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324 MONOPOLY BEHAVIOR (Ch. 26)
(d) What is the the maximum price that the Journal can charge for 100
articles per year if it wants executives to prefer this deal to buying 80
articles a year at the highest price the undergraduates are willing to pay
(e) Suppose that the Mall Street Journal decides to include only 60 ar-
ticles in the student package. What is the most it could charge and still
(f) If the Mall Street Journal offers a “student package” of 60 articles
at this price, how much net consumer surplus would executives get from
(g) What is the most that the Mall Street Journal could charge for a 100-
article package and expect executives to buy this package rather than the
(h) If the number of executives in the population equals the number of
students, would the Mall Street Journal make higher profits by offering a
26.7 (2) Bill Barriers, CEO of MightySoft software, is contemplating
a new marketing strategy: bundling their best-selling wordprocessor and
their spreadsheet together and selling the pair of software products for
one price.
From the viewpoint of the company, bundling software and selling it
at a discounted price has two effects on sales: (1) revenues go up due to
to additional sales of the bundle; and (2) revenues go down since there is
less of a demand for the individual components of the bundle.
The profitability of bundling depends on which of these two effects
dominates. Suppose that MightySoft sells the wordprocessor for $200 and
the spreadsheet for $250. A marketing survey of 100 people who purchased
either of these packages in the last year turned up the following facts:
1) 20 people bought both.
2) 40 people bought only the wordprocessor. They would be willing to
spend up to $120 more for the spreadsheet.
3) 40 people bought only the spreadsheet. They would be willing to
spend up to $100 more for the wordprocessor.
In answering the following questions you may assume the following:
1) New purchasers of MightySoft products will have the same charac-
teristics as this group.
2) There is a zero marginal cost to producing extra copies of either
software package.
3) There is a zero marginal cost to creating a bundle.
NAME 325
(a) Let us assume that MightySoft also offers the products separately
as well as bundled. In order to determine how to price the bundle, Bill
Barriers asks himself the following questions. In order to sell the bundle
to the wordprocessor purchasers, the price would have to be less than
(b) In order to sell the bundle to the spreadsheet users, the price would
(c) What would MightySoft’s profits be on a group of 100 users if it priced
(d) What would MightySoft’s profits be on a group of 100 users if
it priced the bundle at $350? 20 people would buy
both anyway, 40 people would buy the
(e) If MightySoft offers the bundle, what price should it set? $320
(f) What would profits be without offering the bundle? Without
(g) What would be the profits with the bundle? 100 ×320 =
326 MONOPOLY BEHAVIOR (Ch. 26)
(h) Is it more profitable to bundle or not bundle? Bundle.
(i) Suppose that MightySoft worries about the reliability of their market
survey and decides that they believe that without bundling tof the 100
people will buy both products, and (100−t)/2 will buy the wordprocessor
only and (100 −t)/2 will buy the spreadsheet only. Calculate profits as a
(k) At what values of twould it be unprofitable to offer the bundle?
Solve for the tthat equates the two
(l) This analysis so far has been concerned only with customers who
would purchase at least one of the programs at the original set of prices.
Is there any additional source of demand for the bundle? What does
this say about the calculations we have made about the profitability of
bundling? Yes, it may be that there are
some consumers who were not willing to pay
26.8 (0) Colonel Tom Barker is about to open his newest amusement
park, Elvis World. Elvis World features a number of exciting attractions:
you can ride the rapids in the Blue Suede Chutes, climb the Jailhouse
Rock and eat dinner in the Heartburn Hotel. Colonel Tom figures that
Elvis World will attract 1,000 people per day, and each person will take
x=50−50prides, where pis the price of a ride. Everyone who visits
Elvis World is pretty much the same and negative rides are not allowed.
The marginal cost of a ride is essentially zero.
NAME 327
(a) What is each person’s inverse demand function for rides? p(x)=
1−x/50.
(b) If Colonel Tom sets the price to maximize profit, how many rides will
be taken per day by a typical visitor? 25.
(f) If Colonel Tom charged the Pareto efficient price for a ride, how many
(g) How much consumers’ surplus would be generated at this price and
(h) If Colonel Tom decided to use a two-part tariff, he would set an
26.9 (1) The city of String Valley is squeezed between two mountains
and is 36 miles long, running from north to south, and only about 1
block wide. Within the town, the population has a uniform density of
100 people per mile. Because of the rocky terrain, nobody lives outside
the city limits on either the north or the south edge of town. Because of
strict zoning regulations, the city has only three bowling alleys. One of
these is located at the city limits on the north edge of town, one of them is
located at the city limits on the south edge of town, and one is located at
the exact center of town. Travel costs including time and gasoline are $1
per mile. All of the citizens of the town have the same preferences. They
are willing to bowl once a week if the cost of bowling including travel
costs and the price charged by the bowling alley does not exceed $15.
(a) Consider one of the bowling alleys at either edge of town. If it charges
$10 for a night of bowling, how far will a citizen of String Valley be willing
328 MONOPOLY BEHAVIOR (Ch. 26)
(b) Write a formula for the number of customers that a bowling alley
at the edge of town will have if it charges $pper night of bowling.
(c) Write a formula for this bowling alley’s inverse demand function.
(d) Suppose that the bowling alleys at the end of town have a marginal
cost of $3 per customer and set their prices to maximize profits. (For
the time being assume that these bowling alleys face no competition from
the other bowling alleys in town.) How many customers will they have?
600. What price will they charge? $9. How far away from the edge
(f) If the bowling alley in the center of town also has marginal costs
of $3 per customer and maximizes its profits, what price will it charge?
$9. How many customers will it have per week? 1,200. How far
(g) Suppose that the city relaxes its zoning restrictions on where the
bowling alleys can locate, but continues to issue operating licenses to
only 3 bowling alleys. Both of the bowling alleys at the end of town
are about to lose their leases and can locate anywhere in town that they
like at about the same cost. The bowling alley in the center of town is
committed to stay where it is. Would either of the alleys at the edge of
town improve its profits by locating next to the existing bowling alley in
the center of town? No. What would be a profit-maximizing location
for each of these two bowling alleys? One would be located
NAME 329
26.10 (1) In a congressional district somewhere in the U.S. West a
new representative is being elected. The voters all have one-dimensional
political views that can be neatly arrayed on a left-right spectrum. We
can define the “location” of a citizen’s political views in the following way.
The citizen with the most extreme left-wing views is said to be at point
0 and the citizen with the most extreme right-wing views is said to be at
point 1. If a citizen has views that are to the right of the views of the
fraction xof the state’s population, that citizen’s views are said to be
located at the point x. Candidates for office are forced to publically state
their own political position on the zero-one left-right scale. Voters always
vote for the candidate whose stated position is nearest to their own views.
(If there is a tie for nearest candidate, voters flip a coin to decide which
to vote for.)
(a) There are two candidates for the congressional seat. Suppose that
each candidate cares only about getting as many votes as possible. Is
there an equilibrium in which each candidate chooses the best position
given the position of the other candidate? If so, describe this equilibrium.
26.11 (2) In the congressional district described by the previous problem,
let us investigate what will happen if the two candidates do not care
about the number of votes that they get but only about the amount
of campaign contributions that they receive. Therefore each candidate
chooses his ideological location in such a way as to maximize the amount
of campaign contributions he receives, given the position of the other.*
Let us define a left-wing extremist as a voter whose political views
lie to the left of the leftmost candidate, a right-wing extremist as a voter
whose political views lie to the right of the rightmost candidate, and a
moderate voter as one whose political views lie between the positions
of the two candidates. Assume that each extremist voter contributes to
the candidate whose position is closest to his or her own views and that
moderate voters make no campaign contributions. The number of dol-
lars that an extremist voter contributes to his or her favorite candidate
is proportional to the distance between the two candidates. Specifically,
we assume that there is some constant Csuch that if the left-wing can-
didate is located at xand the right-wing candidate is located at y, then
total campaign contributions received by the left-wing candidate will be
$Cx(y−x) and total campaign contributions received by the right-wing
candidate will be $C(1 −y)(y−x).
* This assumption is a bit extreme. Candidates typically spend at least
some of their campaign contributions on advertising for votes, and this
advertising affects the voting outcomes.
330 MONOPOLY BEHAVIOR (Ch. 26)
(a) If the right-wing candidate is located at y, the contribution-
maximizing position for the left-wing candidate is x=y/2If the
left-wing candidate is located at x, the contribution-maximizing position
tive and set it equal to zero.)
(b) Solve for the unique pair of ideological positions for the two can-
didates such that each takes the position that maximizes his campaign
(c) Suppose that in addition to collecting contributions from extremists
on their side, candidates can also collect campaign contributions from
moderates whose views are closer to their position than to that of their
rivals’ position. Suppose that moderates, like extremists, contribute to
their preferred candidate and that they contribute in proportion to the
difference between their own ideological distance from their less-preferred
candidate and their ideological distance from their more-preferred can-
didate. Show that in this case the unique positions in which the left-
and right-wing candidates are each maximizing their campaign contribu-
tions, given the position of the other candidate, occurs where x=1/4
and y=3/4. Total contributions received
by the left wing candidate will be
