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
Chapter1: Making Economics Decisions
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cbb3a16-d911-4d4e-ac4a-559489c6b9b1%2F209b5d18-4e33-4ab6-b0a4-cd1867a2d7cc%2Fxx9yzba_processed.jpeg&w=3840&q=75)
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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