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CHAPTER 11 - PHALL-82241 PINDYCK CHAPTER 11 page 7 of 30...

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Unformatted text preview: PHALL-82241 PINDYCK CHAPTER 11 page 7 of 30 FIGURE 11.1 Capturing Consumer Surplus Pmax $/Q P1 A P* B P2 MC Pc D MR Q* Quantity If a firm can charge only one price for all its customers, that price will be P* and the quantity produced will be Q*. Ideally, the firm would like to charge a higher price to consumers willing to pay more than P*, thereby capturing some of the consumer surplus under region A of the demand curve. The firm would also like to sell to consumers willing to pay prices lower than P*, but only if doing so does not entail lowering the price to other consumers. In that way, the firm could also capture some of the surplus under region B of the demand curve. Fig 11-01.EPS PHALL-82241 PINDYCK CHAPTER 11 page 8 of 30 FIGURE 11.2 Additional Profit from Perfect First-Degree Price Discrimination Pmax $/Q Consumer surplus when a single price P * is charged Variable profit when a single price P * is charged Additional profit from perfect price discrimination P* MC Pc D � AR MR Q* Q* * Because the firm charges each consumer her reservation price, it is profitable to expand output to Q**. When only a single price, P*, is charged, the firm’s variable profit is the area between the marginal revenue and marginal cost curves. With perfect price discrimination, this profit expands to the area between the demand curve and the marginal cost curve. Fig 11-02.EPS Quantity PHALL-82241 PINDYCK CHAPTER 11 FIGURE 11.3 First-Degree Price Discrimination in Practice $/Q P1 P2 P3 P* 4 MC P5 P6 D MR Quantity Firms usually don’t know the reservation price of every consumer, but sometimes reservation prices can be roughly identified. Here, six different prices are charged. The firm earns higher profits, but some consumers may also benefit. With a single price , there are fewer consumers. The consumers who now pay P5 or P6 enjoy a surplus. Fig 11-03.EPS page 9 of 30 PHALL-82241 PINDYCK CHAPTER 11 page 10 of 30 FIGURE 11.4 Second-Degree Price Discrimination $/Q P1 P0 P2 AC P3 MC D MR Q1 1st Block Q0 2nd Block Q2 Q3 Quantity 3rd Block Different prices are charged for different quantities, or “blocks,” of the same good. Here, there are three blocks, with corresponding prices P1, P2, and P3. There are also economies of scale, and average and marginal costs are declining. Second-degree price discrimination can then make consumers better off by expanding output and lowering cost. Fig 11-04.EPS PHALL-82241 PINDYCK CHAPTER 11 page 11 of 30 FIGURE 11.5 Third-Degree Price Discrimination $/Q P1 MC P2 D2 � AR2 MR T MR 1 Q1 MR 2 D1 � AR1 Q2 QT Quantity Consumers are divided into two groups, with separate demand curves for each group. The optimal prices and quantities are such that the marginal revenue from each group is the same and equal to marginal cost. Here group 1, with demand curve D1, is charged P1, and group 2, with the more elastic demand curve D2, is charged the lower price P2. Marginal cost depends on the total quantity produced QT. Note that Q1 and Q2 are chosen so that MR1 = MR2 = MC. Fig 11-05.EPS PHALL-82241 PINDYCK CHAPTER 11 page 12 of 30 FIGURE 11.6 No Sales to Smaller Market $/Q MC P* D2 MR 2 D1 MR1 Q* Quantity Even if third-degree price discrimination is feasible, it may not pay to sell to both groups of consumers if marginal cost is rising. Here the first group of consumers, with demand D1, are not willing to pay much for the product. It is unprofitable to sell to them because the price would have to be too low to compensate for the resulting increase in marginal cost. Fig 11-06.EPS PHALL-82241 PINDYCK CHAPTER 11 page 13 of 30 FIGURE 11.7 Intertemporal Price Discrimination $/Q P1 P2 D2 � AR2 AC � MC MR2 MR1 Q1 D1 � AR1 Q2 Consumers are divided into groups by changing the price over time. Initially, the price is high. The firm captures surplus from consumers who have a high demand for the good and who are unwilling to wait to buy it. Later the price is reduced to appeal to the mass market. Fig 11-07.EPS Quantity PHALL-82241 PINDYCK CHAPTER 11 page 14 of 30 FIGURE 11.8 Peak-Load Pricing $/Q MC P1 D1 � AR 1 P2 MR 1 D 2 � AR 2 MR 2 Q2 Q1 Quantity Demands for some goods and services increase sharply during particular times of the day or year. Charging a higher price P1 during the peak periods is more profitable for the firm than charging a single price at all times. It is also more efficient because marginal cost is higher during peak periods. Fig 11-08.EPS PHALL-82241 PINDYCK CHAPTER 11 FIGURE 11.9 Two-Part Tariff with a Single Consumer $/Q P* T* MC D Quantity The consumer has demand curve D. The firm maximizes profit by setting usage fee P equal to marginal cost and entry fee T* equal to the entire surplus of the consumer. Fig 11-09.EPS page 15 of 30 PHALL-82241 PINDYCK CHAPTER 11 FIGURE 11.10 Two-Part Tariff with Two Consumers $/Q T* A P* B MC D1 C D2 Q2 Q1 Quantity The profit-maximizing usage fee P* will exceed marginal cost. The entry fee T* is equal to the surplus of the consumer with the smaller demand. The resulting profit is 2T* + (P* ? MC)(Q1 + Q2). Note that this profit is larger than twice the area of triangle ABC. Fig 11-10.EPS page 16 of 30 PHALL-82241 PINDYCK CHAPTER 11 page 17 of 30 FIGURE 11.11 Two-Part Tariff with Many Different Consumers Profit � Total �s T* �a T Total profit is the sum of the profit from the entry fee a and the profit from sales s. Both a and s depend on T, the entry fee. Therefore = a + s = n(T)T + (P? MC)Q(n) where n is the number of entrants, which depends on the entry fee T, and Q is the rate of sales, which is greater the larger is n. Here T* is the profitmaximizing entry fee, given P. To calculate optimum values for P and T, we can start with a number for P, find the optimum T, and then estimate the resulting profit. P is then changed and the corresponding T recalculated, along with the new profit level. Fig 11-11.EPS PHALL-82241 PINDYCK CHAPTER 11 page 18 of 30 FIGURE 11.12 Reservation Prices r2 C $10 $6 $5 A B $3.25 $3.25 $5 $8.25 $10 r1 Reservation prices r1 and r2 for two goods are shown for three consumers, labeled A, B, and C. Consumer A is willing to pay up to $3.25 for good 1 and up to $6 for good 2. Fig 11-12.EPS PHALL-82241 PINDYCK CHAPTER 11 page 19 of 30 FIGURE 11.13 Consumption Decisions When Products Are Sold Separately r2 II I Consumers buy only good 2 Consumers buy both goods P2 III IV Consumers buy neither good Consumers buy only good 1 P1 r1 The reservation prices of consumers in region I exceed the prices P1 and P2 for the two goods, so these consumers buy both goods. Consumers in regions II and IV buy only one of the goods, and consumers in region III buy neither good. Fig 11-13.EPS PHALL-82241 PINDYCK CHAPTER 11 page 20 of 30 FIGURE 11.14 Consumption Decisions When Products Are Bundled r2 I Consumers buy bundle PB r2 = PB – r1 II Consumers do not buy bundle PB r1 Consumers compare the sum of their reservation prices r1 + r2, with the price of the bundle PB. They buy the bundle only if r1 + r2 is at least as large as PB. Fig 11-14.EPS PHALL-82241 PINDYCK CHAPTER 11 page 21 of 30 FIGURE 11.15 Reservation Prices r2 r2 PB P2 P1 (a) r1 PB r1 (b) In (a), because demands are perfectly positively correlated, the firm does not gain by bundling: It would earn the same profit by selling the goods separately. In (b), demands are perfectly negatively correlated. Bundling is the ideal strategyall the consumer surplus can be extracted. Fig 11-15.EPS PHALL-82241 PINDYCK CHAPTER 11 page 22 of 30 FIGURE 11.16 Movie Example (Gertie) r2 $10,000 5000 B 4000 A 3000 $5000 10,000 12,000 14,000 r1 (Wind) Consumers A and B are two movie theaters. The diagram shows their reservation prices for the films Gone with the Wind and Getting Gertie’s Garter. Because the demands are negatively correlated, bundling pays. Fig 11-16.EPS PHALL-82241 PINDYCK CHAPTER 11 page 23 of 30 FIGURE 11.17 Mixed versus Pure Bundling r2 c1 � $20 $100 A 90 80 70 60 B 50 C 40 30 c2 � $30 20 D 10 $10 20 30 40 50 60 70 80 90 100 With positive marginal costs, mixed bundling may be more profitable than pure bundling. Consumer A has a reservation price for good 1 that is below marginal cost c1, and consumer D has a reservation price for good 2 that is below marginal cost c2. With mixed bundling, consumer A is induced to buy only good 2, and consumer D is induced to buy only good 1, thus reducing the firm’s cost. Fig 11-17.EPS r1 PHALL-82241 PINDYCK CHAPTER 11 page 24 of 30 FIGURE 11.18 Mixed Bundling with Zero Marginal Costs r2 $120 100 90 A B 80 60 C 40 20 D 10 $10 20 40 60 80 90 100 120 If marginal costs are zero, and if consumers’ demands are not perfectly negatively correlated, mixed bundling is still more profitable than pure bundling. In this example, consumers B and C are willing to pay $20 more for the bundle than are consumers A and D. With pure bundling, the price of the bundle is $100. With mixed bundling, the price of the bundle can be increased to $120 and consumers A and D can still be charged $90 for a single good. Fig 11-18.EPS r1 PHALL-82241 PINDYCK CHAPTER 11 page 25 of 30 FIGURE 11.19 Mixed Bundling in Practice r2 PB III—Buy Only Good 2 II—Buy Bundle P2 I—Buy Nothing IV—Buy Only Good 1 P1 PB The dots in this figure are estimates of reservation prices for a representative sample of consumers. A company could first choose a price for the bundle, PB, such that a diagonal line connecting these prices passes roughly midway through the dots. The company could then try individual prices P1 and P2. Given P1, P2, and PB, profits can be calculated for this sample of consumers. Managers can then raise or lower P1, P2, and PB and see whether the new pricing leads to higher profits. This procedure is repeated until total profit is roughly maximized. Fig 11-19.EPS r1 PHALL-82241 PINDYCK CHAPTER 11 page 26 of 30 FIGURE 11.20 Effects of Advertising $/Q π1 MC P1 AR ′ AC ′ AC P0 π0 MR ′ AR MR Q0 Q1 Quantity AR and MR are average and marginal revenue when the firm doesn’t advertise, and AC and MC are average and marginal cost. The firm produces Q0 and receives a price P0. Its total profit 0 is given by the gray-shaded rectangle. If the firm advertises, its average and marginal revenue curves shift to the right. Average cost rises (to AC?) but marginal cost remains the same. The firm now produces Q1 (where MR? = MC), and receives a price P1. Its total profit, 1, is now larger. Fig 11-20.EPS PHALL-82241 PINDYCK CHAPTER 11 page 27 of 30 FIGURE A11.1 Race Car Motors, Inc. $/Q PA MCE AR PE MCA MR QA = Q E Quantity NMRE = (MR – MCA) The firm’s upstream division should produce a quantity of engines QE that equates its marginal cost of engine production MCE with the downstream division’s net marginal revenue of engines NMRE. Because the firm uses one engine in every car, NMRE is the difference between the marginal revenue from selling cars and the marginal cost of assembling them, i.e., MR ? MCA. The optimal transfer price for engines PE equals the marginal cost of producing them. Finished cars are sold at price PA. Fig A11-01.eps PHALL-82241 PINDYCK CHAPTER 11 page 28 of 30 FIGURE A11.2 Buying Engines in a Competitive Outside Market $/Q PA MCE AR PE, M MCA MC E * MR Q E, 1 Q E, 2 � QE Quantity NMRE = ( MR � MCA) Race Car Motors’ marginal cost of engines is the upstream division’s marginal cost for quantities up to QE,1 and the market price PE,M for quantities above QE,1. The downstream division should use a total of QE,2 engines to produce an equal number of cars; in that case, the marginal cost of engines equals net marginal revenue. QE,2 ? QE,1 of these engines are bought in the outside market. The downstream division “pays” the upstream division the transfer price PE,M for the remaining QE,1 engines. Fig A11-02.eps PHALL-82241 PINDYCK CHAPTER 11 page 29 of 30 FIGURE A11.3 Selling Engines in a Competitive Outside Market $/Q PA MCE PE, M MC E * AR MCA MR Q E, 2 � QA Q E, 1 Quantity NMRE = ( MR � MCA) The optimal transfer price for Race Car Motors is again the market price PE,M. This price is above the point at which MCE intersects NMRE, so the upstream division sells some of its engines in the outside market. The upstream division produces QE,1 engines, the quantity at which MCE equals PE,M. The downstream division uses only QE,2 of these engines, the quantity at which NMRE equals PE,M. Compared with Figure A11.1, in which there is no outside market, more engines but fewer cars are produced. Fig A11-03.eps PHALL-82241 PINDYCK CHAPTER 11 page 30 of 30 FIGURE A11.4 Race Car Motors-A Monopoly Supplier of Engines to an Outside Market $/Q PA MCE PE, M AR P* E NMRE DE,M MCA MRE,M MR Q E, 3 Q E, 2 � QA Q E, 1 Quantity ( MR � MCA ) DE,M is the outside market demand curve for engines; MRE,M is the corresponding marginal revenue curve; (MR ? MCA) is the net marginal revenue from the use of engines by the downstream division. The total net marginal revenue curve for engines NMRE is the horizontal sum of these two marginal revenues. The optimal transfer price and the quantity of engines that the upstream division produces, QE,1, are found where MCE = NMRE. QE,2 of these engines are used by the downstream division, the quantity at which the downstream division’s net marginal revenue, MR ? MCA, is equal to the transfer price . The remaining engines, QE,3, are sold in the outside market at the price PE,M. Fig A11-04.eps ...
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