p₁ = c) holds only in the extreme case of t = 0.

(c) Calculate the limits of the equilibrium prices and profits as t→ 0. What is Pi(qi, Pj) as t→ 0? Is it downward sloping? Ar- gue that the Bertrand Paradox (i.e., the prediction of the static Bertrand duopoly model, where p₁ = p₁ = c) holds only in the extreme case of t = 0.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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