The short-run supply curve of a competitive ﬁrm is the portion of its
short-run marginal cost curve that is upward sloping and lies above its
average variable cost curve. The long-run supply curve of a competitive
ﬁrm is the portion of its short-run marginal cost curve that is upwardsloping
and lies above its long-run average cost curve.
A ﬁrm has the long-run cost function c(y) = 2y2
+ 200 for y > 0 and
c(0) = 0. Let us ﬁnd its long-run supply curve. The ﬁrm’s marginal
cost when its output is y is MC(y) = 4y. If we graph output on the
horizontal axis and dollars on the vertical axis, then we ﬁnd that the
long-run marginal cost curve is an upward-sloping straight line through
the origin with slope 4. The long-run supply curve is the portion of this
curve that lies above the long-run average cost curve. When output is y,
long-run average costs of this ﬁrm are AC(y) = 2y + 200/y. This is a Ushaped
curve. As y gets close to zero, AC(y) becomes very large because
200/y becomes very large. When y is very large, AC(y) becomes very
large because 2y is very large. When is it true that AC(y) < MC(y)?
This happens when 2y +200/y < 4y. Simplify this inequality to ﬁnd that
AC(y) < MC(y) when y > 10. Therefore the long-run supply curve is
the piece of the long-run marginal cost curve for which y > 10. So the
long-run supply curve has the equation p = 4y for y > 10. If we want to
ﬁnd quantity supplied as a function of price, we just solve this expression
for y as a function of p. Then we have y = p/4 whenever p > 40.
Suppose that p < 40. For example, what if p = 20, how much will
the ﬁrm supply? At a price of 20, if the ﬁrm produces where price equals
long-run marginal cost, it will produce 5 = 20/4 units of output. When
the ﬁrm produces only 5 units, its average costs are 2 × 5 + 200/5 = 50.
Therefore when the price is 20, the best the ﬁrm can do if it produces a
positive amount is to produce 5 units. But then it will have total costs of
5×50 = 250 and total revenue of 5×20 = 100. It will be losing money. It
would be better oﬀ producing nothing at all. In fact, for any price p < 40,
the ﬁrm will choose to produce zero output.
22.1 (0) Remember Otto’s brother Dent Carr, who is in the auto repair
business? Dent found that the total cost of repairing s cars is c(s) =
2s2
+ 100.
(a) This implies that Dent’s average cost is equal to , his
average variable cost is equal to , and his marginal cost is equal
to On the graph below, plot the above curves, and also plot
Dent’s supply curve.
Dollars
80
60
40
20
0 5 10 15 20
Output
(b) If the market price is $20, how many cars will Dent be willing to
repair? If the market price is $40, how many cars will Dent
repair? .
(c) Suppose the market price is $40 and Dent maximizes his proﬁts. On
the above graph, shade in and label the following areas: total costs, total
revenue, and total proﬁts.
22.2 (0) A competitive ﬁrm has the following short-run cost function:
c(y) = y3
− 8y2
+ 30y + 5.
(a) The ﬁrm’s marginal cost function is MC(y) = .
(b) The ﬁrm’s average variable cost function is AV C(y) =
(Hint: Notice that total variable costs equal c(y) − c(0).)
(c) On the axes below, sketch and label a graph of the marginal cost
function and of the average variable cost function.
(d) Average variable cost is falling as output rises if output is less than
and rising as output rises if output is greater than .
(e) Marginal cost equals average variable cost when output is .
(f) The ﬁrm will supply zero output if the price is less than .
(g) The smallest positive amount that the ﬁrm will ever supply at any
price is At what price would the ﬁrm supply exactly 6 units of
output? .
Costs
40
30
20
10
0 2 4 6 8
y
22.3 (0) Mr. McGregor owns a 5-acre cabbage patch. He forces his
wife, Flopsy, and his son, Peter, to work in the cabbage patch without
wages. Assume for the time being that the land can be used for nothing
other than cabbages and that Flopsy and Peter can ﬁnd no alternative
employment. The only input that Mr. McGregor pays for is fertilizer. If
he uses x sacks of fertilizer, the amount of cabbages that he gets is 10
√
x.
Fertilizer costs $1 per sack.
(a) What is the total cost of the fertilizer needed to produce 100 cabbages?
What is the total cost of the amount of fertilizer needed to
produce y cabbages? .
(b) If the only way that Mr. McGregor can vary his output is by varying
the amount of fertilizer applied to his cabbage patch, write an expression
for his marginal cost, as a function of y. MC(y) = .
(c) If the price of cabbages is $2 each, how many cabbages will Mr. McGregor
produce? How many sacks of fertilizer will he buy?
How much proﬁt will he make? .
(d) The price of fertilizer and of cabbages remain as before, but Mr. McGregor
learns that he could ﬁnd summer jobs for Flopsy and Peter in
a local sweatshop. Flopsy and Peter would together earn $300 for the
summer, which Mr. McGregor could pocket, but they would have no time
to work in the cabbage patch. Without their labor, he would get no cabbages.
Now what is Mr. McGregor’s total cost of producing y cabbages?
.
(e) Should he continue to grow cabbages or should he put Flopsy and
Peter to work in the sweatshop? .
22.4 (0) Severin, the herbalist, is famous for his hepatica. His total cost
function is c(y) = y2
+ 10 for y > 0 and c(0) = 0. (That is, his cost of
producing zero units of output is zero.)
(a) What is his marginal cost function? What is his average cost
function? .
(b) At what quantity is his marginal cost equal to his average cost?
At what quantity is his average cost minimized? .
(c) In a competitive market, what is the lowest price at which he will
supply a positive quantity in long-run equilibrium? How
much would he supply at that price? .
22.5 (1) Stanley Ford makes mountains out of molehills. He can do this
with almost no eﬀort, so for the purposes of this problem, let us assume
that molehills are the only input used in the production of mountains.
Suppose mountains are produced at constant returns to scale and that
it takes 100 molehills to make 1 mountain. The current market price of
molehills is $20 each. A few years ago, Stan bought an “option” that
permits him to buy up to 2,000 molehills at $10 each. His option contract
explicitly says that he can buy fewer than 2,000 molehills if he wishes, but
he can not resell the molehills that he buys under this contract. In order
to get governmental permission to produce mountains from molehills,
Stanley would have to pay $10,000 for a molehill-masher’s license.
(a) The marginal cost of producing a mountain for Stanley is
if he produces fewer than 20 mountains. The marginal cost of producing
a mountain is if he produces more than 20 mountains.
(b) On the graph below, show Stanley Ford’s marginal cost curve (in blue
ink) and his average cost curve (in red ink).
Dollars
4000
3000
2000
1000
0 10 20 30 40
Output
(c) If the price of mountains is $1,600, how many mountains will Stanley
produce? .
(d) The government is considering raising the price of a molehill-masher’s
license to $11,000. Stanley claims that if it does so he will have to go
out of business. Is Stanley telling the truth? What is the
highest fee for a license that the government could charge without driving
him out of business?
.
(e) Stanley’s lawyer, Eliot Sleaze, has discovered a clause in Stanley’s
option contract that allows him to resell the molehills that he purchased
under the option contract at the market price. On the graph above,
use a pencil to draw Stanley’s new marginal cost curve. If the price of
mountains remains $1,600, how many mountains will Stanley produce
now? .
22.6 (1) Lady Wellesleigh makes silk purses out of sows’ ears. She is
the only person in the world who knows how to do so. It takes one sow’s
ear and 1 hour of her labor to make a silk purse. She can buy as many
sows’ ears as she likes for $1 each. Lady Wellesleigh has no other source
of income than her labor. Her utility function is a Cobb-Douglas function
U(c, r) = c1/3
r2/3
, where c is the amount of money per day that she has
to spend on consumption goods and r is the amount of leisure that she
has. Lady Wellesleigh has 24 hours a day that she can devote either to
leisure or to working.
(a) Lady Wellesleigh can either make silk purses or she can earn $5 an
hour as a seamstress in a sweatshop. If she worked in the sweat shop, how
many hours would she work? (Hint: To solve for this amount,
write down Lady Wellesleigh’s budget constraint and recall how to ﬁnd
the demand function for someone with a Cobb-Douglas utility function.)
(b) If she could earn a wage of $w an hour as a seamstress, how much
would she work? .
(c) If the price of silk purses is $p, how much money will Lady Wellesleigh
earn per purse after she pays for the sows’ ears that she uses? .
(d) If she can earn $5 an hour as a seamstress, what is the lowest price
at which she will make any silk purses? .
(e) What is the supply function for silk purses? (Hint: The price of silk
purses determines the “wage rate” that Lady W. can earn by making silk
purses. This determines the number of hours she will choose to work and
hence the supply of silk purses.) .
22.7 (0) Remember Earl, who sells lemonade in Philadelphia? You
met him in the chapter on cost functions. Earl’s production function is
f(x1, x2) = x
1/3
1 x
1/3
2 , where x1 is the number of pounds of lemons he
uses and x2 is the number of hours he spends squeezing them. As you
found out, his cost function is c(w1, w2, y) = 2w
1/2
1 w
1/2
2 y3/2
, where y is
the number of units of lemonade produced.
(a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the
price of lemonade is p, Earl’s marginal cost function is MC(y) =
and his supply function is S(p) = If lemons cost $4
per pound and the wage rate is $9 per hour, his supply function will be
S(p) = .
(b) In general, Earl’s marginal cost depends on the price of lemons and
the wage rate. At prices w1 for lemons and w2 for labor, his marginal
cost when he is producing y units of lemonade is MC(w1, w2, y) =
The amount that Earl will supply depends on the three
variables, p, w1, w2. As a function of these three variables, Earl’s supply
is S(p, w1, w2) = .
22.8 (0) As you may recall from the chapter on cost functions, Irma’s
handicrafts has the production function f(x1, x2) = (min{x1, 2x2})1/2
,
where x1 is the amount of plastic used, x2 is the amount of labor used,
and f(x1, x2) is the number of lawn ornaments produced. Let w1 be the
price per unit of plastic and w2 be the wage per unit of labor.
(a) Irma’s cost function is c(w1, w2, y) = .
(b) If w1 = w2 = 1, then Irma’s marginal cost of producing y units of
output is MC(y) = The number of units of output that she would
supply at price p is S(p) = At these factor prices, her average
cost per unit of output would be AC(y) = .
(c) If the competitive price of the lawn ornaments she sells is p = 48, and
w1 = w2 = 1, how many will she produce? How much proﬁt will
she make? .
(d) More generally, at factor prices w1 and w2, her marginal cost is a function
MC(w1, w2, y) = At these factor prices and an output
price of p, the number of units she will choose to supply is S(p, w1, w2) =
.
22.9 (0) Jack Benny can get blood from a stone. If he has x stones, the
number of pints of blood he can extract from them is f(x) = 2x
1
3 . Stones
cost Jack $w each. Jack can sell each pint of blood for $p.
(a) How many stones does Jack need to extract y pints of blood?
.
(b) What is the cost of extracting y pints of blood? .
(c) What is Jack’s supply function when stones cost $8 each?
When stones cost $w each? .
(d) If Jack has 19 relatives who can also get blood from a stone in the
same way, what is the aggregate supply function for blood when stones
cost $w each? .
22.10 (1) The Miss Manners Reﬁnery in Dry Rock, Oklahoma, converts
crude oil into gasoline. It takes 1 barrel of crude oil to produce 1 barrel of
gasoline. In addition to the cost of oil there are some other costs involved
in reﬁning gasoline. Total costs of producing y barrels of gasoline are
described by the cost function c(y) = y2
/2 + poy, where po is the price of
a barrel of crude oil.
(a) Express the marginal cost of producing gasoline as a function of po
and y. .
(b) Suppose that the reﬁnery can buy 50 barrels of crude oil for $5 a
barrel but must pay $15 a barrel for any more that it buys beyond 50
barrels. The marginal cost curve for gasoline will be up to
50 barrels of gasoline and thereafter.
(c) Plot Miss Manners’ supply curve in the diagram below using blue ink.
Price of gasoline
80
60
40
20
0 25 50 75 100
Barrels of gasoline
(d) Suppose that Miss Manners faces a horizontal demand curve for gasoline
at a price of $30 per barrel. Plot this demand curve on the graph
above using red ink. How much gasoline will she supply? .
(e) If Miss Manners could no longer get the ﬁrst 50 barrels of crude for
$5, but had to pay $15 a barrel for all crude oil, how would her output
change? .
(f) Now suppose that an entitlement program is introduced that permits
reﬁneries to buy one barrel of oil at $5 for each barrel of oil that they buy
for $15. What will Miss Manners’ supply curve be now?
Assume that it can buy fractions of a barrel in the same manner.
Plot this supply curve on the graph above using black ink. If the demand
curve is horizontal at $30 a barrel, how much gasoline will Miss Manners
supply now? .
To ﬁnd the industry supply of output, just add up the supply of output
coming from each individual ﬁrm. Remember to add quantities, not
prices. The industry supply curve will have a kink in it where the market
price becomes low enough that some ﬁrm reduces its quantity supplied to
zero.
The series of problems about the garden gnome industry are designed
to help you to understand the distinction between the long run and the
short run. To solve these problems, you need to pay careful attention to
the timing of decisions. In particular, in this problem, units of capital
(gnome molds) can be produced and delivered only one year after they
are ordered.
The last three questions of this chapter apply supply and demand
analysis to some problems in the economics of illegal activities. In these
examples, you will make use of your knowledge of where supply functions
come from.
23.0 Warm Up Exercise. Here are some drills for you on ﬁnding
market supply functions from linear ﬁrm supply functions. The trick here
is to remember that the market supply function may have kinks in it. For
example, if the ﬁrm supply functions are s1(p) = p and s2(p) = p − 2,
then the market supply function is S(p) = p for p ≤ 2 and S(p) = 2p − 2
for p > 2; that is, only the ﬁrst ﬁrm supplies a positive output at prices
below $2, and both ﬁrms supply output at prices above $2. Now try to
construct the market supply function in each of the following cases.
(a) s1(p) = p, s2(p) = 2p, s3(p) = 3p. .
(b) s1(p) = 2p, s2(p) = p − 1. .
(c) 200 ﬁrms each have a supply function s1(p) = 2p − 8 and 100 ﬁrms
each have a supply function s2(p) = p − 3.
.
(d) s1(p) = 3p−12, s2(p) = 2p−8, s3(p) = p−4. .
23.1 (1) Al Deardwarf’s cousin, Zwerg, makes plaster garden gnomes.
The technology in the garden gnome business is as follows. You need a
gnome mold, plaster, and labor. A gnome mold is a piece of equipment
that costs $1,000 and will last exactly one year. After a year, a gnome
mold is completely worn out and has no scrap value. With a gnome
mold, you can make 500 gnomes per year. For every gnome that you
make, you also have to use a total of $7 worth of plaster and labor. The
total amounts of plaster and labor used are variable in the short run. If
you want to produce only 100 gnomes a year with a gnome mold, you
spend only $700 a year on plaster and labor, and so on. The number
of gnome molds in the industry cannot be changed in the short run. To
get a newly built one, you have to special-order it from the gnome-mold
factory. The gnome-mold factory only takes orders on January 1 of any
given year, and it takes one whole year from the time a gnome mold is
ordered until it is delivered on the next January 1. When a gnome mold
is installed in your plant, it is stuck there. To move it would destroy it.
Gnome molds are useless for anything other than making garden gnomes.
For many years, the demand function facing the garden-gnome industry
has been D(p) = 60, 000−5, 000p, where D(p) is the total number
of garden gnomes sold per year and p is the price. Prices of inputs have
been constant for many years and the technology has not changed. Nobody
expects any changes in the future, and the industry is in long-run
equilibrium. The interest rate is 10%. When you buy a new gnome mold,
you have to pay for it when it is delivered. For simplicity of calculations,
we will assume that all of the gnomes that you build during the one-year
life of the gnome mold are sold at Christmas and that the employees and
plaster suppliers are paid only at Christmas for the work they have done
during the past year. Also for simplicity of calculations, let us approximate
the date of Christmas by December 31.
(a) If you invested $1,000 in the bank on January 1, how much money
could you expect to get out of the bank one year later? If
you received delivery of a gnome mold on January 1 and paid for it at
that time, by how much would your revenue have to exceed the costs of
plaster and labor if it is to be worthwhile to buy the machine? (Remember
that the machine will be worn out and worthless at the end of the year.)
.
(b) Suppose that you have exactly one newly installed gnome mold in
your plant; what is your short-run marginal cost of production if you
produce up to 500 gnomes? What is your average variable cost
for producing up to 500 gnomes? If you have only one gnome
mold, is it possible in the short run to produce more than 500 gnomes?
.
(c) If you have exactly one newly installed gnome mold, you would produce
500 gnomes if the price of gnomes is above dollars. You
would produce no gnomes if the price of gnomes is below dol-
lars. You would be indiﬀerent between producing any number of gnomes
between 0 and 500 if the price of gnomes is dollars.
(d) If you could sell as many gnomes as you liked for $10 each and none
at a higher price, what rate of return would you make on your $1,000 by
investing in a gnome mold? Is this higher than the return
from putting your money in the bank? What is the lowest
price for gnomes such that the rate of return you get from ivesting $1000
in a gnome mold is as at least 10%? Could the long-run
equilibrium price of gnomes be lower than this? .
(e) At the price you found in the last section, how many gnomes would be
demanded each year? How many molds would be purchased
each year? Is this a long-run equilibrium price? .
23.2 (1) We continue our study of the garden-gnome industry. Suppose
that initially everything was as described in the previous problem. To
the complete surprise of everyone in the industry, on January 1, 2001,
the invention of a new kind of plaster was announced. This new plaster
made it possible to produce garden gnomes using the same molds, but
it reduced the cost of the plaster and labor needed to produce a gnome
from $7 to $5 per gnome. Assume that consumers’ demand function for
gnomes in 2001 was not changed by this news. The announcement came
early enough in the day for everybody to change his order for gnome
molds to be delivered on January 1, 2002, but of course, but the total
number of molds available to be used in 2001 was just the 28 molds that
had been ordered the previous year. The manufacturer of garden gnome
molds contracted to sell them for $1,000 when they were ordered, so it
can’t change the price it charges on delivery.
(a) On the graph below, draw the short run industry supply curve and
teh demand curve for garden gnomes that applies in the year 2001, after
the discovery of the new plaster is announced.
Price
16
12
8
4
0 4 8 12 16 20 24
Number of gnomes (in thousands)
(b) In 2001, what is the short run equilibrium total output of garden
gnomes, and what is the short run equilibrium price of garden
gnomes? (Hint: Look at the intersection of the supply and
demand curves you just drew. Cousin Zwerg bought a gnome mold that
was delivered on January 1, 2001, and, as had been agreed, he paid $1,000
for it on that day. On January 1, 2002, when he sold the gnomes he had
made during the year and when he paid the workers and the suppliers of
plaster, he received a net cash ﬂow of $ Did he make more
than a 10% rate of return on his investment in the gnome mold?
What rate of return did he make? .
(c) Zwerg’s neighbor, Munchkin, also makes garden gnomes, and he has
a gnome mold that is to be delivered on January 1, 2001. On this day,
Zwerg, who is looking for a way to invest some more money, is considering
buying Munchkin’s new mold from Munchkin and installing it in his own
plant. If Munchkin keeps his mold, he will get a net cash ﬂow of $
in one year. If the interest rate that Munchkin faces, both for
borrowing and lending is 10%, then should he be willing to sell his mold
for $1,000? What is the lowest price that he would be willing to
sell it for? If the best rate of return that Zwerg can make on
alternative investments of additional funds is 10%, what is the most that
Zwerg would be willing to pay for Munchkin’s new mold? .
(d) What do you think will happen to the number of garden gnomes
ordered for delivery on January 1, 2002? Will it be larger, smaller, or
the same as the number ordered the previous year? After
the passage of suﬃcient time, the industry will reach a new long-run
equilibrium. What will be the new equilibrium price of gnomes?
.
23.3 (1) In the previous problem, we studied the eﬀects of a cost-saving
invention. For this problem, we suppose that there was no such invention,
but that a tax is introduced. Suppose that on January 1, 2001, the
industry was as described in the previous problem (without the invention
of the new kind of plaster). On this day, the government surprised the
garden gnome industry by introducing a tax on the production of garden
gnomes. For every garden gnome produced, the manufacturer must pay
a $1 tax. The announcement came early enough in the day so that there
was time for gnome producers to change their orders of gnome molds for
2002. But the gnome molds available to be used in 2001 are those that
had been ordered a year previously. Gnome makers had signed contracts
promising to pay $1,000 for each gnome mold that they ordered, and they
couldn’t back out of these promises. Thus in the short run, during the
year 2001, the number of gnome molds is stuck at 28.
(a) On the graph below, draw the short run industry supply curve for garden
gnomes that applies in the year 2001, after the new tax is introduced.
On the same graph, show the demand curve for garden gnomes.
Price
16
12
8
4
0 4 8 12 16 20 24
Number of gnomes (in thousands)
(b) In 2001, after the tax is introduced, what is the short run equilibrium
total output of garden gnomes, and what is the short run
equilibrium price of garden gnomes? (Hint: Look at the
intersection of the supply and demand curves you just drew.)
(c) If you have a garden gnome mold, the marginal cost of producing a
garden gnome, including the tax, is Therefore all gnome molds
(will, will not) be used up to capacity in 2001.
(d) In 2001, what will be the total output of garden gnomes?
What will be the price of garden gnomes? What rate of
return will Deardwarf’s cousin Zwerg make on his investment in a garden
gnome mold that he ordered a year ago and paid $1,000 for at that time?
.
(e) Remember that Zwerg’s neighbor, Munchkin, also has a gnome mold
that is to be delivered on January 1, 2001. Knowing about the tax makes
Munchkin’s mold a less attractive investment than it was without the
tax, but still Zwerg would buy it if he can get it cheap enough so that he
makes a 10% rate of return on his investment. How much should he be
willing to pay for Munchkin’s new mold? .
(f) What do you think will happen to the number of gnome molds ordered
for delivery on January 1, 2002? Will it be larger, smaller, or the same
as the number ordered the previous year? .
(g) The tax on garden gnomes was left in place for many years, and nobody
expected any further changes in the tax or in demand or supply conditions.
After the passage of suﬃcient time, the industry reached a new
long-run equilibrium. What was the new equilibrium price of gnomes?
.
(h) In the short run, who would end up paying the tax on garden gnomes,
the producers or the consumers? In the long run, did the
price of gnomes go up by more, less, or the same amount as the tax per
gnome? .
(i) Suppose that early in the morning of January 1, 2001, the government
had announced that there would be a $1 tax on garden gnomes, but
that the tax would not go into eﬀect until January 1, 2002. Would the
producers of garden gnomes necessarily be worse oﬀ than if there were
no tax? Why or why not?
.
(j) Is it reasonable to suppose that the government could introduce “surprise”
taxes without making ﬁrms suspicious that there would be similar
“surprises” in the future? Suppose that the introduction of the tax in January
2001 makes gnome makers suspicious that there will be more taxes
introduced in later years. Will this aﬀect equilibrium prices and supplies?
How?
.
23.4 (0) Consider a competitive industry with a large number of ﬁrms,
all of which have identical cost functions c(y) = y2
+ 1 for y > 0 and
c(0) = 0. Suppose that initially the demand curve for this industry is
given by D(p) = 52 − p. (The output of a ﬁrm does not have to be an
integer number, but the number of ﬁrms does have to be an integer.)
(a) What is the supply curve of an individual ﬁrm? S(p) = If
there are n ﬁrms in the industry, what will be the industry supply curve?
.
(b) What is the smallest price at which the product can be sold?
.
(c) What will be the equilibrium number of ﬁrms in the industry? (Hint:
Take a guess at what the industry price will be and see if it works.)
.
(d) What will be the equilibrium price? What will be the
equilibrium output of each ﬁrm? .
(e) What will be the equilibrium output of the industry? .
(f) Now suppose that the demand curve shifts to D(p) = 52.5 − p. What
will be the equilibrium number of ﬁrms? (Hint: Can a new ﬁrm enter the
market and make nonnegative proﬁts?)
.
(g) What will be the equilibrium price?
What will be the equilibrium output of each ﬁrm?
What will be the equilibrium proﬁts of each ﬁrm? .
(h) Now suppose that the demand curve shifts to D(p) = 53 − p. What
will be the equilibrium number of ﬁrms? What will be the
equilibrium price? .
(i) What will be the equilibrium output of each ﬁrm? What
will be the equilibrium proﬁts of each ﬁrm? .
23.5 (3) In 1990, the town of Ham Harbor had a more-or-less free market
in taxi services. Any respectable ﬁrm could provide taxi service as long
as the drivers and cabs satisﬁed certain safety standards.
Let us suppose that the constant marginal cost per trip of a taxi ride
is $5, and that the average taxi has a capacity of 20 trips per day. Let
the demand function for taxi rides be given by D(p) = 1, 200−20p, where
demand is measured in rides per day, and price is measured in dollars.
Assume that the industry is perfectly competitive.
(a) What is the competitive equilibrium price per ride? (Hint: In competitive
equilibrium, price must equal marginal cost.) What is
the equilibrium number of rides per day? How many taxicabs
will there be in equilibrium? .
(b) In 1990 the city council of Ham Harbor created a taxicab licensing
board and issued a license to each of the existing cabs. The board stated
that it would continue to adjust the taxicab fares so that the demand for
rides equals the supply of rides, but no new licenses will be issued in the
future. In 1995 costs had not changed, but the demand curve for taxicab
rides had become D(p) = 1, 220 − 20p. What was the equilibrium price
of a ride in 1995? .
(c) What was the proﬁt per ride in 1995, neglecting any costs associated
with acquiring a taxicab license? What was the proﬁt per taxicab
license per day? If the taxi operated every day, what was the
proﬁt per taxicab license per year? .
(d) If the interest rate was 10% and costs, demand, and the number of
licenses were expected to remain constant forever, what would be the
market price of a taxicab license? .
(e) Suppose that the commission decided in 1995 to issue enough new
licenses to reduce the taxicab price per ride to $5. How many more
licenses would this take? .
(f) Assuming that demand in Ham Harbor is not going to grow any more,
how much would a taxicab license be worth at this new fare?
.
(g) How much money would each current taxicab owner be willing to pay
to prevent any new licenses from being issued? What
is the total amount that all taxicab owners together would be willing
to pay to prevent any new licences from ever being issued?
The total amount that consumers would be willing to pay to
have another taxicab license issued would be (more than, less than, the
same as) this amount.
23.6 (2) In this problem, we will determine the equilibrium pattern
of agricultural land use surrounding a city. Think of the city as being
located in the middle of a large featureless plain. The price of wheat at
the market at the center of town is $10 a bushel, and it only costs $5 a
bushel to grow wheat. However, it costs 10 cents a mile to transport a
bushel of wheat to the center of town.
(a) If a farm is located t miles from the center of town, write down a
formula for its proﬁt per bushel of wheat transported to market.
.
(b) Suppose you can grow 1,000 bushels on an acre of land. How much
will an acre of land located t miles from the market rent for?
.
(c) How far away from the market do you have to be for land to be worth
zero? .
23.7 (1) Consider an industry with three ﬁrms. Suppose the ﬁrms have
the following supply functions: S1(p) = p, S2(p) = p − 5, and S3(p) = 2p
respectively. On the graph below plot each of the three supply curves and
the resulting industry supply curve.
Price
20
15
10
5
0 10 20 30 40
Quantity
(a) If the market demand curve has the form D(p) = 15, what is the
resulting market price? Output? What is the output
level for ﬁrm 1 at this price? Firm 2? Firm 3?
.
23.8 (0) Suppose all ﬁrms in a given industry have the same supply
curve given by Si(p) = p/2. Plot and label the four industry supply
curves generated by these ﬁrms if there are 1, 2, 3, or 4 ﬁrms operating
in the industry.
Price
20
15
10
5
0 10 20 30 40
Quantity
(a) If all of the ﬁrms had a cost structure such that if the price was below
$3, they would be losing money, what would be the equilibrium price and
output in the industry if the market demand was equal to D(p) = 3.5?
Answer: price = , quantity = How many ﬁrms
would exist in such a market? .
(b) What if the identical conditions as above held except that the market
demand was equal to D(p) = 8 − p? Now, what would be the equilibrium
price and output? How many ﬁrms would operate in
such a market? .
23.9 (0) There is free entry into the pollicle industry. Anybody can
enter this industry and have the same U-shaped average cost curve as all
of the other ﬁrms in the industry.
(a) On the diagram below, draw a representative ﬁrm’s average and marginal
cost curves using blue ink. Also, indicate the long-run equilibrium
level of the market price.
Price
20
15
10
5
0 10 20 30 40
Quantity
(b) Suppose the government imposes a tax, t, on every unit of output sold
by the industry. Use red ink to draw the new conditions on the above
graph. After the industry has adjusted to the imposition of the tax, the
competitive model would predict the following: the market price would
(increase, decrease) by amount , there would be
(more, the same, fewer) ﬁrms operating in the industry, and
the output level for each ﬁrm operating in the industry would
(increase, stay the same, decrease).
(c) What if the government imposes a tax, l, on every ﬁrm in the industry.
Draw the new cost conditions on the above graph using black ink. After
the industry has adjusted to the imposition of the tax the competitive
model would predict the following: the market price would (increase,
decrease) , there would be (more, the same, fewer)
ﬁrms operating in the industry, and the output level for each ﬁrm
operating in the industry would (increase, stay the same,
decrease).
23.10 (0) In many communities, a restaurant that sells alcoholic beverages
is required to have a license. Suppose that the number of licenses
is limited and that they may be easily transferred to other restaurant
owners. Suppose that the conditions of this industry closely approximate
perfect competition. If the average restaurant’s revenue is $100,000 a
year, and if a liquor license can be leased for a year for $85,000 from
an existing restaurant, what is the average variable cost in the industry?
.
23.11 (2) In order to protect the wild populations of cockatoos, the
Australian authorities have outlawed the export of these large parrots.
An illegal market in cockatoos has developed. The cost of capturing an
Australian cockatoo and shipping him to the United States is about $40
per bird. Smuggled parrots are drugged and shipped in suitcases. This is
extremely traumatic for the birds and about 50% of the cockatoos shipped
die in transit. Each smuggled cockatoo has a 10% chance of being discovered,
in which case the bird is conﬁscated and a ﬁne of $500 is charged.
Conﬁscated cockatoos that are alive are returned to the wild. Conﬁscated
cockatoos that are found dead are donated to university cafeterias.∗
(a) The probability that a smuggled parrot will reach the buyer alive
and unconﬁscated is Therefore when the price of smuggled
parrots is p, what is the expected gross revenue to a parrot-smuggler from
shipping a parrot? .
(b) What is the expected cost, including expected ﬁnes and the cost of
capturing and shipping, per parrot? .
(c) The supply schedule for smuggled parrots will be a horizontal line at
the market price (Hint: At what price does a parrot-smuggler
just break even?)
(d) The demand function for smuggled cockatoos in the United States is
D(p) = 7, 200 − 20p per year. How many smuggled cockatoos will be sold
in the United States per year at the equilibrium price? How
many cockatoos must be caught in Australia in order that this number of
live birds reaches U.S. buyers? .
(e) Suppose that instead of returning live conﬁscated cockatoos to the
wild, the customs authorities sold them in the American market. The
proﬁts from smuggling a cockatoo do not change from this policy change.
Since the supply curve is horizontal, it must be that the equilibrium price
of smuggled cockatoos will have to be the same as the equilibrium price
when the conﬁscated cockatoos were returned to nature. How many live
cockatoos will be sold in the United States in equilibrium?
∗
The story behind this problem is based on actual fact, but the numbers
we use are just made up for illustration. It would be very interesting
to have some good estimates of the actual demand functions and cost
functions.
How many cockatoos will be permanently removed from the Australian
wild? .
(f) Suppose that the trade in cockatoos is legalized. Suppose that it
costs about $40 to capture and ship a cockatoo to the United States
in a comfortable cage and that the number of deaths in transit by this
method is negligible. What would be the equilibrium price of cockatoos
in the United States? How many cockatoos would be sold in
the United States? How many cockatoos would have to be
caught in Australia for the U.S. market? .
23.12 (0) The horn of the rhinoceros is prized in Japan and China for its
alleged aphrodisiac properties. This has proved to be most unfortunate for
the rhinoceroses of East Africa. Although it is illegal to kill rhinoceroses
in the game parks of Kenya, the rhinoceros population of these parks has
been almost totally depleted by poachers. The price of rhinoceros horns
in recent years has risen so high that a poacher can earn half a year’s
wages by simply killing one rhinoceros. Such high rewards for poaching
have made laws against poaching almost impossible to enforce in East
Africa. There are also large game parks with rhinoceros populations in
South Africa. Game wardens there were able to prevent poaching almost
completely and the rhinoceros population of South Africa has prospered.
In a recent program from the television series Nova, a South African game
warden explained that some rhinoceroses even have to be “harvested” in
order to prevent overpopulation of rhinoceroses. “What then,” asked the
interviewer, “do you do with the horns from the animals that are harvested
or that die of natural causes?” The South African game warden proudly
explained that since international trade in rhinoceros horns was illegal,
South Africa did not contribute to international crime by selling these
horns. Instead the horns were either destroyed or stored in a warehouse.
(a) Suppose that all of the rhinoceros horns produced in South Africa
are destroyed. Label the axes below and draw world supply and demand
curves for rhinoceros horns with blue ink. Label the equilibrium price
and quantity.
(b) If South Africa were to sell its rhinoceros horns on the world market,
which of the curves in your diagram would shift and in what direction?
Use red ink to illustrate the shifted curve
or curves. If South Africa were to do this, would world consumption
of rhinoceros horns be increased or decreased? Would
the world price of rhinoceros horns be increased or decreased?
Would the amount of rhinoceros poaching be increased or
decreased? .
23.13 (1) The sale of rhinoceros horns is not prohibited because of concern
about the wicked pleasures of aphrodisiac imbibers, but because the
supply activity is bad for rhinoceroses. Similarly, the Australian reason
for restricting the exportation of cockatoos to the United States is not because
having a cockatoo is bad for you. Indeed it is legal for Australians
to have cockatoos as pets. The motive for the restriction is simply to
protect the wild populations from being overexploited. In the case of
other commodities, it appears that society has no particular interest in
restricting the supply activities but wishes to restrict consumption. A
good example is illicit drugs. The growing of marijuana, for example, is a
simple pastoral activity, which in itself is no more harmful than growing
sweet corn or brussels sprouts. It is the consumption of marijuana to
which society objects.
Suppose that there is a constant marginal cost of $5 per ounce for
growing marijuana and delivering it to buyers. But whenever the marijuana
authorities ﬁnd marijuana growing or in the hands of dealers, they
seize the marijuana and ﬁne the supplier. Suppose that the probability
that marijuana is seized is .3 and that the ﬁne if you are caught is $10
per ounce.
(a) If the “street price” is $p per ounce, what is the expected revenue
net of ﬁnes to a dealer from selling an ounce of marijuana?
What then would be the equilibrium price of marijuana? .
(b) Suppose that the demand function for marijuana has the equation
Q = A − Bp. If all conﬁscated marijuana is destroyed, what will be
the equilibrium consumption of marijuana? Suppose
that conﬁscated marijuana is not destroyed but sold on the open market.
What will be the equilibrium consumption of marijuana? .
(c) The price of marijuana will (increase, decrease, stay the same)
.
(d) If there were increasing rather than constant marginal cost in marijuana
production, do you think that consumption would be greater if
conﬁscated marijuana were sold than if it were destroyed? Explain.
.