978-0393123982 Chapter 24 Solution Manual Part 1

Unlock access to all the studying documents.

View Full Document

Chapter 24 NAME

Industry Supply

Introduction. 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.

24.0 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)=pand s2(p)=p−2,

then the market supply function is S(p)=pfor p≤2andS(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.

296 INDUSTRY SUPPLY (Ch. 24)

24.1 (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 in-

dustry has been D(p)=60,000 −5,000p,whereD(p) is the total number

of garden gnomes sold per year and pis the price. Prices of inputs have

been constant for many years and the technology has not changed. No-

body 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 approxi-

mate 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. 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

NAME 297

for producing up to 500 gnomes? $7. If you have only one gnome

mold, is it possible in the short run to produce more than 500 gnomes?

duce 500 gnomes if the price of gnomes is above 7dollars. You

would produce no gnomes if the price of gnomes is below 7dol-

lars. You would be indifferent between producing any number of gnomes

(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%. Is this higher than the return

from putting your money in the bank? Yes. What is the lowest

price for gnomes such that the rate of return you get from ivesting $1000

(e) At the price you found in the last section, how many gnomes would

24.2 (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.

298 INDUSTRY SUPPLY (Ch. 24)

(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.

(b) In 2001, what is the short run equilibrium total output of garden

gnomes, 14,000. 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. 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 $ 2,100. Did

he make more than a 10% rate of return on his investment in the gnome

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 $

2,100 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? No. What is the lowest price that he would be

willing to sell it for? $1,909. IfthebestrateofreturnthatZwerg

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?

NAME 299

(d) What do you think will happen to the number of garden gnomes or-

dered for delivery on January 1, 2002? Will it be larger, smaller, or the

passage of suffcient time, the industry will reach a new long-run equilib-

24.3 (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 gar-

den gnomes that applies in the year 2001, after the new tax is introduced.

On the same graph, show the demand curve for garden gnomes.

(b) In 2001, after the tax is introduced, what is the short run equilibrium

intersection of the supply and demand curves you just drew.)

300 INDUSTRY SUPPLY (Ch. 24)

(d) In 2001, what will be the total output of garden gnomes?

What rate of return will Deardwarf’s cousin Zwerg make on his invest-

ment in a garden gnome mold that he ordered a year ago and paid $1,000

(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

(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

(g) The tax on garden gnomes was left in place for many years, and no-

body expected any further changes in the tax or in demand or supply con-

ditions. After the passage of suffcient 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 price of gnomes go up by more, less, or the same amount as the tax

(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

NAME 301

(j) Is it reasonable to suppose that the government could introduce “sur-

prise” taxes without making firms suspicious that there would be similar

“surprises” in the future? Suppose that the introduction of the tax in Jan-

uary 2001 makes gnome makers suspicious that there will be more taxes

introduced in later years. Will this affect equilibrium prices and supplies?

24.4 (0) Consider a competitive industry with a large number of firms,

all of which have identical cost functions c(y)=y2+1 for y>0and

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)= p/2.If

there are nfirms in the industry, what will be the industry supply curve?

(b) What is the smallest price at which the product can be sold? p∗=

Take a guess at what the industry price will be and see if it works.)

(d) What will be the equilibrium price? p∗=2.What will be the

(e) What will be the equilibrium output of the industry? Y∗=50.

302 INDUSTRY SUPPLY (Ch. 24)

(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?) If a new

(g) What will be the equilibrium price? Solve 52.5−p=

50p/2to get p∗=2.02.What will be the equilibrium

output of each firm? y∗=1.01.What will be the equilibrium

(h) Now suppose that the demand curve shifts to D(p)=53−p. What will

be the equilibrium number of firms? 51. What will be the equilibrium

(i) What will be the equilibrium output of each firm? y=1.What

24.5 (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 com-

petitive equilibrium, price must equal marginal cost.) 5. What