P1+10p2 + 5p3. p2 + 10p1 + 5p3. Op3 + 5p1 + 5p2.

FINANCIAL ACCOUNTING
10th Edition
ISBN:9781259964947
Author:Libby
Publisher:Libby
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
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A6
Three firms compete in the style of Bertrand. All firms have the same cost function: TC(q) = 8q. They produce
differentiated products that are substitutes. The demand system is given by the following equations:
Demand for Firm 1: q1 = 95 – 20p1 + 10p2 + 5p3.
Demand for Firm 2: q2 = 95– 20p2 + 10p1 + 5p3.
Demand for Firm 3: q3 = 100 – 20p3 + 5p1 + 5p2.
A. Please compute the Nash equilibrium prices.
B. Now suppose firm 1 and firm 2 merge and become a single firm. Firm 3 and the merged firm compete in the style
of Bertrand. Now, p1 and p2 are chosen to maximize the total profits of firm 1 and firm 2. Compute the Nash
equilibrium prices now.
Transcribed Image Text:Three firms compete in the style of Bertrand. All firms have the same cost function: TC(q) = 8q. They produce differentiated products that are substitutes. The demand system is given by the following equations: Demand for Firm 1: q1 = 95 – 20p1 + 10p2 + 5p3. Demand for Firm 2: q2 = 95– 20p2 + 10p1 + 5p3. Demand for Firm 3: q3 = 100 – 20p3 + 5p1 + 5p2. A. Please compute the Nash equilibrium prices. B. Now suppose firm 1 and firm 2 merge and become a single firm. Firm 3 and the merged firm compete in the style of Bertrand. Now, p1 and p2 are chosen to maximize the total profits of firm 1 and firm 2. Compute the Nash equilibrium prices now.
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