# Answer to Question #67989 in Microeconomics for Cairna

Question #67989

Two firms, Alpha Vineyard and Beta Winery, produce and sell wine. The demand for

Alphaâ€™s wine is given by the equation,

QA = 200 âˆ’ PA + PB.

In this equation, the price of Alphaâ€™s wine is PA per bottle, and the price of Betaâ€™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 Betaâ€™s wine is given by the equation,

QB = 9000 âˆ’ 100PB + 40PA.

Which firm has the greater market power? Explain.

Alphaâ€™s wine is given by the equation,

QA = 200 âˆ’ PA + PB.

In this equation, the price of Alphaâ€™s wine is PA per bottle, and the price of Betaâ€™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 Betaâ€™s wine is given by the equation,

QB = 9000 âˆ’ 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 âˆ’ PA + PB, PA = 200 - QA + PB, MC A = $20 per bottle, FC A = $6000, QB = 9000 âˆ’ 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.

QA = 200 âˆ’ PA + PB, PA = 200 - QA + PB, MC A = $20 per bottle, FC A = $6000, QB = 9000 âˆ’ 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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