- ECON2101 Microeconomics 2 - Tutorial 11
Jonathan Lim
13th October 2009
Quick Summary
Industry Supply
To nd the industry supply of output, just add up the supply of output coming from each
individual rm. 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 rm reduces its
quantity supplied to zero. The idea is that in the long run we have price equal to average
cost.
Monopoly
The prot-maximizing output of a monopolist is found by solving for the output at which
marginal revenue is equal to marginal cost. Having solved for this output, you nd the
monopolists price by plugging the prot-maximizing output into the demand function. In
general, the marginal revenue function can be found by taking the derivative of the total
revenue function with respect to the quantity. But in the special case of linear demand,
it is easy to nd the marginal revenue curve graphically. With a linear inverse demand
curve, p(y ) = a by , the marginal revenue curve always takes the form M R(y ) = a 2by .
1
1
Question 23.1
In this question we are told that Al Deardwarfs 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?
$1, 100.
This is simple arithmetic!
If you received delivery of a gnome mold on January 1 and paid for it at that time, by
2
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.)
$1, 100.
Remember that the opportunity cost here is $1,100!
(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?
$7.
This is already given in the question
What is your average variable cost for producing up to 500 gnomes?
$7.
This is already given in the question
If you have only one gnome mold, is it possible in the short run to produce more than
500 gnomes?
N o.
This is because he can only have one mould in the short run and if you order one thats
it.
(C) If you have exactly one newly installed gnome mold, you would produce 500 gnomes
if the price of gnomes is above
7 dollars
.
This is a short run thing, thus we assume that he has already invested in the mould thus
the condition is for the price to be at least as great as the average variable cost thus $7 is
the cuto point.
You would produce no gnomes if the price of gnomes is below
3
7 dollars.
You would be indierent between producing any number of gnomes between 0 and
500 if the price of gnomes is
7 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?
50%.
First calculate the quantity demanded which is:
60, 000 5, 000 10 = 10, 000
This implies that 10,000 units are demanded. Because he has only got 1 mould from his
$1,000, this implies that the revenues earned is:
10 500 7 500 1, 000 = $500.
which implies a rate of return of 50%.
Is this higher than the return from putting your money in the bank?
Y es.
What is the lowest price for gnomes such that the rate of return you get from investing
$1000 in a gnome mold is as at least 10%?
$9.20.
To work this out is simple, all we need is the net return to be greater $100, thus we have:
p 500 7 500 1, 000 = 100 500p = 4, 600 p = $9.20
note unless prices are extremely high then we can restrict ourselves to 500 units as the
maximum which we can sell! Thus the reason we know it is 500 units made!
4
Could the long-run equilibrium price of gnomes be lower than this?
N o.
This is logical since the guy has the alternative to bank the money.
(E) At the price you found in the last section, how many gnomes would be demanded
each year?
14, 000.
This is simply a matter of substitution thus we obtain:
60, 000 5, 000 9.2 = 14, 000
How many molds would be purchased each year?
28.
This is simply:
14, 000/500 = 28
Is this a long-run equilibrium price?
Y es.
We have:
128, 800 98, 000 28, 000 = 2, 800 10% return
Thus it is a long run equilibrium since the alternative is not better.
5
2
Question 23.2
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 cant change the price it charges on delivery.
(A) On the graph below, draw the short run industry supply curve and the demand curve
for garden gnomes that applies in the year 2001, after the discovery of the new plaster is
announced.
Basically this plaster reduces the variable cost from$7 to $5 but since weve already made
the order we can have more moulds. Note that the demand curve is:
60, 000 5, 000p = Q.
Note the supply function is limited to
14, 000 units
Thus we have a at horizontal line at $5 since this is the marginal cost for
0 < Q < 14, 000
After that the cost is innitely high due to capacity constraints. This implies the following
diagram:
6
Price
16
12
8
4
0
8
16
24
32
Number of Gnomes(x1000)
(B) In 2001, what is the short run equilibrium total output of garden gnomes,
14, 000.
It remains the same as before since the constraint here is capacity.
and what is the short run equilibrium price of garden gnomes?
$9.20.
(Hint: Look at the intersection of the supply and demand curves you just drew.)
This is obvious again all we do is substitute 14,000 back into the demand function to nd
the price.
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 ow of
7
$2, 100
.
This is a simple calculation all we do is calculate his net return which is:
9.2 500 5 500 = 2, 100.
Did he make more than a 10% rate of return on his investment in the gnome mold?
Y es.
What rate of return did he make?
1, 100
100 = 110%.
1000
(C) Zwergs 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 Munchkins new mold from Munchkin
and installing it in his own plant.
If Munchkin keeps his mold, he will get a net cash ow of
$2, 100 in one year.
Weve already calculated this
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?
No.
What is the lowest price that he would be willing to sell it for?
$1, 909.
What we require is some price of the good to give us a total of $2,100, note that the rate
is 10%. Thus we have:
1.1p = 2100 p = $1, 909
8
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 Munchkins new
mold?
$1, 909.
The way in which you have to look at this part is what is the alternative, in this case he
will earn only 10%. Now consider the return he will earn which in this case is $2,100.
So what is the fair price? This implies at p+10%=2,100, implying 1.1p=2,100, thus we
have:
p = 1, 909
(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?
Larger.
Logically it would be larger since the prot maximizing condition is
MC = p
, thus and reduction in price implies an increase in quantity.
After the passage of sucient time, the industry will reach a new long-run equilibrium.
What will be the new equilibrium price of gnomes?
$7.20.
Remember in the long run price must equal to alternative which implies 10% return. This
implies that the net cashow must be $1,100. Thus we have:
(p 5)500 = 1, 100 p = $7.20
9
3
Question 23.5
We are now told In 1990, the town of Ham Harbor had a more-or-less free market in taxi
services. Any respectable rm could provide taxi service as long as the drivers and cabs
satised 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.)
5.
This is simply knowing what the marginal cost is, in this case it is $5.
What is the equilibrium number of rides per day?
1, 100.
All we do is substitute priced back into the demand function. Thus we have:
Q = 1, 200 20 5 = 1, 100.
How many taxicabs will there be in equilibrium?
55.
All we do is divide 1,100 by 20. Thus we have:
1, 100/20 = 55
(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
10
taxicab rides had become D(p) = 1, 220 20p. What was the equilibrium price of a ride
in 1995?
$6.
We know that the quantity is now xed at 1,100 trips since no new licences are issued.
Thus to nd prices we substitute the quantity back into the demand function. Thus:
1, 100 = 1, 220 20p p = $6
(C) What was the prot per ride in 1995, neglecting any costs associated with acquiring
a taxicab license?
$1.
This is simply the price per ride minus the cost per ride, thus we have:
$6 $5 = $1
What was the prot per taxicab license per day?
1 20 = 20.
If the taxi operated every day, what was the prot per taxicab license per year?
20 365 = $7, 300.
(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?
$73, 000.
Remember that this implies that 10%=7,300. This implies that
100% = $73, 000
11
(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?
1.
This implies that we keep prices at $5 at the new demand curve. This implies that:
1, 220 100 1, 120 trips.
Thus we have:
1, 120/20 56 licences
Thus one extra licence.
(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?
N othing.
Intuitively he is not making prots thus it is worth nothing.
(G) How much money would each current taxicab owner be willing to pay to prevent any
new licenses from being issued?
$73, 000 each.
This is obvious as this is the value of the entire value of the license, given prots of $7,300
at 10% return as the alternative.
What is the total amount that all taxicab owners together would be willing to pay to
prevent any new licences from ever being issued?
55 73, 000 = $4, 015, 000.
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)
more than this amount.
12
Calculate consumer surplus, if there was no extra license, this implies a total consumer
surplus of:
365 (61 6)
1, 100
= 11, 041, 250
2
If there was an extra license this implies the following consumer surplus:
365 (61 5)
1, 120
= 11, 446, 400
2
Implying a loss of
405, 150peryear
Thus consumers are willing to pay more at 10%, this implies the willingness to pay is:
$4, 051, 500 > $4, 015, 000
13
4
Question 23.11
We are now told that 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 conscated and a ne of $500 is charged. Conscated cockatoos
that are alive are returned to the wild. Conscated cockatoos that are found dead are
donated to university cafeterias.
(A) The probability that a smuggled parrot will reach the buyer alive and unconscated
is
.45.
This is just a joint probability of two event occurring. Assuming that the events are
independent we have:
0.5 0.9 = 0.45
Therefore when the price of smuggled parrots is p, what is the expected gross revenue
to a parrot-smuggler from shipping a parrot?
.45p.
Remember that the probability weve calculated is the probability of receiving any payment
at all.
(B) What is the expected cost, including expected nes and the cost of capturing and
shipping, per parrot?
.10 500 + 40 = $90.
Remember that the probability of being caught is 10%, thus the expected cost of being ned
14
is
10% 500
, but there is a shipping cost which we incur which is $40 regardless. Thus we have $90.
(C) The supply schedule for smuggled parrots will be a horizontal line at the market price
$200.
(Hint: At what price does a parrot-smuggler just break even?)
We to need rst calculate the expected price of receiving something this is given by 0.45p.
We then equate the expected price to the expected marginal cost which is $90. Thus we
have:
0.45p = 90 p = $200.
(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?
$3, 200
This is simply a matter of substitution, we have:
7, 200 4, 000 = 3, 200
How many cockatoos must be caught in Australia in order that this number of live
birds reaches U.S. buyers?
3, 200/.45 = 7, 111.
Remember that we need 3,200 with certainty, but we know that only 0.45 will make it to
the U.S.. Thus if we weight it by the appropriate probability we have
0.45 = 3, 200 1 = 7, 111.
(E) Suppose that instead of returning live conscated cockatoos to the wild, the customs
authorities sold them in the American market. The prots from smuggling a cockatoo do
15
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 conscated cockatoos were returned to nature. How many live cockatoos
will be sold in the United States in equilibrium?
3, 200.
This is implicit already in the question! Since prices remain the same this implies that
the quantity demanded remains the same.
How many cockatoos will be permanently removed from the Australian wild?
6, 400.
Now that the conscated cockatoos are sold to the U.S. market this implies that only 0.5
will make it there. Thus to fulll demand now.
0.5 = 3, 200 1 = 6, 400.
(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?
$40.
Remember that price is equal to marginal cost and we know marginal cost is $40 and thus
price is $40
How many cockatoos would be sold in the United States?
Q = 7, 200 20p Q = 6, 400.
How many cockatoos would have to be caught in Australia for the U.S. market?
6, 400
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5
Question 24.3
Suppose that the demand function for Japanese cars in the United States is such that
annual sales of cars (in thousands of cars) will be 250-2P, where P is the price of Japanese
cars in thousands of dollars.
(A) If the supply schedule is horizontal at a price of $5,000 what will be the equilibrium
number of Japanese cars sold in the United States?
240 thousand.
We now have price equals to marginal cost thus we have:
p = 5 Q = 240
How much money will Americans spend in total on Japanese cars?
1.2 billion dollars.
240, 000 5, 000 = 1, 200, 000, 000.
(B) Suppose that in response to pressure from American car manufacturers, the United
States imposes an import duty on Japanese cars in such a way that for every car exported
to the United States the Japanese manufacturers must pay a tax to the U.S. government
of $2,000. How many Japanese automobiles will now be sold in the United States?
236 thousand.
Again this is a straight substitution winse we know that price equals marginal cost and
eectively marginal cost has gone up by $2,000. Thus we have:
250 14 = 236
At what price will they be sold?
17
7 thousand dollars
(C) How much revenue will the U.S. government collect with this tari?
472milliondollars.
2, 000 236, 000 = 472, 000, 000
(D) On the graph below, the price paid by American consumers is measured on the
vertical axis. Use blue ink to show the demand and supply schedules before the import
duty is imposed. After the import duty is imposed, the supply schedule shifts and the
demand schedule stays as before. Use red ink to draw the new supply schedule.
Price (x1000)
8
Supply with Duty
6
Demand
Supply
4
2
0
100
200
300
400
Japanese Cars (x1000)
(E) Suppose that instead of imposing an import duty, the U.S. government persuades the
Japanese government to impose voluntary export restrictions on their exports of cars to
the United States. Suppose that the Japanese agree to restrain their exports by requiring
18
that every car exported to the United States must have an export license. Suppose further
that the Japanese government agrees to issue only 236,000 export licenses and sells these
licenses to the Japanese rms. If the Japanese rms know the American demand curve
and if they know that only 236,000 Japanese cars will be sold in America, what price will
they be able to charge in America for their cars?
7 thousand dollars.
Weve already done this calculation. All you need to do is substitute 236 back into the
demand function and solve for p.
(F) How much will a Japanese rm be willing to pay the Japanese government for an
export license?
2 thousand dollars.
(Hint: Think about what it costs to produce a car and how much it can be sold for if you
have an export license.)
This is simply the dierence between the cost and what we can sell it for which in this
case is
7, 000 5, 000 = 2, 000.
We have this calculation to ensure that we have at least zero prots.
(G) How much will be the Japanese governments total revenue from the sale of export
licenses?
472million dollars.
2, 000 236, 000 = 472, 000, 000
(H) How much money will Americans spend on Japanese cars?
1.652 billion dollars.
7, 000 236, 000 = 1, 652, 000, 000.
(I) Why might the Japanese voluntarily submit to export controls?
19
Total revenue of Japanese companies and government is greater with export controls than
without them. Since there is less output, costs are lower. We manufacture less cars
thus total costs are lower. Furthermore we now receive $7,000 instead of $5,000 per car.
Though not all of it belongs to the rms. Note that total revenue is higher in this case.
Thus higher revenue and lower costs imply more prot.
20
6
Question 24.5
We are told that in Gomorrah, New Jersey, there is only one newspaper, the Daily
Calumny. The demand for the paper depends on the price and the amount of scandal reported. The demand function is Q = 15S 1/2 P 3 , where Q is the number of issues
sold per day, S is the number of column inches of scandal reported in the paper, and P is
the price. Scandals are not a scarce commodity in Gomorrah. However, it takes resources
to write, edit, and print stories of scandal. The cost of reporting S units of scandal is
$10S . These costs are independent of the number of papers sold. In addition it costs
money to print and deliver the paper. These cost $.10 per copy and the cost per unit is
independent of the amount of scandal reported in the paper. Therefore the total cost of
printing Q copies of the paper with S column inches of scandal is $10S + .10Q.
(A) Calculate the price elasticity of demand for the Daily Calumny.
3.
Remember that elasticity is given by
| |=
dQ P
.
dP Q
Thus we have
| | = 45S 1/2 P 4
1
15S 1/2 P 4
= 3
Does the price elasticity depend on the amount of scandal reported?
N o.
This is obvious since it is a constant number.
Is the price elasticity constant over all prices?
Y es.
Again this is obvious.
21
(B) Remember that M R = P (1 + 1/ ). To maximize prots, the Daily Calumny will
set marginal revenue equal to marginal cost. Solve for the prot-maximizing price for the
Calumny to charge per newspaper.
$.15.
First calculate marginal revenues. Thus we have:
2p
.
3
Set it equal to the marginal cost thus we have:
2p
= 0.10 p = 0.15.
3
When the newspaper charges this price, the dierence between the price and the
marginal cost of printing and delivering each newspaper is
$.05.
This is obvious 0.15-0.10=0.05
(C) If the Daily Calumny charges the prot-maximizing price and prints 100 column
inches of scandal, how many copies would it sell? (Round to the nearest integer.)
44, 444.
This is a straight substitution. We know that S doesnt aect the prot maximizing price.
Thus to nd quantity we substitute p = 0.15 and S = 100 to obtain:
Q = 15 10 0.153 = 44, 444
Write a general expression for the number of copies sold as a function of S :
Q(S ) = Q = 15S 1/2 (.15)3 = 4, 444.44S 1/2 .
Again I think this is obvious given we know the prot maximizing price is 0.15
(D) Assuming that the paper charges the prot-maximizing price, write an expression
for prots as a function of Q and S .
22
P rof its = .15Q .10Q 10S.
We know that price is 0.15, thus revenue is 0.15Q. We are also given the total cost which
is .10Q + 10S . Thus we have the above expression
Using the solution for Q(S ) that you found in the last section, substitute Q(S ) for Q
to write an expression for prots as a function of S alone.
P rof its = .05(4, 444.44S 1/2 ) 10S = 222.22S 1/2 10S.
Again this is a straight substitution.
(E) If the Daily Calumny charges its prot-maximizing price, and prints the protmaximizing amount of scandal, how many column inches of scandal should it print?
123.456 inches.
To nd this we need to maximize prot with respect to S , given prices. Thus we have:
111.11s1/2 = 10 S = 123.45.
How many copies are sold
49, 383
This is a straight substitution into the demand function. Thus we have:
Q(S ) = 4, 444.44S 1/2 Q(S ) = 49, 383
and what is the amount of prot for the Daily Calumny if it maximizes its prots?
1, 234.5.
We have
P rof its = 222.22S 1/2 10S 222.22 123.45 10 123.45 = 1234.5.
23
7
Question 23.6
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
prot per bushel of wheat transported to market.
P rof it per bushel = 5 .10t.
First consider the revenue per unit which is 15, the cost per unit which is 10. But there are
also transportation cost 0.10t cents per unit, per mile. Thus we have the above expression.
(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?
Rent = 5, 000 100t.
In the long run there are zero prots. We know that for 1,000 bushels the prots the
person makes is:
P rof it = 5, 000 100t.
Thus this must also be the rent.
(C) How far away from the market do you have to be for land to be worth zero?
50miles.
Equate prots to zero and we obtain:
t = 50.
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8
Question 23.13
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 nd marijuana growing or in
the hands of dealers, they seize the marijuana and ne the supplier. Suppose that the
probability that marijuana is seized is .3 and that the ne if you are caught is $10 per
ounce.
(A) If the street price is $p per ounce, what is the expected revenue net of nes to a
dealer from selling an ounce of marijuana?
.7p 3.
We know that the expected gross revenue is 0.7p. This comes from the fact that you not
caught with probability 0.7. The expected cost is 0.3 10 = 3. Note this is of course
assuming that we are growing marijuana.
What then would be the equilibrium price of marijuana?
$11.4.
Remember that prots must eventually equal to zero implying:
0.7p 3 = 5 p = 11.4.
25
(B) Suppose that the demand function for marijuana has the equation Q = A Bp.
If all conscated marijuana is destroyed, what will be the equilibrium consumption of
marijuana?
A 11.4B
.
Conscation doesnt aect the price above since weve calculated the price based on the
expectation that it will not be in the market. Thus we simply substitute price it back into
the above demand equation. Thus we have the above equation.
Suppose that conscated marijuana is not destroyed but sold on the open market.
What will be the equilibrium consumption of marijuana?
A 11.4B.
The fact that it is conscated implies that the price they face is the same regardless of
whether it is destroyed or sold in the open market. The point it the growers still factor in
the probability of conscation when doing their price calculations.
(C) The price of marijuana will (increase, decrease, stay the same)
Stay the same.
The question is what will happen to the supply curve. Remember that the supply schedule here is kept constant since the marginal cost is eectively horizontal. By selling the
conscated marijuana in the market this would shift the supply schedule to the right thus
eectively implying eect on prices.
(D) If there were increasing rather than constant marginal cost in marijuana production,
do you think that consumption would be greater if conscated marijuana were sold than
if it were destroyed? Explain.
Consumption will increase because the supply curve will shift to the right, lowering the
price. The dierence now is that the supply schedule is upward sloping thus any shift to
the right would lower prices and increase quantity.
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9
Question 24.1
We are now told Professor Bong has just written the rst textbook in Punk Economics.
It is called Up Your Isoquant. Market research suggests that the demand curve for this
book will be Q = 2, 000 100P , where P is its price. It will cost $1,000 to set the book
in type. This setup cost is necessary before any copies can be printed. In addition to the
setup cost, there is a marginal cost of $4 per book for every book printed.
(A) The total revenue function for Professor Bongs book is
R(Q) = 20Q Q2 /100.
We know that total revenue in this case is P Q. So since we want total revenue to be a
function of Q, we need the inverse demand function. Thus:
P = 20
Q
.
20
Thus we have the above equation.
(B) The total cost function for producing Professor Bongs book is
C (Q) = 1, 000 + 4Q.
I think this is very obvious it is already spelt out in the question.
(C) The marginal revenue function is
M R(Q) = 20 Q/50.
This is simply the rst order condition (with respect to quantity) of the total revenue
function.
and the marginal cost function is
M C (Q) = 4.
This is simply the rst order condition (with respect to quantity) of the total cost function.
The prot-maximizing quantity of books for professor Bong to sell is
Q = 800.
Marginal revenue=Marginal Cost, thus we have:
20 Q/50 = 4 Q = 16 50 = 800.
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10
Question 24.4
A monopolist has an inverse demand curve given by p(y ) = 12 y and a cost curve given
by c(y ) = y 2 .
(A) What will be its prot-maximizing level of output?
3.
First we need to nd the prot function which is
= (12 y )y y 2 .
Take rst order conditions and we obtain:
d
= 12 2y 2y = 0 y = 3
dy
(B) Suppose the government decides to put a tax on this monopolist so that for each
unit it sells it has to pay the government $2. What will be its output under this form of
taxation?
2.5.
This implies that the total cost is:
c(y ) = y 2 + 2y.
Thus we have the following as prots:
= (12 y )y y 2 2y.
Take rst order conditions and we obtain:
d
= 12 2y 2y 2 = 0 y = 2.5
dy
(C) Suppose now that the government puts a lump sum tax of $10 on the prots of the
monopolist. What will be its output?
3.
This is the same as a xed cost on prots thus it has no impact on the optimization
problem. One could think of this as a sunk cost.
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