Demand and marginal revenue for the two markets are p

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Demand and marginal revenue for the two markets are: P 1 = 15 Q 1 and MR 1 = 15 2Q 1 P 2 = 25 2Q 2 and MR 2 = 25 4Q 2 The monopolist’s total cost is C = 5 + 3(Q 1 + Q 2 ) What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions?
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MR 1 =MR 2 =MC The marginal cost is equal to 3. The profit maximizing quantities in the two markets are: 15 2Q 1 = 3, or Q 1 = 6 (Market 1), and 25 4Q 2 = 3, or Q 2 = 5.5 (Market 2). Substituting into the respective demand equations, prices for the two markets are: P 1= 15 6=Rs.9, and P 2 =25 2(5.5)=Rs.14. Since total quantity produced is 11.5, then π = 9(6) + 14(5.5) – [5 + 3(11.5)] = Rs. 91.50.
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When MC is constant and demand is linear, the monopoly deadweight loss is: DWL = (0.5)(Q c Q M )(P M P C ), where C and M stand for the competitive and monopoly respectively. Here, P C = MC = 3 and Q C in each market is the amount that is demanded when P = Rs.3. The deadweight Losses in the two markets are DWL 1 = (0.5)(12 6)(9 3) = Rs.18, and DWL 2 = (0.5)(11 5.5)(14 3) = Rs.30.25. Therefore, the total deadweight loss is Rs. 48.25.
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MR 1 = 15 2Q 1 and MR 2 = 25 4Q 2 Now, marginal revenue for the market is MR =25-4Q till Q=5 and P=15 (kink in the Demand curve) and then MR=18.33 1.33Q Since MC=3, profit maximizing condition is, 18.33-1.33Q=3. Q=11.5 and P=10.67 With this price, Q 1 = 4.33 and Q 2 = 7.17. MR 1 = 6.34 and MR 2 = 3.68 Profit is: π = 10.67(11.5) – [5 + 3(11.5)] = 83.21.
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DWL 1 = (0.5)(12 4.33)(10.67 3) = 29.41. DWL 2 = (0.5)(11 7.17)(10.67 3) = 14.69. Total deadweight loss is 44.10. Without price discrimination, profit is lower, but deadweight loss is also lower, and total output is unchanged. The big winners are consumers in market 2 who now pay 10.67 instead of 14. DWL in market 2 drops from 30.25 to 14.69. Consumers in market 1 and the monopolist are worse off when price discrimination is not allowed.
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