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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)
(c) On the same graph, draw and label a separate demand curve for the
2 4 6 8 10 12 14 16
32
64
96
128
160
192
224
256
Actual Market Share (in sixteenths)
Willingness to Pay
0
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
(c) Suppose that the government offers to subsidize “pioneer users” of the
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
sign up only if their buyer values will be at least equal to the price they
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)
(c) Would the total number of copies sold over two years increase, de-
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
be
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−
(c) Solveforthepricepthat maximizes its total revenue net of variable
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.
(c) The total number of new books sold in the first year would be
(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.
440 INFORMATION TECHNOLOGY (Ch. 36)
(c) On the same graph, draw and label a separate demand curve for the
2 4 6 8 10 12 14 16
32
64
96
128
160
192
224
256
Actual Market Share (in sixteenths)
Willingness to Pay
0
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
(c) Suppose that the government offers to subsidize “pioneer users” of the
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
sign up only if their buyer values will be at least equal to the price they
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)
(c) Would the total number of copies sold over two years increase, de-
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
be
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−
(c) Solveforthepricepthat maximizes its total revenue net of variable
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.
(c) The total number of new books sold in the first year would be
(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.
