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

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
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Chapter13: best-practice Tactics: Game Theory
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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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