Consider a standard Cournot oligopoly with n ≥ 2 identical firms, P(x) = a - bX, X ≥ 0, and C(x) = cx2. a. Find the Cournot equilibrium output and profit. b. If m firms wish to merge, what would be their cost function, assuming that they can use all their m production plants but that they otherwise do not have any eciency gains as a result of the merger? c. Given the cost function from part b, when is an m-firm merger profitable to the merged entity? To the non merging firms? d. Give a precise economic intuition explaining your answer relative to the usual (linear cost) case.
Consider a standard Cournot oligopoly with n ≥ 2 identical firms, P(x) = a - bX, X ≥ 0, and C(x) = cx2. a. Find the Cournot equilibrium output and profit. b. If m firms wish to merge, what would be their cost function, assuming that they can use all their m production plants but that they otherwise do not have any eciency gains as a result of the merger? c. Given the cost function from part b, when is an m-firm merger profitable to the merged entity? To the non merging firms? d. Give a precise economic intuition explaining your answer relative to the usual (linear cost) case.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Consider a standard Cournot oligopoly with n ≥ 2 identical firms, P(x) = a - bX, X ≥ 0, and C(x) = cx2.
a. Find the Cournot equilibrium output and profit.
b. If m firms wish to merge, what would be their cost function, assuming that they can use all their m production plants but that they otherwise do not have any eciency gains as a result of the merger?
c. Given the cost function from part b, when is an m-firm merger profitable to the merged entity? To the non merging firms?
d. Give a precise economic intuition explaining your answer relative to the usual (linear cost) case.
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Step 1: Describe the effects of merger in the context of a Cournot oligopoly
VIEWStep 2: Find the Cournot equilibrium output and profit
VIEWStep 3: Derive the new cost function
VIEWStep 4: Examine when is an m-firm merger is profitable to the merged and the non merging firms
VIEWStep 5: Give a precise economic intuition explaining relative to the usual (linear cost) case
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