Problem 3. (Third Degree Price Discrimination) (16 points) A company sells ident
ID: 1134294 • Letter: P
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Problem 3. (Third Degree Price Discrimination) (16 points) A company sells identical products in two separate geographic regions: East Coast and Midwest The firm has estimated the following demand curves for each market: P1 60 0.25q1 (Midwest) P2 100 0.5q2 (East Coast) The firm's total cost function is given as: TC = 40Q and Q = q1 + q2 If the company can practice third-degree price discrimation, calculate the following in each market 1) What is the company's profit-maximizing price & quantity in Midwest? (4 points) 2) What is the company's profit-maximizing price & quantity on East Coast? (4 points) 3) At the profit-maximizing solution, calculate own-price elasticity in Midwest & East Coast; (4 points) 4) Calculate Lerner index in Midwest & East Coast; (4 points)Explanation / Answer
1) In Midwest the firm uses MR = MC rule where MR = 60 - 2*0.25q1 and MC = 40. This gives 60 - 0.5q1 = 40 or q1 = 40 units and P = 60 - 0.25*40 = $50. Hence profit maximizing price in Midwest is $50 and quantity is 40 units
2) In East Coast the firm uses MR = MC rule where MR = 100 - 2*0.5q2 and MC = 40. This gives 100 - q1 = 40 or q1 = 60 units and P = 100 - 0.5*60 = $70. Hence profit maximizing price in East Coast is $70 and quantity is 60 units
3) Own price elasticity has a formula where MC = P (1 - 1/ed) which gives ed = P/(P - MC) .
Hence in Midwest we have ed = 50/50 - 40 = -5 and in East Cost we have 70/70 - 40 = -2.33
4) Lerner Index = 1/|ed| so in Midwest it is 1/5 = 0.20 and in East Coast it is 1/2.33 = 0.43
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