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Dokumen - CH12
Microeconomic (國立高雄大學)
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Besanko & Braeutigam – Microeconomics, 5th editionSolutions Manual
Chapter 12
Capturing Surplus
Solutions to Review Questions
1. Why must a firm have at least some market power to price discriminate?
If a firm has no market power it will not be able to price discriminate to increase profits.
Without market power the firm is a price taker and has no abilit to set different prices for
different units of output. !s the firm attempts to set higher prices for some units, consumers will
simpl purchase elsewhere if the firm has no market power.
2. Does a firm need to be a monopolist to price discriminate?
"o, a firm does not need to be a monopolist to price discriminate. #he firm simpl needs to ha$e
market power and face a downward sloping demand cur$e.
. Why must a firm prevent resale if it is to price discriminate successfully?
If the firm cannot pre$ent resale, then customers who bu at a low price can act as middlemen
and resell the goods to customers willing to pa more. In this case the firm won%t earn the
additional surplus the middlemen will capture the surplus instead of the firm.
!. What are the differences among first"degree# second degree# and third"degree price
discrimination?
With first'degree price discrimination, the firm charges each consumer a price close to the
consumer%s ma(imum willingness to pa. In this wa, the firm is able to e(tract $irtuall all the
a$ailable surplus for itself. With second'degree price discrimination, the firm offers )uantit
discounts. #his induces some customers to purchase more than the would if all units were
priced the same. With third'degree price discrimination the firm charges different prices to
different market segments. *or e(ample, the firm might charge a lower price to students and
senior citi+ens to induce them to purchase when the might not otherwise.
$. With first"degree price discrimination# why is the marginal revenue curve the same as
the demand curve?
With perfect first'degree price discrimination the marginal re$enue and demand cur$es are the
same. #his is because with perfect first'degree price discrimination the firm charges each
consumer their ma(imum willingness to pa, as measured b the demand cur$e. #herefore, the
demand cur$e represents the additional re$enue the firm will bring in for each additional unit it
sells, or marginal re$enue. "ote, with perfect first'degree price discrimination the firm charges
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each indi$idual a different price, so as it lowers its price to gain marginal customers it doesn%t
lose re$enue on the inframarginal customers who would ha$e paid a higher price.
%. &ow large will the deadweight loss be if a profit ma'imi(ing firm engages in perfect first"
degree price discrimination?
With perfect first'degree price discrimination there is no deadweight loss. #he outcome is
economicall efficient because e$er consumer who purchases the good has a willingness to pa
meeting or e(ceeding the marginal cost of production and e$er consumer who does not recei$e
the good has a willingness to pa below marginal cost. "ote, howe$er, that while there is no
deadweight loss, all of the surplus is captured b the firm lea$ing no consumer surplus.
). What is the difference between a uniform price and a nonuniform *nonlinear+ price?
,ive an e'ample of a nonlinear price.
With a uniform price the firm sells e$er unit to e$er consumer at the same price. With non'
uniform or nonlinear pricing, the firm charges different prices for different units of output. *or
e(ample, a telephone compan might charge each user a subscription fee of 30/ and then a usage
fee of 3/./5 per call. "onlinear pricing is one tpe of second'degree price discrimination. With
second'degree price discrimination, the firm charges a lower average price to consumers who are
willing to bu large )uantities of the good.
-. Suppose a company is currently charging a uniform price for its two products# creamy
and crunchy peanut butter. Will third"degree price discrimination necessarily improve its
profit? Would the firm ever be worse off with price discrimination?
#he firm could ne$er do worse with third'degree price discrimination than without it because the
firm could alwas charge the uniform price and earn the same profit. So long as the firm can
reliabl identif a difference in willingness to pa among its customers and pre$ent resale, third'
degree price discrimination should in fact increase its profits.
. &ow might screening help a firm price discriminate? ,ive an e'ample of screening and
e'plain how it works.
Screening is a mechanism that allows a firm to sort consumers according to their willingness to
pa or their price elasticit of demand. *or e(ample, the firm might screen the consumers based
on some obser$able consumer characteristic such as age. #his allows the firm to charge a price
closer to the consumer%s willingness to pa gi$en that the characteristic, such as age, is correlated
with willingness to pa. In addition, because the characteristic is obser$able, it is possible for the
firm to pre$ent arbitrage.
1/. Why might a firm try to implement a tying arrangement? What is the difference
between tying and bundling?
! firm implementing a ting arrangement tries to force a consumer to purchase another product
from the firm in addition to the original product when it is unable to price discriminate on the
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original product. In this wa the firm can earn e(tranormal profits on the supplemental product
that it could not on the original product. !n e(ample would be a computer manufacturer that
allowed onl its software to operate on the computer. In this wa, while the firm might not be
able to price discriminate and earn e(tra profit on the sale of the computer, it can force the
consumer to onl purchase software from the firm and charge a higher price for the software than
it would if the consumer were allowed to use an software. In this wa the firm increases its
profits.
#here is a difference between ting and bundling. #ing re)uires that if ou bu product !, ou
must also bu product B. 4owe$er, it%s possible to purchase product B the tied product6
indi$iduall. Bundling re)uires that ! and B can onl be purchased together, in a package.
11. &ow might bundling increase a firm0s profits? When is bundling not likely to increase
profits?
Bundling can increase the firm%s profits when demands for products are negati$el correlated.
#his means that consumers who are willing to pa more for one good than another consumer are
willing to pa less for another good than another consumer. B bundling the products, the
consumers are induced to bu both products, allowing the firm to earn profits from both
consumers on both goods, increasing total profits. Bundling is not likel to increase profits when
demands for products are not negati$el correlated. If one consumer is willing to pa more for
both goods, the firm is unlikel to be able to increase profits b bundling goods.
12. ven if a monopolist knows that advertising shifts the demand curve for its product to
the right# why might it decide not to advertise at all? f it does advertise# what factors
determine how much advertising it will do?
While ad$ertising will shift the demand cur$e to the right, ad$ertising is costl. ! firm would
not choose to ad$ertise if the increase in total re$enue associated with the demand cur$e shifting
to the right did not e(ceed the ad$ertising costs necessar to induce the shift in demand. #he
amount of ad$ertising a firm will purchase will depend primaril on the firm%s price elasticit of
demand and on the firm%s ad$ertising elasticit of demand. In particular, the ad$ertising'to'sales
ratio should be
ε Q, A
A
PQ
=−
ε Q ,P
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Solutions to Problems
12.1. Which of the following are e'amples of first"degree# second"degree# or third"degree
price discrimination?
a+ 3he publishers of the Journal of Price Discrimination charge a subscription price of 4)$
per year to individuals and 4// per year to libraries.
b+ 3he 5.S. government auctions off leases on tracts of land in the ,ulf of 6e'ico. 7il
companies bid for the right to e'plore each tract of land and to e'tract oil.
c+ 8e 7lde Country Club charges golfers 412 to play the first  holes of golf on a given day#
4 to play an additional  holes# and 4% to play  more holes.
d+ 3he telephone company charges you 4/.1/ per minute to make a long"distance call from
6onday through Saturday and 4/./$ per minute on Sunday.
e+ 8ou can buy one computer disk for 41/# a pack of  for 42)# or a pack of 1/ for 4)$.
f+ When you fly from 9ew 8ork to Chicago# the airline charges you 42$/ if you buy your
ticket 1! days in advance# but 4$/ if you buy the ticket on the day of travel.
a6
#hird degree – the firm is charging a different price to different market segments,
indi$iduals and libraries.
b6
*irst degree – each consumer is paing near their ma(imum willingness to pa.
c6
Second degree – the firm is offering )uantit discounts. !s the number of holes plaed
goes up, the a$erage e(penditure per hole falls.
d6
#hird degree – the firm is charging different prices for different segments. Business
customers M'*6 are being charged a higher price than those using the phone on Sunda, e.g.,
famil calls.
e6
Second degree – the firm is offering a )uantit discount.
f6
#hird degree – the airline is charging different prices to different segments. #hose who
can purchase in ad$ance pa one price while those who must purchase with short notice pa a
different price.
12.2. Suppose a profit"ma'imi(ing monopolist producing Q units of output faces the
demand curve P : 2/ " Q. ts total cost when producing Q units of output is TC : 2! ; Q2.
3he fi'ed cost is sunk# and the marginal cost curve is MC : 2Q.
a+ f price discrimination is impossible# how large will the profit be? &ow large will the
producer surplus be?
b+ Suppose the firm can engage in perfect first"degree price discrimination. &ow large will
the profit be? &ow large is the producer surplus?
c+ &ow much e'tra surplus does the producer capture when it can engage in first"degree
price discrimination instead of charging a uniform price?
a6
If price discrimination is impossible the firm will set MR = MC .
/ − Q = Q
Q=5
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!t this )uantit, price will be P = 05 , total re$enue will be TR = 85 , total cost will be TC = 19 ,
and profit will be π = : . ;roducer surplus is total re$enue less non'sunk cost, or, in this case,
total re$enue less $ariable cost. #hus producer surplus is 85 − 5 = 5/ .
b6
With perfect first'degree price discrimination the firm sets P = MC to determine the
le$el of output.
/ − Q = Q
Q = :.:8
#he price charged each consumer, howe$er, will $ar. #he price charged will be the consumer%s
ma(imum willingness to pa and will correspond with the demand cur$e. #otal re$enue will be
the area underneath the demand cur$e out to Q = :.:8 units, or /.5/ – 07.776:.:86 <
07.77:.:86 = 000.0:. Since the firm is producing a total of :.:8 units, total cost will be
TC = :>.19 . ;rofit is then π = 1.:8 , while producer surplus is re$enue less $ariable cost, or
000.0: − :.:8 = ::.:8 .
c6
B being able to emplo perfect first'degree price discrimination the firm increases profit
and producer surplus b 0:.:8.
12.. Suppose a monopolist producing Q units of output faces the demand curve P : 2/ " Q.
ts total cost when producing Q units of output is TC : F ; Q2# where F is a fi'ed cost. 3he
marginal cost is MC : 2Q.
a+ <or what values of F can a profit"ma'imi(ing firm charging a uniform price earn at least
(ero economic profit?
b+ <or what values of F can a profit"ma'imi(ing firm engaging in perfect first"degree price
discrimination earn at least (ero economic profit?
a6
With demand P = / − Q , MR = / − Q . ! profit'ma(imi+ing firm charging a uniform
price will set MR = MC .
/ − Q = Q
Q=5
!t this )uantit, price will be P = 05 . !t this price and )uantit profit will be
π =
0556 −  F + 5 6
π =
5/ − F
#herefore, the firm will earn positi$e profit as long as F < 5/ .
b6
! firm engaging in first'degree price discrimination with this demand will produce where
demand intersects marginal cost? / – Q = Q or Q = :.:8 units. Its total re$enue will be the
area underneath the demand cur$e out to Q = :.:8 units
TR = .5/ − 07.776:.:86 + 07.77:.:86 = 000.0: . ;rofit will be
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= 000.0: − F + :.:8 6
π = ::.:8 − F
π
#herefore, profit will be positi$e as long as F < ::.:8 . omparing the solution to parts a6 and
b6, for $alues of F between 5/ and ::.:8 the firm would be unwilling to operate unless it is able
to practice first'degree price discrimination.
12.!. = firm serving a market operates with total variable cost TVC : Q2. 3he
corresponding marginal cost is MC : 2Q. 3he firm faces a market demand represented by
P : !/ " Q.
a+ Suppose the firm sets the uniform price that ma'imi(es profit. What would that price
be?
b+ Suppose the firm were able to act as a perfect first degree price"discriminating
monopolist. &ow much would the firm0s profit increase compared with the uniform profit"
ma'imi(ing price you found in *a+?
a6
#he firm would ma(imi+e profit b producing until MR = MC, or 1/ – :Q = Q. #hus Q
= 5 and the profit'ma(imi+ing price is P = 5. With MC = Q and no fi(ed costs, its total costs
are C = Q, so π = 556 – 5 = 0//.
b6
With perfect first degree price discrimination, the firm will charge a price on the demand
cur$e for all units up to the )uantit at which the demand cur$e intersects the marginal cost
cur$e. #he demand cur$e intersects the marginal cost cur$e when 1/ – 7Q = Q, or when Q = >.
#otal re$enue will be the area under the demand cur$e, or /.51/ – 0:6> < 0:>6 = 1. #otal
$ariable cost is the area of the triangle under its marginal cost cur$e up to the )uantit produced,
that is, /.50:6>6 = :1. @conomic profit will be 1 – :1 = 0:/. So b price discriminating, the
firm will be able to earn an e(tra profit of 0:/ – 0//6 = :/.
12.$. = natural monopoly e'ists in an industry with a demand schedule P : 1// " Q. 3he
marginal revenue schedule is then MR : 1// " 2Q. 3he monopolist operates with a fi'ed
cost F# and a total variable cost TVC : 2/Q. 3he corresponding marginal cost is thus
constant and e>ual to 2/.
a+ Suppose the firm sets a uniform price to ma'imi(e profit. What is the largest value of F
for which the firm could earn (ero profit?
b+ Suppose the firm is able to engage in perfect first degree price discrimination. What is
the largest value of F for which the firm could earn (ero profit?
a6
When the firm sets a uniform price, it sets MR = MC? 0// – Q = /. #he )uantit that
ma(imi+es profit is therefore Q = 1/. #he profit ma(imi+ing uniform price is P = 0// – Q = 0//
– 1/ = :/. ;rofit is PQ – F -/Q = :/61/6 – F – /61/6 = 0:// – F. So the firm could earn at
least +ero economic profit as long as F A 0://.
b6
With perfect first degree price discrimination, the firm will charge a price on the demand
cur$e for all units up to the )uantit at which the demand cur$e intersects the marginal cost
cur$e. #he demand cur$e intersects the marginal cost cur$e when 0// – Q = /, or when Q = >/.
#otal re$enue will be the area under the demand cur$e, or /.50// – /6>/ < />/6 = 1>//.
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#otal cost will be F < />/6 = F < 0://. @conomic profit will be 1>// – F – 0:// = 7// – F.
So the firm will be able to earn at least +ero economic profit as long as F A 7//.
12.%. Suppose a monopolist is able to engage in perfect first"degree price discrimination in a
market. t can sell the first unit at a price of 1/ uros# the second at a price of  uros# the
third at a price of - uros# the fourth at a price of ) uros# the fifth at a price of % uros#
and the si'th at a price of $ uros. t must sell whole units# not fractions of units.
a+ What is the firm0s total revenue when it produces two units?
b+ What is the total revenue when it produces three units?
c+ What is the relationship between the price of the third unit and the marginal revenue of
the third unit?
d+ What is the relationship between the price and the marginal revenue of the fourth unit?
a6 #he firm%s total re$enue when it produces  units is 09 @uros 0/ from the first unit and 9 from
the second6.
b6 #he firm%s total re$enue when it produces 7 units is 8 @uros 0/ from the first unit, 9 from
the second, and > from the third6.
c6 #he are e)ual, as we would e(pect with perfect first'degree price discrimination. #he price of
the third unit is > @uros. #he marginal re$enue of the third unit is also > @uros 8 @uros – 09
@uros6.
d6 B similar reasoning, the price and the marginal re$enue of the fourth unit will also be e)ual
to each other in this case 8 @uros6.
12.). Suppose the monopolist in roblem 12.% incurs a marginal cost of $.$/ uros for
every unit it produces. 3he firm has no fi'ed costs.
a+ &ow many units will it produce if it wants to ma'imi(e its profit? *@emember# it must
produce whole units.+
b+ What will its profit be when it ma'imi(es profit?
c+ What will the deadweight loss be when it ma'imi(es profit? 'plain.
a6 #he firm will want to produce a unit when the marginal re$enue of the ne(t unit is greater than
the marginal cost. Since the firm can implement perfect first'degree price discrimination, the
marginal re$enue of the ne(t unit e)uals the price at which it can sell the ne(t unit. It will thus
sell 5 units the marginal re$enue of the fifth unit is si( euros, which e(ceeds the marginal cost.
Since the marginal re$enue of the si(th 5 euros6 does not co$er the marginal cost, the firm will
not want to produce the si(th unit.
b6 #he profit from each unit will be the difference between the price of that unit and the marginal
cost. #otal profit will be the sum of the profits from all 5 units it produces.
#otal profit = 0/ – 5.5/6 from unit 0 < 9 – 5.5/6 from unit < > – 5.5/6 from unit 7 < 8 – 5.5/6
from unit 1 < : – 5.5/6 from unit 5 = 1.5/ < 7.5/ < .5/ < 0.5/ < /.5/6 euros = 0.5/ euros.
c6 #here will be no deadweight loss. #he first fi$e units will be produced and sold this is
economicall efficient because these are the units for which price the $alue the consumer places
on that unit6 e(ceeds marginal cost. #he additional units will not be sold, and that is also efficient
because the price is less than the marginal cost of production.
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12.-. <oreA is a seller of golf balls that wants to increase its revenues by offering a >uantity
discount. <or simplicity# assume that the firm sells to only one customer and that the
demand for <oreA0s golf balls is P : 1// " Q. ts marginal cost is MC : 1/. Suppose that
<oreA sells the first block of Q1 golf balls at a price of P1 per unit.
a+ <ind the profit"ma'imi(ing >uantity and price per unit for the second block if Q1 : 2/
and P1 : -/.
b+ <ind the profit"ma'imi(ing >uantity and price per unit for the second block if Q1 : /
and P1 : )/.
c+ <ind the profit"ma'imi(ing >uantity and price per unit for the second block if Q1 : !/
and P1 : %/.
d+ 7f the three options in parts *a+ through *c+# which block tariff ma'imi(es <oreA0s total
profits?
a6
We can represent the marginal willingness to pa for each unit beond Q0 = / as P =
0// – / < Q6 = >/ – Q. #he associated marginal re$enue is then MR = >/ – Q, so the profit
ma(imi+ing second block is MR = MC? >/ – Q = 0/. #hus Q = 75 and P = >/ – 75 = 15. So
the firm sells the first / units at a price of 3>/ apiece, while the firm sells an )uantit abo$e /
at 315 apiece. #he firm%s total profit will be >/ – 0/6/ < 15 – 0/675 = 3:5.
b6
#he marginal willingness to pa for each unit beond Q0 = 7/ is P = 8/ – Q. So MR =
8/ – Q and we ha$e MR = MC? 8/ – Q = 0/. #hus Q = 7/ and P = 1/. #he firm%s total
profit will be 8/ – 0/67/ < 1/ – 0/67/ = 38//.
c6
#he marginal willingness to pa for each unit beond Q0 = 1/ is P = :/ – Q. So MR =
:/ – Q and we ha$e MR = MC? :/ – Q = 0/. #hus Q = 5 and P = 75. #he firm%s total
profit will be :/ – 0/61/ < 75 – 0/65 = 3:5.
d6
#he option in part b6 ields the highest profits, of 38//.
12.. Consider the manufacturer of golf balls in roblem 12.-. 3he firm faces the demand
curve P : 1// " Q# and operates with a marginal cost of 1/ for all units produced. =mong all
the possible block tariffs *with two blocks+# what block tariff structure will ma'imi(e
profit? n other words# what choices of P1, Q1 for the first block and P2, Q2 for the second
block will ma'imi(e profit?
#o answer this )uestion, we follow the procedure outlined in the te(t%s discussion of *igure 0.5.
In this problem producer surplus will e)ual profit because there are no sunk fi(ed costs – in fact,
no fi(ed costs at all.
Csing the monopol midpoint rule, we know that the optimal )uantit in the second block will
be half wa between Q1 and 9/ thus Q2= (Q1 + 90)/2.
#otal profits will be P1Q1 + P2 (Q2 – Q1 ) – 10Q2
= (100 – Q1)Q1 + (100-Q2)(Q2 – Q1 ) – 10Q2
–Q12 +90Q2 +Q1Q2 – Q22 = -Q12+Q2(90 +Q1 - Q2)
Substituting Q2= (Q1 + 90)/2 into the e(pression for profit leads to?
#otal profits = -Q12+[(Q1 + 90)/2]2 = [-3Q12 + 180Q1 + 8100]/4 = -3(Q1- 30)2/4 + 200.
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#hus, profits are ma(imi+ed when Q1 =30 , with P1 = 0 in the first block, and when Q2 =!0 ,
with P2 = 40 in the second block. #otal profit will be 8//, the shaded area in the graph below.
P
100 W
P1=70 A
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s
B
F
P2=40
K
Z
L
O
G
Y
E
60
Q2
90
100
10
30
Q1
X
Mar
gi
nalCost
Q
N
12.1/. Suppose that you are a monopolist who produces gi(mos# Z, with the total cost
function C*Z+ : F ; $/Z# where F represents the firm0s fi'ed cost. 8our marginal cost is MC
: $/. Suppose also that there is only one consumer in the market for gi(mos# and she has
the demand function P : %/ " Z.
a+ f you use a constant per"unit price for gi(mos# what price ma'imi(es your profits? What
is the smallest value of F such that you could earn positive profits at this price?
b+ Suppose instead that you charge a per"unit price e>ual to marginal cost# that is# P : MC
: $/. &ow many units would the customer purchase at this price? llustrate your answer in
a graph *featuring the individual demand curve and marginal cost+.
c+ 9ow consider charging the customer a Bsubscription fee of S in addition to a usage fee.
f you set the usage fee as in part *b+# what is the largest fi'ed fee you could charge the
consumer# while ensuring that she is willing to participate in this market?
d+ <or what values of F will you be able to earn positive profits if you follow the pricing
strategy you outlined in part *c+? &ow does this relate to your answer in part *a+?
e+ Suppose now that there are  consumers in the market for gi(mos# each with the
individual demand function P : %/ " Z. 'pressing your answer in terms of , how large
can the fi'ed costs F be for you to still earn positive profits if you use the above nonlinear
pricing strategy.
a6
Setting MR =MC, we ha$e :/ – " = 5/ or " = 5, with P = 55. Dou earn # = 555 – $
+ 5/56 = 5 – $, so profits are positi$e onl if $ A 5.
b6
P = MC = 5/ implies the customer purchases " = 0/ units. See the graph below.
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P
:/
Eemand
5/
MC
0/
Q
c6
!t P = 0/, the customer gets C% = F:/ – 5/60/ = 5/. #hus, the largest fi(ed'fee ou
could charge her, while ensuring that she is willing to participate in this market, is F = C% = 5/.
d6
"ow, our re$enues are R = 5/ < 5/5 = 7//, so profits are # = 7// – $ < 5/56 = 5/ –
$. "ow the firm can operate profitabl so long as $ & 5/. B enabling the firm to e(tract more
surplus, here, second'degree6 price discrimination allows ou to operate in a market where sunk
fi(ed costs range as high as $ = 5/, whereas using standard monopol pricing the firm wouldn%t
participate unless $ & 5.
e6
*or ' customers, our profits are # = '7// – $ < 5/5'6 = 5/' – $, so profits are
positi$e onl when $ & 5/'.
12.11. n part *c+ of earning"Ey"Doing 'ercise 12.# we suggested that the profit"
ma'imi(ing structure for the first and second blocks for Softco is something other than the
pricing structure we determined in part *b+# selling the first %/ units at a price of 4!/
apiece# and selling any >uantity above %/ at 42$ apiece. <ind the structure that ma'imi(es
profit.
Suppose the optimal structure is to sell the first Q0 units at the price P0, and an additional units
at P. *irst, we know that P0 = 8/ – /.5Q0. Second, if price is e)ual to marginal cost, then
consumers would demand Q = 0/ units. So in the optimal block tariff, the )uantit sold in the
second block will be halfwa between Q0 and 0/ that is, Q = /.5Q0 < 0/6. #hird, we can then
sa that the optimal price P must satisf P = 8/ – /.5Q. @(pressing in terms of Q0, that
implies P = 1/ – /.5Q0. With a marginal cost of 0/, the firm%s producer surplus is thus
P% = P0Q0 + P ( Q − Q0 ) − 0/Q
=
( 8/ − /.5Q0 ) Q0 + ( 1/ − /.5Q0 ) [ /.5( Q0 + 0/ ) − Q0 ] − 0/ B /.5( Q0 + 0/ )
= −
7
( Q0 − 1/ )  + 1//
>
Since the first term is negati$e, P% is ma(imi+ed at 1//6 when Q0 = 1/. #herefore, these units
should be priced at P0 = 5/. #he optimal second block in$ol$es P = 7/ and Q = >/. #hat is, the
firm will sell the first 1/ units for 35/ apiece and a second 1/ units because Q – Q0 = 1/6 at 37/
apiece.
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12.12. Consider a market with 1// identical individuals# each with the demand schedule for
electricity of P : 1/ " Q. 3hey are served by an electric utility that operates with a fi'ed cost
1#2// and a constant marginal cost of 2. = regulator would like to introduce a two"part
tariff# where S is a fi'ed subscription charge and m is a usage charge per unit of electricity
consumed. &ow should the regulator set S and m to ma'imi(e the sum of consumer and
producer surplus while allowing the firm to earn e'actly (ero economic profit?
#o ma(imi+e the sum of consumer and producer surplus, the regulator must set the usage charge
 =  this will induce consumers to bu units of electricit as long as their willingness to pa is
at least as high as the marginal cost of pro$iding electricit ser$ice. #his means that each
consumer will bu > units of electricit. #here will be +ero deadweight loss in the market.
If there were no subscription charge, each consumer would reali+e a consumer surplus of /.50/
– 6> = 7. #his means that each consumer will be willing to bu electricit as long as the
subscription charge is less than 7. With 0// consumers, the electric utilit can then charge each
customer a subscription fee of 30 to co$er its fi(ed costs of 30//, lea$ing each consumer with
a consumer surplus of 7 – 0 = /. So the total re$enue for the firm will be the sum of the
re$enue from the subscription charge 0//6 and the re$enue from the usage charge 0//> =
//. #otal re$enue will Gust co$er total cost, and the firm will earn +ero economic profit.
12.1. = monopolist faces two market segments. n each market segment# the demand curve
is of the constant elasticity form. n market segment 1# the price elasticity of demand is "#
while in market segment 2# the price elasticity of demand is "1.$. 3he monopolist has a
constant marginal cost of 4$ per unit# which is the same in each market segment. What is
the monopolist0s profit ma'imi(ing price in each segment?
We use the in$erse elasticit rule to determine the profit'ma(imi+ing prices?
;0 = MH00 < 0ε06J = 5H00<0'766J = 576 = 8.5
; = MH00 < 0ε6J = 5H00<0'0.566J = 576 = 05
12.1!. Suppose that =cme harmaceutical Company discovers a drug that cures the
common cold. =cme has plants in both the 5nited States and urope and can manufacture
the drug on either continent at a marginal cost of 1/. =ssume there are no fi'ed costs. n
urope# the demand for the drug is Q! : )/ " P!# where Q! is the >uantity demanded
when the price in urope is P!. n the 5nited States# the demand for the drug is Q" : 11/ "
P"# where Q" is the >uantity demanded when the price in the 5nited States is P".
a+ f the firm can engage in third"degree price discrimination# what price should it set on
each continent to ma'imi(e its profit?
b+ =ssume now that it is illegal for the firm to price discriminate# so that it can charge only
a single price P on both continents. What price will it charge# and what profits will it earn?
c+ Will the total consumer and producer surplus in the world be higher with price
discrimination or without price discrimination? Will the firm sell the drug on both
continents?
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a6 With third'degree price discrimination the firm should set MR = MC in each market to
determine price and )uantit. #hus, in @urope setting MR = MC
8/ − Q* = 0/
Q* = 7/
!t this )uantit, price will be P* = 1/ . ;rofit in @urope is then
π * =  P* − 0/6Q* = 1/ − 0/67/ = 9// . Setting MR = MC in the CS implies
00/ − Q+ = 0/
Q+ = 5/
!t this )uantit price will be P+ = :/ . ;rofit in the CS will then be
π + =  P+ − 0/6Q+ = :/ − 0/65/ = 5// . #otal profit will be π = 71// .
b6
If the firm can onl sell the drug at one price, it will set the price to ma(imi+e total profit.
#he total demand the firm will face is Q = Q* + Q+ . In this case
Q = 8/ − P + 00/ − P
Q = 0>/ −  P
#he in$erse demand is then P = 9/ − /.5Q . Since MC = 0/ , setting MR = MC implies
9/ − Q = 0/
Q = >/
!t this )uantit price will be P = 5/ . If the firm sets price at 5/, the firm will sell Q* = / and
Q+ = :/ . ;rofit will be π = 5/>/6 − 0/>/6 = 7// .
c6
#he firm will sell the drug on both continents under either scenario. If the firm can price
discriminate, total consumer surplus will be /.58/ – 1/67/ < /.500/ – :/65/ = 08// and
producer surplus e)ual to profit6 will be 71//. #hus, total surplus will be 50//. If the firm
cannot price discriminate, consumer surplus will be /.58/ – 5/6/ < /.500/ – 5/6:/ = /// and
producer surplus will be e)ual to profit of 7//. #hus, total surplus will be 5//.
12.1$. Consider roblem 12.1! with the following change. Suppose the demand for the drug
in urope declines to Q! : / " P!. f the firm cannot price discriminate# will it be in the
firm0s interest to sell on both continents?
Ket%s start b assuming that the optimal uniform price ,.e., no price discrimination6 is one at
which the firm would sell in both markets. If the firm cannot price discriminate then
Q = Q* + Q+
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Q = 7/ − P + 00/ − P
Q = 01/ −  P
In$erse demand is P = 8/ – /.5Q. Setting MR = MC implies
8/ − Q = 0/
Q = :/
!t this )uantit, price will be P = 1/ . #his price e(ceeds the choke price in @urope, so the firm
will not be able to sell an units in @urope. Since the firm will not sell an units in @urope, the
firm should set its marginal cost e)ual to the marginal re$enue in the CS market? MR = 00/ –
Q = MC = 0/, impling Q = 5/ and P = :/.
12.1%. Consider roblem 12.1! with the following change. Suppose the demand for the drug
in urope becomes Q! : $$ " /.$ P!. Will third"degree price discrimination increase the
firm0s profits?
Without price discrimination, if Q* = 55 − .5P* , then Q = Q* + Q+ is
Q = 55 − .5P + 00/ − P
Q = 0:5 − 0.5P
In$erse demand is P = 00/ – .7 Q. Setting MR = MC implies
00/ − 1 7 Q = 0/
Q = 85
!t this )uantit the firm will charge a price of P = :/ . !t this price the firm will sell 5 units in
@urope and 5/ units in the CS and earn a total profit of π = 785/ .
#o ma(imi+e profits with third'degree price discrimination the firm should set MR = MC in each
market. In the CS
00/ − Q+ = 0/
Q = 5/
!t this )uantit the firm will charge a price P+ = :/ and profits in the CS will be π = 5// .
Setting MR = MC in @urope implies
00/ − 1Q = 0/
Q = 5
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!t this )uantit the firm will charge a price P* = :/ and profits in @urope will be π = 05/ .
#otal profits with price discrimination will e)ual the sum of the profits from each market
π = π * + π + = 05/ + 5// = 785/ . #his is e)ual to the profits without price discrimination, so
the firm gains no ad$antage b being able to price discriminate. With these demands, the firm
would charge the same price in each market regardless of whether it could price discriminate or
not.
12.1). 3hink about the problem that =cme faces in roblem 12.1!. Consider an# demand
curves for the drug in urope and in the 5nited States. Will its profits ever be lower with
third"degree price discrimination than they would be if price discrimination were
impossible?
! firm could ne$er do worse with third'degree price discrimination than without. WhL
Because with third'degree price discrimination the firm is tring to find a price to charge each
market to increase profits abo$e the profits the firm would earn if it charged each market
segment the same price. ;rofits can ne$er be worse because the firm could alwas choose the
solution where it charges all segments the same price and earn profit e)ual to the non'
discriminating solution. If the firm $aries the solution from this point, it will onl do so if the
profits will increase. #herefore, profits for the discriminating firm could ne$er be worse than the
profits for the non'discriminating firm.
12.1-. 3here is another way to solve earning"Ey"Doing 'ercise 12.$. @ecall that marginal
revenue can be written as MR $ P % *FPGFQ+Q. Ey factoring out P, we can write Since third"
degree price discrimination means that marginal cost e>uals marginal revenue in each
market segment# the profit"ma'imi(ing regular and vacation fares will be determined by
MRR : MRV : MC. *@emember the marginal cost of both classes of service is assumed to
be the same in the e'ercise.+ 3hus use this relationship to verify the answer given in the
e'ercise.
*or this problem, Kearning'B'Eoing @(ercise 0.5 gi$es ε Q , P = −0.05 and ε Q , P = −0.5 .
erifing the relationship in this problem implies
0 
0

PR  0 +
= P- 0 + 

−0.5
 −0.05 

R
R
-
-
/.07/PR = /.71PPR
P-
=
/.71
/.07/
#he same solution as that gi$en in Kearning'B'Eoing @(ercise 0.5.
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12.1. H. Cigliano *Brice and ncome lasticities for =irline 3ravelI 3he 9orth =tlantic
6arket# &usiness !conomics, September 1-/+ estimated the price elasticity of demand
for regular *full"fare+ travel in coach class in the 9orth =tlantic market to be ϵ& : "1.. &e
also found the price elasticity of demand for e'cursion *vacation+ travel to be about ϵV :
"1.-. Suppose 3ransatlantic =irlines faces these price elasticities of demand# and that the
elasticities are constantJ that is# they do not vary with price. Since both are coach fares# you
may also assume that the marginal cost of service is about the same for business and
vacation travelers. Suppose an airline facing these demand elasticities wants to set PR *the
price of a round"trip ticket to regular business travelers+ and PV *the price of a round"trip
ticket to vacation travelers+ to ma'imi(e profit. What prices should the firm charge if the
marginal cost of a round trip is 2//?
Cse the in$erse elasticit pricing rule to find the profit ma(imi+ing le$el of each price. *or
business tra$elers
P. − //
P.
0
= −
−
0.7
which implies P. ≈ >:8.
*or $acation tra$elers
P- − //
P-
0
= −
−
0 .>
which implies P- = 15/.
12.2/. a Dura(no is the only resort hotel on a small desert island off the coast of South
=merica. t faces two market segmentsI bargain travelers and high"end travelers. 3he
demand curve for bargain travelers is given by Q1 : !// " 2P1. 3he demand curve for high"
end travelers is given by Q2 : $// " P2. n each e>uation# Q denotes the number of travelers
of each type who stay at the hotel each day# and P denotes the price of one room per day.
3he marginal cost of serving an additional traveler of either type is 42/ per traveler per
day.
a+ 5nder the assumption that there is a positive demand from each type of traveler# what is
the e>uation of the overall market demand curve facing the resort?
b+ What is the profit"ma'imi(ing price under the assumption that the resort must set a
uniform price for all travelers? <or the purpose of this problem# you may assume that at
the profit"ma'imi(ing price# both types of travelers are served. 5nder the uniform price#
what fraction of customers are bargain travelers# and what fraction are high end?
c+ Suppose that the resort can engage in third"degree price discrimination based on
whether a traveler is a high"end traveler or a bargain traveler. What is the profit"
ma'imi(ing price in each segment? 5nder price discrimination# what fraction of customers
are bargain travelers and what fraction are high end?
d+ 3he management of a Dura(no is probably unable to determine# Kust from looking at a
customer# whether he or she is a high"end or bargain traveler. &ow might a Dura(no
screen its customers so that it can charge the profit"ma'imi(ing discriminatory prices you
derived in part *c+?
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a6
In the range of prices in which consumers in both market segments purchase at a
common price ;, the total market demand cur$e is N0 < N = 1// – ; < 5// – ;, or N = 9// – 7;.
b6
If N = 9// – 7;, then the in$erse market demand cur$e is ; = 7// – 076N. Marginal
re$enue is thus MO = 7// – 76N, and so the profit'ma(imi+ing )uantit is found b sol$ing
7// – 76N = /, or N = 1/. #he profit'ma(imi+ing price is thus? ; = 7// – 0761/6 = 0:/.
!t this price, N0 = 1// – 0:/6 = >/ bargain tra$elers sta at the resort, and N = 5// – 0:/ =
71/ high'end tra$elers sta at the resort. #hus, about 09 percent of the resort%s guests are bargain
tra$elers.
c6
We find the profit ma(imi+ing )uantit and price in each market segment as follows?
Bargain tra$elers?
N0 = 1// – ;0 ⇒ ;0 = // – F N0.

#his implies that marginal re$enue is? MO0 = // – N0.

@)uating marginal re$enue to marginal cost gi$es us? // – N0 = /, or N0 = 0>/.

#his implies ;0 = // – F 0>/6 = 00/.

4igh'end tra$elers?
N0 = 5// – ;0 ⇒ ;0 = 5// – N0.

#his implies that marginal re$enue is? MO0 = 5// – N0.

@)uating marginal re$enue to marginal cost gi$es us? 5// – N0 = /, or N0 = 1/.

#his implies ;0 = 5// – 1/6 = :/.

#he percentage of bargain tra$elers is now 0>/0>/<1/6 = /.1> or about 17 percent.
d6
#here are a number of was the resort can screen passengers.
If there is a correlation between age and membership in the bargain segment perhaps elderl
indi$iduals are more price sensiti$e6, then the resort could screen on the basis of age.
If there is a correlation between a tra$eler%s willingness to pa for a room in the resort and
hisher propensit to purchase complementar resort ser$ices such as spa treatments or workouts
with a personal trainer. If so, the resort ma set a uniform price for rooms but offer the
complementar ser$ices for sale at a high mark'up to allow the resort to, in effect, collect a
higher Po$erallQ price room charge plus other ser$ices6 from high'end tra$elers.
If there is a correlation between the propensit of a tra$eler to mail in rebate cards or coupons
and the tra$eler%s membership in the bargain segment, the resort could screen b offering
discounts to those tra$elers who, upon returning home, mail in a rebate card or coupon.
*inall, the resort could offer a few rooms on ;riceline.com. #his is a selling channel that
appeals disproportionatel to price sensiti$e tra$elers.
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12.21. = pipeline transports gasoline from a refinery at point ' to destinations at R and T.
3he marginal cost of transporting gasoline to each destination is MC : 2. 3he pipeline has a
fi'ed cost of 1%/. 3he demand curve for the transportation of gasoline from ' to R is QR :
1// " 1/ PR# where QR is the number of units transported when PR is the transport price
per unit. 3he demand for pipeline movements from ' to T will be 2/ units as long as if the
customers at T will purchase gasoline from another source# buying no gasoline shipped
through the pipeline. 3hese demand curves are shown below.
a+ f this firm was unable to engage in price discrimination *so that it can only choose a
single P for the two markets+# what would the profit"ma'imi(ing tariff be? What level of
profit would the firm reali(e?
b+ f this firm were able to implement third"degree price discrimination to ma'imi(e
profits# what would the profit"ma'imi(ing prices be? What level of profits would the firm
reali(e?
a6
Rne wa to sol$e the problem is to form the aggregate demand?  = R + T = 0// – 0/P
< / = 0/ – 0/P. #he in$erse form of this demand is P = 0 – /.0. #hen set MR = MC? 0 –
/. = . #hus,  = 5/, and P = 0 – /.05/6 = 8. # = P – 0:/ –  = 85/6 – 0:/ – 5/6 = 9/.
b6
In T, the firm should e(tract all consumer surplus b setting PT = 0 for all T = / units.
In R, in$erse demand is PR = 0/ – /.0R. Setting MR = MC, we ha$e 0/ – /.R = , which
implies R = 1/ and PR = :. #hen # = PRR < PTT – 0:/ – R + T6 = :1/6 < 0/6 – 0:/ –
:/6 = //.
12.22. = seller produces output with a constant marginal cost MC : 2. Suppose there is one
group of consumers with the demand curve P1 : 1% " Q1# and another with the demand
curve P2 : 1/ " *1G2+Q2.
a+ f the seller can discriminate between the two markets# what prices would she charge to
each group of consumers? *8ou may want to e'ploit the monopoly midpoint rule from
earning"Ey"Doing 'ercise 11.$.+
b+ f the seller cannot discriminate# but instead must charge the same price P1 : P2 : P to
each consumer group# what will be her profit"ma'imi(ing price? c+ Which# if any#
consumer group benefits from price discrimination?
d+ f instead P1 : 1/ " Q1# does either group benefit from price discrimination?
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a6
With linear demand and constant marginal costs, we can use the monopol midpoint rule
to )uickl determine that the profit'ma(imi+ing prices are P0 = /.501 < 6 = > and P = /.50/ <
6 = :.
b6
Market demand will be Q = Q0 < Q = 0: – P < / – P. In$erse market demand is then
P = 0 – Q. So the profit'ma(imi+ing non'discriminator price will be P = /.50 < 6 = 8.
c6
*or an two general demand cur$es P0= a0 – Q0 and P = a – /.5Q and constant
marginal cost , the profit'ma(imi+ing discriminator prices will be P0 = /.5a0 < 6 and P =
/.5a < 6.
In the case where the seller cannot discriminate, market demand will be Q = Q0 < Q = a0
< a – 7P. In$erse demand is P = a0 < a6 – Q. So the profit'ma(imi+ing non'
discriminator price will be P = FHa0 < a6 < J.
"ote that P – P0 = a – a06 while P – P = 0:6a0 – a6. If a0 T a, then group  i.e.,
consumers with the lower choke price6 benefits from relati$el lower prices under price
discrimination while group 0 is hurt b relati$el higher prices.
d6
If a0 = a, then all three prices are the same? P0 = P = P. #hat is, e$en though the
demand cur$es ha$e different slopes, because each has the same intercept choke price6, the
monopol midpoint rule implies that the profit'ma(imi+ing monopol price is the same
regardless of whether the seller uses price discrimination or not. #hus, neither group benefits
nor is harmed b6 price discrimination.
12.2. = cruise line has space for $// passengers on each voyage. 3here are two market
segmentsI elderly passengers and younger passengers. 3he demand curve for the elderly
market segment is Q1 : )$/ " !P1. 3he demand curve for the younger market segment is
Q2 : -$/ " 2P2. n each e>uation# Q denotes the number of passengers on a cruise of a given
length and P denotes the price per day. 3he marginal cost of serving a passenger of either
type is 4!/ per person per day. =ssuming the cruise line can price discriminate# what is the
profit"ma'imi(ing number of passengers of each type? What is the profit"ma'imi(ing price
for each type of passenger?
N0 = 85/ – 1;0 ⇒ ;0 = 0>8.5 – 016N0. #his implies MO0 = 0>8.5 – 06N0.
N = >5/ – ; ⇒ ; = 15 – 06N. #his implies MO = 15 – N.
When we ha$e limited capacit we sol$e the following two e)uations?
MO0 = MO ⇒ 0>8.5 – 06N0 = 15 – N. @)uate the MOs6
N0 < N = 5//. Nuantities sold must add up to capacit6
We thus ha$e two e)uations in two unknowns?
0>8.5 – 06N0 = 15 – N
N0 < N = 5//
Sol$ing these e)uations ields?
N0 = 085.
N = 75.
;lugging these back into the in$erse demand cur$es gi$es us the profit'ma(imi+ing prices?
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;0 = 0>8.5 – 0160856 = 017.85.
; = 15 – 06756 = :.5.
12.2!. =n airline has 2// seats in the coach portion of the cabin of an =irbus =!/. t is
attempting to determine how many seats it should sell to business travelers and how many
to vacation travelers on a flight between Chicago and Dubai that departs on 6onday
morning# Hanuary 2$. t has tentatively decided to sell 1$/ seats to business travelers and $/
seats to vacation travelers at 4!#/// and 41#///# respectively. t also knowsI
a+ 3o sell an additional seat to business travelers# it would need to reduce price by 42$. 3o
reduce demand by business travelers by one seat# it would need to increase price by 42$.
b+ 3o reduce demand by one unit among vacation travelers# it would need to increase price
by 4$. 3o sell an additional seat to vacation travelers# it would need to reduce price by 4$.
=ssuming that the marginal cost of carrying either type of passenger is (ero# is the current
allocation of seats profit ma'imi(ing? f not# would you sell more seats to business travelers
or vacation travelers?
#he easiest wa to check whether the current allocation of seats is optimal is to compare the
marginal re$enues of the two market segments. In the e)uations below, let%s let P0Q denote the
business tra$eler segment and PQ denote the $acation tra$eler segment.
"ote that the marginal re$enue in each segment is gi$en b?
MO0 = ;0 < ∆;0∆N06N0
MO = ; < ∆;∆N6N
We know?
;0 = 31,///, N0 = 05/, and ∆;0∆N0 = ' 35. 4ence, MO0 = 31,/// ' 3505/6 = 35/.
; = 30,///, N = 5/, and ∆;∆N = ' 35. 4ence, MO = 30,/// ' 355/6 = 385/.
Since MO T MO0, the airline can increase its profits b selling more seats to $acation tra$eler
and fewer seats to business tra$elers.
12.2$. = summer theater has a capacity of 2// seats for its Saturday evening concerts. 3he
marginal cost of admitting a spectator is (ero up to that capacity. 3he theater wants to
ma'imi(e profits and recogni(es that there are two kinds of customers. t offers discounts
to senior citi(ens and students# who generally are more price sensitive than other
customers. 3he demand curve for tickets by seniors and students is described by P1 : 1% "
/./!Q1, where Q1 is the number of discount tickets sold at a price of P1. 3he demand
schedule for tickets by customers who do not >ualify for a discount is represented by P2 :
2- " /.1Q2, where Q2 is the number of nondiscount tickets sold at a price of P2. What are
the two prices that would ma'imi(e profit for the Saturday evening concerts?
#he theater would want to set the prices to e)uate the marginal re$enue for the two tpes of
customers. #hus, it would choose the )uantities so that?
MR1 = 1! – 0.08Q1 = MR2 = 28 – 0.2Q2.
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In addition, the capacit constraint must be satisfied, so that Q1 + Q2 = 200.
#hus, 1! – 0.08Q1 = 28 – 0.2(200 – Q1) which tells us that Q1 = 100 and Q2 = 100.
"ote that this implies that the marginal re$enue from each tpe of ticket is >. Since this e(ceeds
that marginal cost which is +ero6, the firm does want sell all its capacit.
#he profit ma(imi+ing prices are as follows?
P1 = 1! – 0.04Q1 = 1! – 0.04(100) = 12.
P2 = 28 – 0.1Q2 = 28 – 0.1(100) = 18.
12.2%. = small island near a maKor city has a beautiful beach. 3he company that owns the
island sells day passes for the beach# including travel by ferry to and from the beach.
Eecause the beach is small# the company does not want to sell more than 2// e'cursion
tickets per day. 3he company knows there are two kinds of visitorsI those who are willing
to buy tickets a month in advance and those who want to buy on the day of the trip. 3hose
willing to buy in advance are typically more price sensitive. 3he demand curve for advance
purchase e'cursion tickets is described by P1 : 1// " /.2 Q1, where Q1 is the number of
advance purchase tickets sold at a price of P1. 3he demand schedule for tickets by day"of"
travel e'cursions is represented by P2 : 2// " /.-Q2, where Q2 is the number of tickets sold
at a price of P2.
a+ Suppose the marginal cost of the ferry trip and use of beach is $/ per customer. What
prices should the firm charge for its e'cursion tickets?
b+ f the marginal cost were high enough# the firm would want to sell fewer than 2//
tickets. Suppose the marginal cost of the ferry trip and use of beach is -/ per customer.
What prices should the firm charge for its beach e'cursion tickets?
a6 #he compan would want to set the prices to e)uate the marginal re$enue for the two tpes of
customers. Ket%s assume that the compan wants to sell its capacit of // tickets. We will
$erif that it does in a moment.6 It would choose the )uantities so that?
MR1 = 100 – 0.4Q1 = MR2 = 200 – 1.!Q2.
In addition, the capacit constraint would be satisfied, so that Q1 + Q2 = 200.
#hus, 100 – 0.4Q1 = MR2 = 200 – 1.!(200 – Q1) which tells us that Q1 = 110 and Q2 = 90.
"ote that this implies that the marginal re$enue from each tpe of ticket is 5:.
Since the marginal re$enue e(ceeds that marginal cost which is 5/6, the firm does want sell all
its capacit. #hus, our assumption that the firm would want to sell to capacit when the marginal
cost is 5/ is correct.
#he profit ma(imi+ing prices are as follows?
P1 = 100 – 0.2Q1= 100 – 0.2(110) = 8.
P2 = 200 – 0.4Q2 = 200 – 0.8(90) = 128.
b6 !s we showed in part a6, if the firm sells tickets to e(haust its capacit, the marginal re$enue
from sales to each tpe of customer is 5:. So it will not want to sell to capacit if the marginal
cost is >/. Instead, it will Gust set the price so that MO = M in each market.
MR1 = 100 – 0.4Q1 = 80. #his implies that Q1 = 0 with P1 = 100 – 0.2(0) = 90.
MR2 = 200 – 1.!Q2 = 80. #his implies that Q2 =  with P2 = 200 – 0.8() = 140.
"ote that the firm now sells onl Q1 + Q2 = 0 +  = 12 e(cursion tickets – less than the
capacit of //.
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12.2). 8ou are the only uropean firm selling vacation trips to the 9orth ole. 8ou know
only three customers are in the market. 8ou offer two services# round trip airfare and a
stay at the olar Eear &otel. t costs you // euros to host a traveler at the olar Eear and
// euros for the airfare. f you do not bundle the services# a customer might buy your
airfare but not stay at the hotel. = customer could also travel to the 9orth ole in some
other way *by private plane+# but still stay at the olar Eear. 3he customers have the
following reservation prices for these servicesI
a+ f you do not bundle the hotel and airfare# what are the optimal prices P' and P(# and
what profits do you earn?
b+ f you only sell the hotel and airfare in a bundle# what is the optimal price of the bundle
P&# and what profits do you earn?
c+ f you follow a strategy of mi'ed bundling# what are the optimal prices of the separate
hotel# the separate airfare# and the bundle * P'# P(# and P&# respectively+ and what profits
do you earn?
a6
Without bundling, the best the firm can do is set the price of airfare at 3>// and the price
of hotel at 3>//. In each case the firm attracts a single customer and earns profit of 35// from
each for a total profit of 30///. #he firm could attract two customers for each ser$ice at a price
of 35//, but it would earn profit of 3// on each customer for a total of 3>// profit, less profit
than the 3>// price.
b6
With bundling, the best the firm can do is charge a price of 39// for the airfare and hotel.
!t this price the firm will attract all three customers and earn 37// profit on each for a total
profit of 39//. #he firm could raise its price to 30///, but then it would onl attract one
customer and total profit would be 31//. "otice that with bundling the firm cannot do as well as
it could with mi(ed bundling. #his is because while a6 the demands are negati$el correlated, a
ke to increasing profit through bundling, b6 customer 0 has a willingness'to'pa for airfare
below marginal cost and customer 7 has a willingness'to'pa for hotel below marginal cost. #he
firm should be able to do better with mi(ed bundling
c6
Because customer 0 has a willingness'to'pa for airfare below marginal cost and
customer 7 has willingness'to'pa for hotel below marginal cost, the firm can potentiall earn
greater profits through mi(ed bundling. In this problem, if the firm charges 3>// for airfare onl,
3>// for hotel onl, and 30/// for the bundle, then customer 0 will purchase hotel onl,
customer  will purchase the bundle, and customer 7 will purchase airfare onl. #his will earn
the firm 301// profit, impling that mi(ed bundling is the best option in this problem.
12.2-. 8ou operate the only fast"food restaurant in town# selling burgers and fries. 3here
are only two customers# one of whom is on the =tkins diet and the other on the Lone diet#
whose willingness to pay for each item is displayed in the following table. <or simplicity#
assume you have (ero fi'ed and marginal costs for each item.
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a+ f ) : 1 and you do not bundle the two products# what are your profit"ma'imi(ing prices
P& and PF? Calculate total surplus under this outcome.
b+ 9ow assume only that ) M /. nstead# suppose that you hired an economist who tells you
that the profit"ma'imi(ing bundle price *for a burger and fries+ is 4-# while if you sold the
items individually *and did not offer a bundle+ your profit"ma'imi(ing price for fries would
be greater than 4. 5sing this information# what is the range of possible values for )?
a6
Dou should sell two burgers for P = 5, and one order of fries for PF = 7. #otal surplus is
then P% + C% = 0/ < 76 < 7 < /6 = 0:.
b6
In order for the profit'ma(imi+ing bundle price to be 3>, it must be true that > <  A >,
i.e. that  A >. In order for the profit'ma(imi+ing price of fries to be greater than 37, it must be
true that   7, or   :. #hus, we know that : U  A >.
12.2. Suppose your company produces athletic footwear. 6arketing studies indicate that
your own price elasticity of demand is " and that your advertising elasticity of demand is
/.$. 8ou may assume these elasticities to be appro'imately constant over a wide range of
prices and advertising e'penses.
a+ Ey how much should the company mark up price over marginal cost for its footwear?
b+ What should the company0s advertising"to"sales ratio be?
a6
Csing the in$erse elasticit price rule,
P − MC
=−
P
P − MC
P
P
MC
=−
0
ε Q,P
0
−7
= 0.5
#he firm should set price at about 0.5 times marginal cost.
b6
#he optimal ad$ertising'to'sales ratio can be found be e)uating
ε
A
= − Q, A
PQ
ε Q ,P
A
PQ
A
PQ
=−
/.5
−7
= /.0:8
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#hus, ad$ertising e(pense should be about 0: or 08 percent of sales re$enue.
12./. 3he motor home industry consists of a small number of large firms. n 2//#
producers of motor homes had an average advertising sales ratio of 1.- percent. =ssuming
that the price elasticity of demand facing a typical motor home producer is "!# what is the
advertising elasticity of demand facing a typical producer# under the assumption that each
producer has chosen its price and advertising level to ma'imi(e profits?
#he condition for the ratio profit'ma(imi+ing ad$ertising'to'sales ratio is?
!d$ertising'to'sales ratio
ε Q, A
=
−
,
ε Q,P
where εN,! is the ad$ertising elasticit of demand and εN,; is the price elasticit of demand. We
know that the ad$ertising'to'sales ratio of a tpical producer of motor homes is 0.> percent or
/./0>. We also know that the price elasticit of demand of a tpical firm is '1. We thus ha$e?
/./0> =
ε Q, A
=
−
−
1
,
which implies εN,! = 16/./0>6 = /./8.
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