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NAME 447
the cost of using Microeconomics for the Muddleheaded for a student who
buys the book when it is first published and resells it at the end of the
first year with the cost for a student who buys the book at the beginning
36.8 (2) The Silicon Valley company Intoot produces checkwriting soft-
ware. The program itself, Fasten, sells for $50 and includes a package of
checks. Check refill packets for Fasten cost $20 to produce and Intoot sells
the checks at cost. Suppose that a consumer purchases Fasten for $50 in
period 1 and spends $20 on checks in each subsequent period. Assume
for simplicity that the consumer uses the program for an infinite number
of periods.
(a) If the interest rate is r=.10 per period, what is the present value
of the stream of payments made by the consumer? (Hint: a stream of
payments of xstarting next period has a present value of x/r.) The total
(b) Fasten’s competitor produces an equally effective product called
Czechwriter. Czechwriter can do everything Fasten can do and vice versa
except that Fasten cannot use check refill packets that are sold by anyone
other than Fasten. Czechwriter also sells for $50 and sells its checks for
$20 per period. A Fasten customer can switch to Czechwriter simply by
(c) Fasten is contemplating raising the price of checks to $30 per period.
If so, will its customers switch to Czechwriter? Explain. Yes, the
448 INFORMATION TECHNOLOGY (Ch. 36)
(d) Fasten contemplates raising the price of checks to $22 per period. Will
its customers switch? No. The present value of
(e) At what price for checks will Fasten’s customers just be indifferent to
switching? (Hint: Let xbe this amount. Compare the present value of
staying with Fasten with the present value of switching to Czechwriter.)
(f) If it charges the highest price that it can without making its customers
switch, what profit does Fasten make on checks from each of its customers
per period? $5. What is the present value of the profit per customer
that Fasten gets if it sets the price of checks equal to the number deter-
(g) Suppose now that the cost of switching also involves several hours
of data conversion that the consumer values at $100. The total cost of
switching is the cost of the new program plus the data conversion cost
(h) Making allowances for the cost of data conversion, what is the highest
price that Intoot can charge for its checks? Solve x/.10 =
(i) Suppose that someone writes a computer program that eliminates
the cost of converting data and makes this program available for free.
Suppose that Intoot continues to price its check refill packages at $25. A
new customer is contemplating buying Fasten at a price of $50 and paying
$25 per period for checks, versus paying $50 for Czechwriter and paying
$20 for checks. If the functionality of the software is identical, which will
NAME 449
(j) Intoot decides to distribute a coupon that offers a discount of $50
off of the regular purchase price. What price would it have to set to
make consumers indifferent between purchasing Fasten and Czechwriter?
(k) Suppose that consumers are shortsighted and only look at the cost
of the software itself, neglecting the cost of the checks. Which program
would they buy if Intoot offered this coupon? Fasten. How might
36.9 (2) Sol Microsystems has recently invented a new language, Guava,
which runs on a proprietary chip, the Guavachip. The chip can only be
used to run Guava, and Guava can only run on the Guavachip. Sol
estimates that if it sells the chip for a price pcand the language for a
price pg, the demand for the chip-language system will be
x= 120 −(pc+pg).
(a) Sol initially sets up two independent subsidiaries, one to produce the
chip and one to produce the language. Each of the subsidiaries will price
its product so as to maximize its profits, while assuming that a change in
its own price will not affect the pricing decision of the other subsidiary.
.
(b) Differentiate this profit function with respect to pcand set the result
equal to zero to calculate the optimal choice of pcas a function of pg.
(c) Now consider the language subsidiary’s pricing decision. The optimal
(d) Solving these two equations in two unknowns, we find that pc=
.
450 INFORMATION TECHNOLOGY (Ch. 36)
(e) Sol Microsystems decides that the independent subsidiary system is
cumbersome, so it sets up Guava Computing which sells a bundled system
consisting of the chip and the language. Let pbe the price of the bundle.
(f) Differentiate this profit with respect to pand set the resulting expres-
(g) Compare the prices charged by the integrated system and the separate
36.10 (2) South Belgium Press produces the academic journal Nano-
economics, which has a loyal following among short microeconomists, and
Gigaeconomics, a journal for tall macroeconomists. It offers a license for
the electronic version of each journal to university libraries at a subscrip-
tion cost per journal of $1,000 per year. The 200 top universities all
subscribe to both journals, each paying $2,000 per year to South Bel-
gium. By revealed preference, their willingness to pay for each journal is
at least $1,000.
(a) In an attempt to lower costs, universities decide to form pairs, with
one member of each pair subscribing to Nanoeconomics and one member
of each pair subscribing to Gigaeconomics. They agree to use interlibrary
loan to share the other journal. Since the copies are electronic, there is
no incremental cost to doing this. Under this pairing scheme, how many
subscriptions of each journal will South Belgium sell? 100
(b) In order to stem the revenue hemorrhage, South Belgium raises the
price of each journal. Assuming library preferences and budgets haven’t
(c) How does library expenditure and South Belgium’s revenue compare
NAME 451
(d) If there were a cost of interlibrary loan, how would your an-
swer change? Assuming they still bought
36.11 (2) Henrietta Fowler publishes Metropolitan Chicken, a maga-
zine devoted to raising poultry in urban environments. She has con-
ducted extensive surveys from potential readers and potential advertisers.
The amount that advertisers are willing to pay for an ad in Metropolitan
Chicken is proportional to the number of subscribers. She estimates that
if she charges advertisers a rate of PAcents per-subscriber for each ad,
she could attract QA=80−PAadvertisements. Suppose that the cost of
printing and distributing an advertisement is negligible. The number of
subscribers to Metropolitan Chicken is determined by the demand equa-
tion QS=4,000 −PSwhere PSis the subscription price measured in
cents. The cost of printing, handling, and mailing a copy of Metropolitan
Chicken is 400 cents per subscriber.
(a) Write an expression for Metropolitan Chicken’s total revenue from
advertising as a function of the variables QAand QS. (Remember that
total revenue is revenue per reader times the number of readers.) (80−
QA)QAQSSolve for the number of ads and the price per-subscriber
(b) Write an expression for Metropolitan Chicken’s net revenue (in cents)
from subscriptions (total subscription revenue minus costs of printing,
handling, and mailing to subscribers) as a function of QS.(4,000 −
452 INFORMATION TECHNOLOGY (Ch. 36)
(c) Write an expression for Henrietta’s total profit from advertising and
subscriptions as a function of the two variables QAand QS.(80 −
Calculus 36.12 (2) Sam Hitchem owns the dance hall in Lonely Pine, Wisconsin.
He holds a dance every week. This dance hall is one of the few suitable
locations in the county for unattached men and women to meet each other.
Sam charges admission fee Pmfor men and admission fee Pwfor women.
At any price, individuals are more likely to come if they expect to see
more persons of the opposite sex. Sam has discovered that if he charges
price Pmto men and if they expect Qwwomen to be in attendance, then
the number of men who will attend is
If he charges Pwto women and if they expect Qmmen to be present, the
number of women who will attend is
(a) Rearrange the two demand equations above to produce “inverse de-
mand functions” in which prices are expressed in terms of quantities. We
4
4
(b) Sam chooses prices so as to maximize his total revenue PmQm+
PwQw. Using your answer to the previous question, you can write Sam’s
revenue simply as a function of the two variables Qmand Qw. Write this
(c) Sam chooses admission prices so as to maximize his revenue. We
can solve for these admission prices by first finding the values of Qmand
Qwthat maximize revenue and then substituting these quantities into
the demand functions to find the prices at which these quantities will be
demanded. You have found an expression for revenue as a function of Qm
and Qw. Set the partial derivatives of this expression with respect to Qm
NAME 453
and Qwequal to zero and solve these two equations for the two variables
Qmand Qw. Sam will maximize his revenue if the number of men who
.
448 INFORMATION TECHNOLOGY (Ch. 36)
(d) Fasten contemplates raising the price of checks to $22 per period. Will
its customers switch? No. The present value of
(e) At what price for checks will Fasten’s customers just be indifferent to
switching? (Hint: Let xbe this amount. Compare the present value of
staying with Fasten with the present value of switching to Czechwriter.)
(f) If it charges the highest price that it can without making its customers
switch, what profit does Fasten make on checks from each of its customers
per period? $5. What is the present value of the profit per customer
that Fasten gets if it sets the price of checks equal to the number deter-
(g) Suppose now that the cost of switching also involves several hours
of data conversion that the consumer values at $100. The total cost of
switching is the cost of the new program plus the data conversion cost
(h) Making allowances for the cost of data conversion, what is the highest
price that Intoot can charge for its checks? Solve x/.10 =
(i) Suppose that someone writes a computer program that eliminates
the cost of converting data and makes this program available for free.
Suppose that Intoot continues to price its check refill packages at $25. A
new customer is contemplating buying Fasten at a price of $50 and paying
$25 per period for checks, versus paying $50 for Czechwriter and paying
$20 for checks. If the functionality of the software is identical, which will
NAME 449
(j) Intoot decides to distribute a coupon that offers a discount of $50
off of the regular purchase price. What price would it have to set to
make consumers indifferent between purchasing Fasten and Czechwriter?
(k) Suppose that consumers are shortsighted and only look at the cost
of the software itself, neglecting the cost of the checks. Which program
would they buy if Intoot offered this coupon? Fasten. How might
36.9 (2) Sol Microsystems has recently invented a new language, Guava,
which runs on a proprietary chip, the Guavachip. The chip can only be
used to run Guava, and Guava can only run on the Guavachip. Sol
estimates that if it sells the chip for a price pcand the language for a
price pg, the demand for the chip-language system will be
x= 120 −(pc+pg).
(a) Sol initially sets up two independent subsidiaries, one to produce the
chip and one to produce the language. Each of the subsidiaries will price
its product so as to maximize its profits, while assuming that a change in
its own price will not affect the pricing decision of the other subsidiary.
.
(b) Differentiate this profit function with respect to pcand set the result
equal to zero to calculate the optimal choice of pcas a function of pg.
(c) Now consider the language subsidiary’s pricing decision. The optimal
(d) Solving these two equations in two unknowns, we find that pc=
.
450 INFORMATION TECHNOLOGY (Ch. 36)
(e) Sol Microsystems decides that the independent subsidiary system is
cumbersome, so it sets up Guava Computing which sells a bundled system
consisting of the chip and the language. Let pbe the price of the bundle.
(f) Differentiate this profit with respect to pand set the resulting expres-
(g) Compare the prices charged by the integrated system and the separate
36.10 (2) South Belgium Press produces the academic journal Nano-
economics, which has a loyal following among short microeconomists, and
Gigaeconomics, a journal for tall macroeconomists. It offers a license for
the electronic version of each journal to university libraries at a subscrip-
tion cost per journal of $1,000 per year. The 200 top universities all
subscribe to both journals, each paying $2,000 per year to South Bel-
gium. By revealed preference, their willingness to pay for each journal is
at least $1,000.
(a) In an attempt to lower costs, universities decide to form pairs, with
one member of each pair subscribing to Nanoeconomics and one member
of each pair subscribing to Gigaeconomics. They agree to use interlibrary
loan to share the other journal. Since the copies are electronic, there is
no incremental cost to doing this. Under this pairing scheme, how many
subscriptions of each journal will South Belgium sell? 100
(b) In order to stem the revenue hemorrhage, South Belgium raises the
price of each journal. Assuming library preferences and budgets haven’t
(c) How does library expenditure and South Belgium’s revenue compare
NAME 451
(d) If there were a cost of interlibrary loan, how would your an-
swer change? Assuming they still bought
36.11 (2) Henrietta Fowler publishes Metropolitan Chicken, a maga-
zine devoted to raising poultry in urban environments. She has con-
ducted extensive surveys from potential readers and potential advertisers.
The amount that advertisers are willing to pay for an ad in Metropolitan
Chicken is proportional to the number of subscribers. She estimates that
if she charges advertisers a rate of PAcents per-subscriber for each ad,
she could attract QA=80−PAadvertisements. Suppose that the cost of
printing and distributing an advertisement is negligible. The number of
subscribers to Metropolitan Chicken is determined by the demand equa-
tion QS=4,000 −PSwhere PSis the subscription price measured in
cents. The cost of printing, handling, and mailing a copy of Metropolitan
Chicken is 400 cents per subscriber.
(a) Write an expression for Metropolitan Chicken’s total revenue from
advertising as a function of the variables QAand QS. (Remember that
total revenue is revenue per reader times the number of readers.) (80−
QA)QAQSSolve for the number of ads and the price per-subscriber
(b) Write an expression for Metropolitan Chicken’s net revenue (in cents)
from subscriptions (total subscription revenue minus costs of printing,
handling, and mailing to subscribers) as a function of QS.(4,000 −
452 INFORMATION TECHNOLOGY (Ch. 36)
(c) Write an expression for Henrietta’s total profit from advertising and
subscriptions as a function of the two variables QAand QS.(80 −
Calculus 36.12 (2) Sam Hitchem owns the dance hall in Lonely Pine, Wisconsin.
He holds a dance every week. This dance hall is one of the few suitable
locations in the county for unattached men and women to meet each other.
Sam charges admission fee Pmfor men and admission fee Pwfor women.
At any price, individuals are more likely to come if they expect to see
more persons of the opposite sex. Sam has discovered that if he charges
price Pmto men and if they expect Qwwomen to be in attendance, then
the number of men who will attend is
If he charges Pwto women and if they expect Qmmen to be present, the
number of women who will attend is
(a) Rearrange the two demand equations above to produce “inverse de-
mand functions” in which prices are expressed in terms of quantities. We
4
4
(b) Sam chooses prices so as to maximize his total revenue PmQm+
PwQw. Using your answer to the previous question, you can write Sam’s
revenue simply as a function of the two variables Qmand Qw. Write this
(c) Sam chooses admission prices so as to maximize his revenue. We
can solve for these admission prices by first finding the values of Qmand
Qwthat maximize revenue and then substituting these quantities into
the demand functions to find the prices at which these quantities will be
demanded. You have found an expression for revenue as a function of Qm
and Qw. Set the partial derivatives of this expression with respect to Qm
NAME 453
and Qwequal to zero and solve these two equations for the two variables
Qmand Qw. Sam will maximize his revenue if the number of men who
.
