978-0393123982 Chapter 26 Solution Manual Part 2

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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

(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.

(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

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