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In an industry there are two firms, R₁ and R₂, producing differentiated products that engage in price setting competition. They both have constant marginal costs c₁ and c2 and the deman functions of their respective products are D1(P1, P2, P3) = 70-2p1 + P2 = 140+ p₁-2p2 D2(P1, P2, P3) (i) Firm R₁ chooses its price p₁ first, followed by firm R₂ who sets its own price p2 after observ

In an industry there are two firms, R₁ and R₂, producing differentiated products that engage in price setting competition. They both have constant marginal costs c₁ and c2 and the deman functions of their respective products are D1(P1, P2, P3) = 70-2p1 + P2 = 140+ p₁-2p2 D2(P1, P2, P3) (i) Firm R₁ chooses its price p₁ first, followed by firm R₂ who sets its own price p2 after observ

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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In an industry there are two firms, R₁ and R₂, producing differentiated products that engage in price setting competition. They both have constant marginal costs c₁ and c2 and the demand functions of their respective products are D1 (P1, P2, P3) = 70-2p1 + P2 = 140+ p1 - 2p2 D2(P1, P2, P3) (i) Firm R₁ chooses its price p₁ first, followed by firm R₂ who sets its own price p2 after observ- ing the price set by its opponent. Compute the equilibrium prices in this market as a function of the marginal costs. (ii) Suppose that marginal costs evolve over continuous time according to the system: dc₁ 1 ₁ - C₂ + 60 dt dc2 = C1- C2+5 dt By studying the above system, compute the long run equilibrium prices in this market. 1
Transcribed Image Text:In an industry there are two firms, R₁ and R₂, producing differentiated products that engage in price setting competition. They both have constant marginal costs c₁ and c2 and the demand functions of their respective products are D1 (P1, P2, P3) = 70-2p1 + P2 = 140+ p1 - 2p2 D2(P1, P2, P3) (i) Firm R₁ chooses its price p₁ first, followed by firm R₂ who sets its own price p2 after observ- ing the price set by its opponent. Compute the equilibrium prices in this market as a function of the marginal costs. (ii) Suppose that marginal costs evolve over continuous time according to the system: dc₁ 1 ₁ - C₂ + 60 dt dc2 = C1- C2+5 dt By studying the above system, compute the long run equilibrium prices in this market. 1
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