PROBLEM (3) Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at på and pв. The demand for each firm's product is given by qA = 400 - 3pA - 2 pв and qв = 400 - 3p³ - 2pA, and MCA(qA) = ATCA(q) = 40 and MCB(qB) = ATCB(qB) = 40. (a) Are the two goods substitutes or complements? Do the firms want to charge higher prices or lower prices, the higher the opponent's price? (Is the best response price increasing (or decreasing, or neither) in the opponent's price?) Calculate the Bertrand equilibrium prices. (b) Now suppose the firms -instead of competing to maximize their own individual profits- decide to "collude" and charge prices to maximize their joint profits (sum of their profits). What would be each firm's optimal price? Are these prices greater/smaller/the same compared to the prices in (a)?

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
Chapter13: best-practice Tactics: Game Theory
Section: Chapter Questions
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PROBLEM (3) Consider the differentiated goods Bertrand price competition model where firms A and B
produce similar goods and sell them at pA and på. The demand for each firm's product is given by
qA = 400 - 3pA - 2 pв and q³ = 400 – 3p³ - 2pª, and MC^(q) = ATC₁(qA) = 40 and MC³(q³) = ATC³(q³) = 40.
(a) Are the two goods substitutes or complements? Do the firms want to charge higher prices or lower
prices, the higher the opponent's price? (Is the best response price increasing (or decreasing, or neither) in the
opponent's price?) ♣ Calculate the Bertrand equilibrium prices.
(b) Now suppose the firms -instead of competing to maximize their own individual profits- decide to "collude"
and charge prices to maximize their joint profits (sum of their profits). What would be each firm's optimal
price? Are these prices greater/smaller/the same compared to the prices in (a)?
Transcribed Image Text:PROBLEM (3) Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at pA and på. The demand for each firm's product is given by qA = 400 - 3pA - 2 pв and q³ = 400 – 3p³ - 2pª, and MC^(q) = ATC₁(qA) = 40 and MC³(q³) = ATC³(q³) = 40. (a) Are the two goods substitutes or complements? Do the firms want to charge higher prices or lower prices, the higher the opponent's price? (Is the best response price increasing (or decreasing, or neither) in the opponent's price?) ♣ Calculate the Bertrand equilibrium prices. (b) Now suppose the firms -instead of competing to maximize their own individual profits- decide to "collude" and charge prices to maximize their joint profits (sum of their profits). What would be each firm's optimal price? Are these prices greater/smaller/the same compared to the prices in (a)?
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