978-0393123982 Chapter 36 Solution Manual Part 1

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Chapter 36 NAME

Information Technology

Introduction. We all recognize that information technology has revolu-

tionized the way we produce and consume. Some think that it is necessary

to have a “new economics” to understand this New Economy. We think

not. The economic tools that you have learned in this course can offer

very powerful insights into the economics of information technology, as

we illustrate in this set of problems.

36.1 (2) Bill Barriers, the president of MightySoft software company is

about to introduce a new computer operating system called DoorKnobs.

Because it is easier to swap files with people who have the same operating

system, the amount people are willing to pay to have DoorKnobs on their

computers is greater the larger they believe DoorKnobs’s market share to

be.

The perceived market share for DoorKnobs is the fraction of all com-

puters that the public believes is using DoorKnobs. When the price of

DoorKnobs is p,thenitsactual market share is the fraction of all com-

puter owners that would be willing to pay at least $pto have DoorKnobs

installed on their computers. Market researchers have discovered that if

DoorKnobs’s perceived market share is sand the price of DoorKnobs is

$p, then its actual market share will be x,wherexis related to the price

pand perceived market share sby the formula

p= 256s(1 −x).(1)

In the short run, MightySoft can influence the perceived market share

of DoorKnobs by publicity, advertising, giving liquor and gifts to friendly

journalists, and giving away copies in conspicuous ways. In the long run,

the truth will emerge, and DoorKnobs’s perceived market share smust

equal its actual market share x.

(a) If the perceived market share is s, then the demand curve for Door-

Knobs is given by Equation 1. On the graph below, draw the demand

(b) On the demand curve that you just drew with s=1/2, mark a

red dot on the point at which the actual market share of DoorKnobs is

1/2. (This is the point on the demand curve directly above x=1/2.)

440 INFORMATION TECHNOLOGY (Ch. 36)

2 4 6 8 10 12 14 16

128

160

192

224

256

Actual Market Share (in sixteenths)

Willingness to Pay

S=1/8

S=1/4

S=1/2

S=3/4

S=7/8

S=1

(d) On the demand curve for a perceived market share of s=1/4, put

a red dot on the point at which the actual market share of DoorKnobs

(e) Just as you did for s=1/2ands=1/4, make red marks on the

demand curves corresponding to s= 1/8, 3/4, 7/8, and 1, showing the

(f) Let us now draw the long-run demand curve for DoorKnobs, where we

assume that computer owners’ perceived market shares sare the same as

the actual market shares x. If this is the case, it must be that s=x,so

(g) Suppose that MightySoft sets a price of $48 for DoorKnobs and sticks

with that price. There are three different perceived market shares such

that the fraction of consumers who would actually want to buy Door-

(h) Suppose that by using its advertising and media influence, MightySoft

can temporarily set its perceived market share at any number between

0 and 1. If DoorKnobs’s perceived market share is xand if MightySoft

charges a price p= 256x(1 −x), the actual market fraction will also be x

and the earlier perceptions will be reinforced and maintained. Assuming

that MightySoft chooses a perceived market share xand a price that

makes the actual market share equal to the perceived market share, what

market share xshould MightySoft choose in order to maximize its revenue

and what price should it charge in order to maintain this market share?

(Hint: Revenue is px = 256x2(1 −x).) Use calculus and show your

36.2 (1) Suppose that demand for DoorKnobs is as given in the previous

problem, and assume that the perceived market share in any period is

equal to the actual market share in the previous period. Then where xt

is the actual market share in period t, the equation p= 256xt−1(1 −xt)

is satisfied. Rearranging this equation, we find that xt=1−(p/256xt−1)

whenever p/256xt−1≤1. If p/256xt−1≤0, then xt=0. Withthis

formula, if we know actual market share for any time period, we can

calculate market share for the next period.

Let us assume that DoorKnobs sets the price at p= $32 and never

changes this price. (To answer the following questions, you will find a

calculator useful.)

(a) If the actual market share in the first period was 1/2, find the actual

442 INFORMATION TECHNOLOGY (Ch. 36)

(b) Notice that when price is held constant at p, if DoorKnobs’s mar-

ket share converges to a constant ¯x, it must be that ¯x=1−(p/256¯x).

Solve this equation for ¯xin the case where p= $32. What do you make

36.3 (1) A group of 13 consumers are considering whether to connect to a

new computer network. Consumer 1 has an initial value of $1 for hooking

up to the network, consumer 2 has an initial value of $2, consumer 3 has

an iinitial value of $3, and so on up to consumer 13. Each consumer’s

willingness to pay to connect to the network depends on the total number

of persons who are connected to it. In fact, for each i, consumer i’s

willingness to pay to connect to the network is itimes the total number

of persons connected. Thus if 5 people are connected to the network,

consumer 1’s willingness to pay is $5, consumer 2’s willingness to pay is

$10 and so on.

(a) What is the highest price at which 9 customers could hook up to the

(b) Suppose that the industry that supplies the computer network is com-

petitive and that the cost of hooking up each consumer to the network is

$45. Suppose that consumers are very conservative and nobody will sign

up for the network unless her buyer value will be at least as high as the

price she paid as soon as she signs up. How many people will sign up if

system. The first two users are allowed to connect for $10 each. After

the first two users are hooked up, the government allows the next two

to connect for $25. After that, everyone who signs up will have to pay

the full cost of $45. Assume that users remain so conservative that will

are charged when they connect. With the subsidy in place, how many

36.4 (2) Professor Kremepuff has written a new, highly simplified eco-

nomics text, Microeconomics for the Muddleheaded, which will be pub-

lished by East Frisian Press. The first edition of this book will be in print

for two years, at which time it will be replaced by a new edition. East

NAME 443

Frisian Press has already made all its fixed cost investments in the book

and must pay a constant marginal cost of $cfor each copy that it sells.

Let p1be the price charged for new copies sold in the first year of

publication and let p2be the price charged for new copies sold in the

second year of publication. The publisher and the students who buy

the book are aware that there will be an active market for used copies of

Microeconomics for the Muddleheaded one year after publication and that

used copies of the first edition will have zero resale value two years after

publication. At the end of the first year of publication, students can resell

their used textbooks to bookstores for 40% of the second-year price, p2.

The net cost to a student of buying the book in the first year, using it

for class, and reselling it at the end of the year is p1−0.4p2. The number

of copies demanded in the first year of publication is given by a demand

function, q1=D1(p1−0.4p2).

Some of the students who use the book in the first year of publication

will want to keep their copies for future reference, and some will damage

their books so that they cannot be resold. The cost of keeping one’s old

copy or of damaging it is the resale price 0.4p2. The number of books that

are either damaged or kept for reference is given by a “keepers” demand

function, Dk(0.4p2). It follows that the number of used copies available

at the end of the first year will be D1(p1−0.4p2)−Dk(0.4p2).

Students who buy Microeconomics for the Muddleheaded in the sec-

ond year of publication will not be able to resell their used copies, since

a new edition will then be available. These students can, however, buy

either a new copy or a used copy of the book. For simplicity of calcula-

tions, let us assume that students are indifferent between buying a new

copy or a used copy and that used copies cost the same as new copies in

the book store. (The results would be the same if students preferred new

to used copies, but bookstores priced used copies so that students were

indifferent between buying new and used copies.) The total number of

copies, new and used, that are purchased in the second year of publication

is q2=D2(p2).

(a) Write an expression for the number of new copies that East Frisian

Press can sell in the second year after publication if it sets prices p1in year

(b) Write an expression for the total number of new copies of Microeco–

nomics for the Muddleheaded that East Frisian can sell over two years at

444 INFORMATION TECHNOLOGY (Ch. 36)

crease, or remain constant if p1were increased and p2remained constant?

(d) Write an expression for the total revenue that East Frisian Press will

receive over the next two years if it sets prices p1and p2.p1D1(p1−

(e) To maximize its total profits over the next two years, East Frisian

must maximize the difference between its total revenue and its variable

costs. Show that this difference can be written as

(p1−p2)D1(p1−0.4p2)+(p2−c)D2(p2)+Dk(0.4p2).

(f) Suppose that East Frisian has decided that it must charge the same

price for the first edition in both years that it is sold. Thus it must

set p=p1=p2. Write an expression for East Frisian’s revenue net

of variable costs over the next two years as a function of p.

36.5 (2) Suppose that East Frisian Press, discussed in the previous

problem, has a constant marginal cost of c= $10 for each copy of Micro-

economics for the Muddleheaded that it sells and let the demand functions

D1(p1−0.4p2) = 100 (90 −p1+0.4p2)

D2(p2) = 100(90 −p2).

The number of books that people either damage or keep for reference

after the first year is

Dk(0.4p2) = 100(90 −0.8p2).

(This assumption is consistent with the assumption that everyone’s will-

ingness to pay for keeping the book is half as great as her willingness to

pay to have the book while she is taking the course.) Assume that East

Frisian Press is determined to charge the same price in both years, so that

p1=p2=p.

NAME 445

(a) If East Frisian Press charges the same price pfor Microeconomics for

the Muddleheaded in the first and second years, show that the total sales

of new copies over the two years are equal to

18,000 −180p.

(b) Write an expression for East Frisian’s total revenue, net of variable

costs, over the first two years as a function of the price p.(p−

costs over the first two years. p= $55.At this price, the net cost

to students in the first year of buying the text and reselling it is $33.

36.6 (2) East Frisian Press is trying to decide whether it would be prof-

itable to produce a new edition of Microeconomics for the Muddleheaded

after one year rather than after two years. If it produces a new edition

after one year, it will destroy the used book market and all copies that

are purchased will be new copies. In this case, the number of new copies

that will be demanded in each of the two years will be 100(90 −p), where

pis the price charged. The variable cost of each copy sold remains $10.

(a) Write an expression for the total number of copies sold over the course

446 INFORMATION TECHNOLOGY (Ch. 36)

(b) Find the price that maximizes total revenue net of variable costs.

(d) East Frisian’s total revenue net of variable costs, if it markets a new

(e) Would it be more profitable for East Frisian Press to produce a new

edition after one year or after two years? After two years.

Which would be better for students? (Hint: The answer is not the same

36.7 (3) Suppose that East Frisian Press publishes a new edition only af-

ter two years and that demands and costs are as in the previous problems.

Suppose that it sets two different prices p1and p2in the two periods.

(a) Write an expression for the total number of new copies sold at prices

p1and p2and show that this number depends on p2but not on p1.

(b) Show that at prices p1and p2, the difference between revenues and

variable costs is equal to

100 90p1+ 108p2+1.4p1p2−p2

1−2.2p2

2−1,800.