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 p1 and p2 simultaneously. The deriveddemand functions for the two firms are: D1 (P1, P2) = ; +and 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.SP2-P12tS(a) Derive the Nash equilibrium of this game, including the prices,outputs and profits of the two firms.Pj-Pi derive(b) From the demand functions, q; = D; (pi, Pj) =the residual inverse demand functions: p; = P;(qi, Pi) (work outP:(qi, Pi)). Show that for t > 0, P:(q;, P;) is downward-sloping,aP:(gi-Pj)+2ti.e.,< 0. Argue that, taking p; > 0 as given, firm iis like a monopolist facing a residual inverse demand, and theoptimal q; (which equates marginal revenue and marginal cost)or pi makes P;(qi, P¡) = Pi > c, i.e., firm i has market power.

Demand Function for Firm 1Q1 = S2+P2-P12tDemand Function for Firm 2Q2 = S2+P1-P22tBoth Firm Have…

Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = ; + and D2 (p1, P2) =+2, where S> 0 and the parameter t >0 measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. P2-P1 2t S (a) Derive the Nash equilibrium of this game, including the prices, outputs and profits of the two firms. (b) From the demand functions, q; = D; (pi, P;) = + ", derive the residual inverse demand functions: p; = P;(qi, P¡) (work out P:(qi, P;)). Show that for t > 0, P;(q;, P;) is downward-sloping, < 0. Argue that, taking p; 20 as given, firm i is like a monopolist facing a residual inverse demand, and the optimal q; (which equates marginal revenue and marginal cost) or p; makes P:(qi, p;) = pi > c, i.e., firm i has market power. Pj-Pi i.e., !be

Consider a duopoly market, where two firms sell differentiated prod- ucts, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = ; + and D2 (p1, P2) =+2, where S> 0 and the parameter t >0 measures the degree of product differentiation. Both firms have constant marginal cost c > 0 for production. P2-P1 2t S (a) Derive the Nash equilibrium of this game, including the prices, outputs and profits of the two firms. (b) From the demand functions, q; = D; (pi, P;) = + ", derive the residual inverse demand functions: p; = P;(qi, P¡) (work out P:(qi, P;)). Show that for t > 0, P;(q;, P;) is downward-sloping, < 0. Argue that, taking p; 20 as given, firm i is like a monopolist facing a residual inverse demand, and the optimal q; (which equates marginal revenue and marginal cost) or p; makes P:(qi, p;) = pi > c, i.e., firm i has market power. Pj-Pi i.e., !be

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter12: Price And Output Determination: Oligopoly

Section: Chapter Questions

Problem 1E

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