Unformatted text preview: PHALL82241 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 1101.EPS PHALL82241 PINDYCK CHAPTER 11 page 8 of 30 FIGURE 11.2 Additional Profit from Perfect FirstDegree 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 1102.EPS Quantity PHALL82241 PINDYCK CHAPTER 11 FIGURE 11.3 FirstDegree 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 1103.EPS page 9 of 30 PHALL82241 PINDYCK CHAPTER 11 page 10 of 30 FIGURE 11.4 SecondDegree 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. Seconddegree price discrimination
can then make consumers better off by expanding output and lowering cost. Fig 1104.EPS PHALL82241 PINDYCK CHAPTER 11 page 11 of 30 FIGURE 11.5 ThirdDegree 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 1105.EPS PHALL82241 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 thirddegree 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 1106.EPS PHALL82241 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 1107.EPS Quantity PHALL82241 PINDYCK CHAPTER 11 page 14 of 30 FIGURE 11.8 PeakLoad 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 1108.EPS PHALL82241 PINDYCK CHAPTER 11 FIGURE 11.9 TwoPart 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 1109.EPS page 15 of 30 PHALL82241 PINDYCK CHAPTER 11 FIGURE 11.10 TwoPart Tariff with Two Consumers $/Q T*
A P*
B MC
D1 C
D2 Q2 Q1 Quantity The profitmaximizing 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 1110.EPS page 16 of 30 PHALL82241 PINDYCK CHAPTER 11 page 17 of 30 FIGURE 11.11 TwoPart 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 1111.EPS PHALL82241 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 1112.EPS PHALL82241 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 1113.EPS PHALL82241 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 1114.EPS PHALL82241 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 1115.EPS PHALL82241 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 1116.EPS PHALL82241 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 1117.EPS r1 PHALL82241 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 1118.EPS r1 PHALL82241 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 1119.EPS r1 PHALL82241 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 grayshaded 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 1120.EPS PHALL82241 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 A1101.eps PHALL82241 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 A1102.eps PHALL82241 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 A1103.eps PHALL82241 PINDYCK CHAPTER 11 page 30 of 30 FIGURE A11.4 Race Car MotorsA 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 A1104.eps ...
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 Spring '11
 Prof.Eco
 Consumer Surplus, race car, mR T, mc E, PHALL82241 PINDYCK CHAPTER

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