Two firms produce complementary products. Suppose the demand for their products is given by q1(p) = a−2p1−p2, and q2(p) = a−p1−2p2. Both firms face a constant marginal costs k, and a fixed cost of 0 (so TCi(qi) = kqi). .For each firm, write profit as a function of prices. Derive the best response function of each firm. Thus, write p1 = R1(p2) as a function of p2, and similarly p2 = R2(p1) as a function of p1. For a = 8 and k = 1, sketch the best response functions on a graph. Are the prices strategic substitutes or complements? Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits. Suppose now the two firms decide to merge as one so that they want to maximize the joint profit πm = π1 +π2. Write down the profit function and derive the first order conditions for maximizing the joint profit. Compute the equilibrium prices, quantities, and profits. Compare the results with when the firms were independent and comment on if the firms are better off with the merger. Are the consumers better off? Problem 1. Two firms produce complementary products. Suppose the demand for their products isgiven by q₁(p) = a-2p1-p2, and q2(p) = a-p₁-2p2. Both firms face a constant marginal costs k, and afixed cost of 0 (so TCi(qi) = kqi).(1) For each firm, write profit as a function of prices.(2) Derive the best response function of each firm. Thus, write p₁ = R₁(p2) as a function of p2, andsimilarly p2 = R₂(p₁) as a function of p₁. For a = 8 and k = 1, sketch the best response functionson a graph. Are the prices strategic substitutes or complements?(3) Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits.(4) Suppose now the two firms decide to merge as one so that they want to maximize the jointprofit π = π₁ +72. Write down the profit function and derive the first order conditions formaximizing the joint profit.(5) Compute the equilibrium prices, quantities, and profits. Compare the results with when thefirms were independent and comment on if the firms are better off with the merger. Are theconsumers better off?

An oligopoly is a market with few large firms, high barriers to entry, and significant…

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Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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Two firms produce complementary products. Suppose the demand for their products is given by q₁(p) = a−2p₁−p₂, and q₂(p) = a−p₁−2p₂. Both firms face a constant marginal costs k, and a fixed cost of 0 (so TC_i(q_i) = kq_i). .

For each firm, write profit as a function of prices.

Derive the best response function of each firm. Thus, write p₁= R₁(p₂) as a function of p₂, and similarly p₂= R₂(p₁) as a function of p₁. For a = 8 and k = 1, sketch the best response functions on a graph. Are the prices strategic substitutes or complements?
Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits.
Suppose now the two firms decide to merge as one so that they want to maximize the joint profit π_m= π₁+π₂. Write down the profit function and derive the first order conditions for maximizing the joint profit.
Compute the equilibrium prices, quantities, and profits. Compare the results with when the firms were independent and comment on if the firms are better off with the merger. Are the consumers better off?

Problem 1. Two firms produce complementary products. Suppose the demand for their products is
given by q₁(p) = a-2p1-p2, and q2(p) = a-p₁-2p2. Both firms face a constant marginal costs k, and a
fixed cost of 0 (so TCi(qi) = kqi).
(1) For each firm, write profit as a function of prices.
(2) Derive the best response function of each firm. Thus, write p₁ = R₁(p2) as a function of p2, and
similarly p2 = R₂(p₁) as a function of p₁. For a = 8 and k = 1, sketch the best response functions
on a graph. Are the prices strategic substitutes or complements?
(3) Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits.
(4) Suppose now the two firms decide to merge as one so that they want to maximize the joint
profit π = π₁ +72. Write down the profit function and derive the first order conditions for
maximizing the joint profit.
(5) Compute the equilibrium prices, quantities, and profits. Compare the results with when the
firms were independent and comment on if the firms are better off with the merger. Are the
consumers better off?

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How do you know that the equillibrium prices are lower, the quantities produced are higher and the profits produced are lower in the merged scenario

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Let a = 8 and k = 1. Compute the equilibrium prices, quantities and profits. .

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Suppose now the two firms decide to merge as one so that they want to maximize the joint profit π_m= π₁+π₂. Write down the profit function and derive the first order conditions for maximizing the joint profit.

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Compute the equilibrium prices, quantities, and profits. Compare the results with when the firms were independent and comment on if the firms are better off with the merger. Are the consumers better off?

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