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Chapter 9 NAME
Buying and Selling
Introduction. In previous chapters, we studied the behavior of con-
sumers who start out without owning any goods, but who had some money
with which to buy goods. In this chapter, the consumer has an initial en-
dowment, which is the bundle of goods the consumer owns before any
trades are made. A consumer can trade away from his initial endowment
by selling one good and buying the other.
The techniques that you have already learned will serve you well here.
To find out how much a consumer demands at given prices, you find his
budget line and then find a point of tangency between his budget line and
an indifference curve. To determine a budget line for a consumer who
is trading from an initial endowment and who has no source of income
other than his initial endowment, notice two things. First, the initial
endowment must lie on the consumer’s budget line. This is true because,
no matter what the prices are, the consumer can always afford his initial
endowment. Second, if the prices are p1and p2, the slope of the budget
line must be −p1/p2.This is true, since for every unit of good 1 the
consumer gives up, he can get exactly p1/p2units of good 2. Therefore
if you know the prices and you know the consumer’s initial endowment,
then you can always write an equation for the consumer’s budget line.
After all, if you know one point on a line and you know its slope, you
can either draw the line or write down its equation. Once you have the
budget equation, you can find the bundle the consumer chooses, using the
same methods you learned in Chapter 5.
Example: A peasant consumes only rice and fish. He grows some rice and
some fish, but not necessarily in the same proportion in which he wants
to consume them. Suppose that if he makes no trades, he will have 20
units of rice and 5 units of fish. The price of rice is 1 yuan per unit, and
the price of fish is 2 yuan per unit. The value of the peasant’s endowment
is (1 ×20) + (2 ×5) = 30. Therefore the peasant can consume any bundle
(R, F ) such that (1 ×R)+(2×F) = 30.
Perhaps the most interesting application of trading from an initial
endowment is the theory of labor supply. To study labor supply, we
consider the behavior of a consumer who is choosing between leisure and
other goods. The only thing that is at all new or “tricky” is finding
the appropriate budget constraint for the problem at hand. To study
labor supply, we think of the consumer as having an initial endowment of
leisure, some of which he may trade away for goods.
In most applications we set the price of “other goods” at 1. The
wage rate is the price of leisure. The role that is played by income in
the ordinary consumer-good model is now played by “full income.” A
worker’s full income is the income she would have if she chose to take no
leisure.
112 BUYING AND SELLING (Ch. 9)
Example: Sherwin has 18 hours a day which he divides between labor and
leisure. He can work as many hours a day as he wishes for a wage of $5
per hour. He also receives a pension that gives him $10 a day whether he
works or not. The price of other goods is $1 per unit. If Sherwin makes no
trades at all, he will have 18 hours of leisure and 10 units of other goods.
Therefore Sherwin’s initial endowment is 18 hours of leisure a day and
$10 a day for other goods. Let Rbe the amount of leisure that he has per
day, and let Cbe the number of dollars he has to spend per day on other
goods. If his wage is $5 an hour, he can afford to consume bundle (R, C)
if it costs no more per day than the value of his initial endowment. The
value of his initial endowment (his full income) is $10 + ($5 ×18) = $100
per day. Therefore Sherwin’s budget equation is 5R+C= 100.
9.1 (0) Abishag Appleby owns 20 quinces and 5 kumquats. She has no
income from any other source, but she can buy or sell either quinces or
kumquats at their market prices. The price of kumquats is four times the
price of quinces. There are no other commodities of interest.
(a) How many quinces could she have if she was willing to do without
0102030
40
10
20
30
Quinces
Kumquats
40
Red line
Blue line
e
c
Squiggly
line
(b) Draw Abishag’s budget set, using blue ink, and label the endowment
bundle with the letter E. If the price of quinces is 1 and the price of
If the price of quinces is 2 and the price of kumquats is 8, write Abishag’s
NAME 113
prices have on the set of commodity bundles that Abishag can afford?
(c) Suppose that Abishag decides to sell 10 quinces. Label her final
(d) Now, after she has sold 10 quinces and owns the bundle labeled C,
(e) If Abishag obeys the weak axiom of revealed preference, then there are
some points on her red budget line that we can be sure Abishag will not
9.2 (0) Mario has a small garden where he raises eggplant and tomatoes.
He consumes some of these vegetables, and he sells some in the market.
(a) What is the monetary value of Mario’s endowment of vegetables?
(b) On the graph below, use blue ink to draw Mario’s budget line. Mario
of eggplant. Draw the indifference curve through the consumption bundle
that Mario chooses and label this bundle A.
(c) Suppose that before Mario makes any trades, the price of tomatoes
rises to $15 a pound, while the price of eggplant stays at $5 a pound.
(d) Suppose that Mario had sold his entire crop at the market for a total
of $200, intending to buy back some tomatoes and eggplant for his own
consumption. Before he had a chance to buy anything back, the price of
tomatoes rose to $15, while the price of eggplant stayed at $5. Draw his
114 BUYING AND SELLING (Ch. 9)
(e) Assuming that the price of tomatoes rose to $15 from $5 before Mario
made any transactions, the change in the demand for tomatoes due to
0102030
40
10
20
30
40
Red line
Blue line
a
Black line
Tomatoes
Eggplant
9.3 (0) Lucetta consumes only two goods, Aand B. Her only source of
income is gifts of these commodities from her many admirers. She doesn’t
always get these goods in the proportions in which she wants to consume
them, but she can always buy or sell Aat the price pA=1andBat the
price pB= 2. Lucetta’s utility function is U(a, b)=ab,whereais the
amount of Ashe consumes and bis the amount of Bshe consumes.
(a) Suppose that Lucetta’s admirers give her 100 units of Aand 200 units
of B. In the graph below, use red ink to draw her budget line. Label her
initial endowment E.
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(d) Suppose that before Lucetta has made any trades, the price of good
Bfalls to 1, and the price of good Astays at 1. Draw Lucetta’s budget
line at these prices on your graph, using blue ink.
0 225 300
100
200
300
400
500
600
75
Good A
Good B
Red budget line
Blue budget line
150
e
(f) Suppose that before the price of good Bfell, Lucetta had exchanged all
of her gifts for money, planning to use the money to buy her consumption
(g) Explain why her consumption is different depending on whether she
116 BUYING AND SELLING (Ch. 9)
9.4 (0) Priscilla finds it optimal not to engage in trade at the going
prices and just consumes her endowment. Priscilla has no kinks in her
indifference curves, and she is endowed with positive amounts of both
goods. Use pencil or black ink to draw a budget line and an indifference
curve for Priscilla that would be consistent with these facts. Suppose
that the price of good 2 stays the same, but the price of good 1 falls.
Use blue ink to show her new budget line. Priscilla satisfies the weak
axiom of revealed preference. Could it happen that Priscilla will consume
X2
X1
e
Black
budget
line
Blue
budget
line
9.5 (0) Potatoes are a Giffen good for Paddy, who has a small potato
farm. The price of potatoes fell, but Paddy increased his potato consump-
tion. At first this astonished the village economist, who thought that a
decrease in the price of a Giffen good was supposed to reduce demand.
But then he remembered that Paddy was a net supplier of potatoes. With
the help of a graph, he was able to explain Paddy’s behavior. In the axes
below, show how this could have happened. Put “potatoes” on the hor-
izontal axis and “all other goods” on the vertical axis. Label the old
equilibrium Aand the new equilibrium B. Draw a point Cso that the
NAME 117
Slutsky substitution effect is the movement from Ato Cand the Slutsky
income effect is the movement from Cto B. On this same graph, you are
also going to have to show that potatoes are a Giffen good. To do this,
draw a budget line showing the effect of a fall in the price of potatoes if
Paddy didn’t own any potatoes, and only had money income. Label the
new consumption point under these circumstances by D.(Warning:You
probably will need to make a few dry runs on some scratch paper to get
the whole story straight.)
All other goods
Potatoes
b
e
c
a
d
9.6 (0) Recall the travails of Agatha, from the previous chapter. She had
to travel 1,500 miles from Istanbul to Paris. She had only $200 with which
to buy first-class and second-class tickets on the Orient Express when the
price of first-class tickets was $.20 a mile and the price of second-class
tickets was $.10 a mile. She bought tickets that enabled her to travel all
the way to Paris, with as many miles of first class as she could afford.
After she boarded the train, she discovered to her amazement that the
price of second-class tickets had fallen to $.05 a mile while the price of
first-class tickets remained at $.20 a mile. She also discovered that on the
train it was possible to buy or sell first-class tickets for $.20 a mile and
to buy or sell second-class tickets for $.05 a mile. Agatha had no money
left to buy either kind of ticket, but she did have the tickets that she had
already bought.
(a) On the graph below, use pencil to show the combinations of tickets
that she could afford at the old prices. Use blue ink to show the combina-
tions of tickets that would take her exactly 1,500 miles. Mark the point
that she chooses with the letter A.
118 BUYING AND SELLING (Ch. 9)
0 400 800 1200 1600
400
800
1200
Second-class miles
First-class miles
1600
Red line
Blue line
a
Pencil line
(b) Use red ink to draw a line showing all of the combinations of first-class
and second-class travel that she can afford when she is on the train, by
trading her endowment of tickets at the new prices that apply on board
the train.
(c) On your graph, show the point that she chooses after finding out
about the price change. Does she choose more, less, or the same amount
9.7 (0) Mr. Cog works in a machine factory. He can work as many
hours per day as he wishes at a wage rate of w.LetCbe the number of
dollars he spends on consumer goods and let Rbe the number of hours
of leisure that he chooses.
(a) Mr. Cog earns $8 an hour and has 18 hours per day to devote to labor
or leisure, and he has $16 of nonlabor income per day. Write an equation
Use blue ink to draw his budget line in the graph below. His initial
endowment is the point where he does no work and enjoys 18 hours of
leisure per day. Mark this point on the graph below with the letter A.
(Remember that although Cog can choose to work and thereby “sell” some
of his endowment of leisure, he cannot “buy leisure” by paying somebody
else to loaf for him.) If Mr. Cog has the utility function U(R, C)=CR,
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012162024
40
80
120
160
200
240
4
Leisure
Consumption
Black budget line
Red budget line
Blue budget line
8
a
(b) Suppose that Mr. Cog’s wage rate rises to $12 an hour. Use red ink
to draw his new budget line. (He still has $16 a day in nonlabor income.)
If he continued to work exactly as many hours as he did before the wage
increase, how much more money would he have each day to spend on
(c) Suppose that Mr. Cog still receives $8 an hour but that his nonlabor
income rises to $48 per day. Use black ink to draw his budget line. How
(d) Suppose that Mr. Cog has a wage of $wper hour, a nonlabor income
of $m, and that he has 18 hours a day to divide between labor and leisure.
Cog’s budget line has the equation C+wR =m+18w. Using the same
methods you used in the chapter on demand functions, find the amount
of leisure that Cog will demand as a function of wages and of nonlabor
income. (Hint: Notice that this is the same as finding the demand for R
when the price of Ris w, the price of Cis 1, and income is m+18w.)
120 BUYING AND SELLING (Ch. 9)
9.8 (0) Fred has just arrived at college and is trying to figure out how to
supplement the meager checks that he gets from home. “How can anyone
live on $50 a week for spending money?” he asks. But he asks to no
avail. “If you want more money, get a job,” say his parents. So Fred
glumly investigates the possibilities. The amount of leisure time that he
has left after allowing for necessary activities like sleeping, brushing teeth,
and studying for economics classes is 50 hours a week. He can work as
many hours per week at a nearby Taco Bell for $5 an hour. Fred’s utility
function for leisure and money to spend on consumption is U(C, L)=CL.
(a) Fred has an endowment that consists of $50 of money to spend on
for money. The money value of Fred’s endowment bundle, including both
his money allowance and the market value of his leisure time is therefore
line for someone who can buy these two goods at a price of $1 per unit
difference is that this budget line doesn’t run all the way to the horizontal
axis.
(b) On the graph below, use black ink to show Fred’s budget line. (Hint:
Find the combination of leisure and consumption expenditures that he
could have if he didn’t work at all. Find the combination he would have
if he chose to have no leisure at all. What other points are on your graph?)
On the same graph, use blue ink to sketch the indifference curves that
give Fred utility levels of 3,000, 4,500, and 7,500.
(c) If you maximized Fred’s utility subject to the above budget, how
to solve for the demand function of someone with a Cobb-Douglas utility
function?)
