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Answer to Question #67989 in Microeconomics for Cairna

Question #67989
Two firms, Alpha Vineyard and Beta Winery, produce and sell wine. The demand for
Alpha’s wine is given by the equation,
QA = 200 − PA + PB.
In this equation, the price of Alpha’s wine is PA per bottle, and the price of Beta’s wine is
PB per bottle. Alpha Vineyard has a marginal cost of MC A = $20 per bottle, and a fixed
cost of FC A = $6000. The demand for Beta’s wine is given by the equation,
QB = 9000 − 100PB + 40PA.

Which firm has the greater market power? Explain.
Expert's answer
Two firms, Alpha Vineyard and Beta Winery, produce and sell wine.
QA = 200 − PA + PB, PA = 200 - QA + PB, MC A = $20 per bottle, FC A = $6000, QB = 9000 − 100PB + 40PA, PB = MC B = $10 per bottle, FC B =$10,000.
Total quantity demanded is: Q = 9200 + 39PA - 99PB.
We can decide, that firms set the same price for their homogeneous product, so PA = PB and Q = 9200 - 60P.
To calculate firm's market power we should use Lerner index L = (P - MC)/P.
LA = (PA - 20)/PA, LB = (PB - 10)/PB, so LA < LB, if PA = PB.

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