Practice Questions_Chap 11

Practice Questions_Chap 11 - PracticeQuestions Question5 A...

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Practice Questions Pricing with Market Power Question 5 A   monopolist   is   deciding   how   to   allocate   output   between   two   geographically  separated markets (East Coast and Midwest).  Demand and marginal revenue for the  two markets are: P 1  = 15 - Q 1 MR 1  = 15 - 2Q 1 P 2  = 25 - 2Q 2 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? With price discrimination, the monopolist chooses quantities in each market such  that the marginal revenue in each market is equal to marginal cost.  The marginal  cost is equal to 3 (the slope of the total cost curve). In the first market 15 - 2 Q 1  = 3, or  Q 1  = 6. In the second market 25 - 4 Q 2  = 3, or  Q 2  = 5.5. Substituting into the respective demand equations, we find the following prices for  the two markets: P 1  = 15 - 6 = $9  and                  P 2  = 25 - 2(5.5) = $14. Noting that the total quantity produced is 11.5, then π  = ((6)(9) + (5.5)(14)) - (5 + (3)(11.5)) = $91.5. The monopoly deadweight loss in general is equal to       DWL  = (0.5)( Q C  - Q M )( P M  - P C   ). Here, DWL 1  = (0.5)(12 - 6)(9 - 3) = $18  and                  DWL 2  = (0.5)(11 - 5.5)(14 - 3) = $30.25. Therefore, the total deadweight loss is $48.25.
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Without price discrimination, the monopolist must charge a single price for the  entire market.  To maximize profit, we find quantity such that marginal revenue is  equal to marginal cost.  Adding demand equations, we find that the total demand  curve has a kink at  Q  = 5:      P = 25 - 2 Q , if Q 5 18.33 - 0.67 Q , if Q 5 . This implies marginal revenue equations of MR = 25 - 4 Q , if Q 5 18.33 - 1.33 Q , if Q 5 . With marginal cost equal to 3,  MR  = 18.33 - 1.33 Q  is relevant here because the  marginal   revenue   curve   “kinks”   when   P   =   $15.     To   determine   the   profit- maximizing quantity, equate marginal revenue and marginal cost: 18.33 - 1.33 Q  = 3, or  Q  = 11.5. Substituting the profit-maximizing quantity into the demand equation to determine price: P  = 18.33 - (0.67)(11.5) = $10.6. With this price,  Q 1  = 4.3 and  Q 2  = 7.2.  (Note that at these quantities  MR 1  = 6.3 and  MR 2  = -3.7). Profit is
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This note was uploaded on 04/19/2011 for the course ECON 101 taught by Professor Gul during the Spring '11 term at Lahore School of Economics.

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Practice Questions_Chap 11 - PracticeQuestions Question5 A...

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