CHAPTER 9: Buying and Selling
TRUE/FALSE
1. If a rational utility maximizer is a net demander of a good and if an increase in its price causes him to
buy more of it, then it must be an inferior good.
2. If a person is a net supplier of a normal good and its price increases while all other prices stay the
same, then his demand for the good must decrease.
3. If a consumer is a buyer of some goods and a seller of others, then a change in prices will generate an
extra income effect in the Slutsky equation due to the revaluation of the consumer’s endowment.
4. If a consumer is initially endowed with a positive amount of two goods and sells some of one to get
more of the other and if she has no other sources of income, then her budget line will pass through her
endowment point.
5. If a utility maximizer is a net seller of something and the price of that good rises while other prices
stay constant, her situation might improve so much that she becomes a net buyer.
6. If a person is a net seller of some good and the price of that good decreases, she might possibly
become a net buyer.
7. Wilhelm consumes only apples and bananas. His endowment is 5 units of apples and 10 units of
bananas. Both goods are normal goods for Wilhelm. At current prices, Wilhelm is a net seller of
apples. If the price of apples rises and the price of bananas stays the same, his demand for apples must
decrease.
8. Bill receives half of his income in wages and half of his income in dividends. Bill would be indifferent
between a 50% increase in his wage rate and a 50% increase in his dividend income.
9. If all goods, including leisure, are normal goods, then an increase in the wage rate will necessarily
make people want to work more hours.
10. If someone has a Cobb-Douglas utility function and no income from any source other than labor
earnings, then an increase in wages will not change the amount that person chooses to work.
11. If leisure is a normal good, then an increase in nonlabor income will reduce labor supply.
12. A person’s full income is the amount of income that he or she would have if there were no taxes.
13. If a person has no nonlabor income, a decrease in wages causes the budget line between leisure and
other goods to shift downward in a parallel fashion.
14. If leisure is an inferior good, then an increase in the wage rate will make a person work more.
15. Jack has a backward-bending labor supply curve. At wages of $5 an hour he chooses to work 50 hours
a week. His boss wants him to work more hours per week and offers him $5 an hour for the first 50
hours per week and $7 an hour for every hour beyond 50 hours per week. Because of his backward
-bending supply curve, Jack might actually choose to work fewer hours.
16. Les is allowed to work only 8 hours a day at his main job, although he would like to work more hours.
He takes a second job. He can work as many hours as he wishes at the second job, but at a lower wage.
If leisure is a normal good, then an increase in the wage rate for his first job will reduce the number of
hours he chooses to work at his second job.
17. Suppose a consumer is initially endowed with a positive amount of two goods, sells some of one to get
more of the other, and has no other sources of income. If the price of one good falls, his new budget
line is everywhere above his old budget line.
MULTIPLE CHOICE
1. Marsha Mellow is very flexible. She consumes x and y. She says, “Give me x or give me y, I don’t
care. I can’t tell the difference between them.” She is currently endowed with 14 units of x and 3 units
of y. The price of x is 3 times the price of y. Marsha can trade x and y at the going prices but has no
other source of income. How many units of y will Marsha consume?
a.
48
b.
17
c.
45
d.
3
e.
23
2. Marsha Mellow is very flexible. She consumes x and y. She says, “Give me x or give me y, I don’t
care. I can’t tell the difference between them.” She is currently endowed with 8 units of x and 17 units
of y. The price of x is 3 times the price of y. Marsha can trade x and y at the going prices but has no
other source of income. How many units of y will Marsha consume?
a.
17
b.
44
c.
25
d.
41
e.
21
3. Yoram insists on consuming 4 times as much of y as he consumes of x (so he always has y = 4x). He
will consume these goods in no other ratio. The price of x is 3 times the price of y. Yoram has an
endowment of 20 x’s and 45 y’s which he can trade at the going prices. He has no other source of
income. What is Yoram’s gross demand for x?
a.
105
b.
65
c.
15
d.
12
e.
We can’t determine the answer without knowing the price of x.
4. Nick insists on consuming 3 times as much of y as he consumes of x (so he always has y = 3x). He will
consume these goods in no other ratio. The price of x is 2 times the price of y. Nick has an endowment
of 20 x’s and 75 y’s which he can trade at the going prices. He has no other source of income. What is
Nick’s gross demand for x?
a.
21
b.
115
c.
23
d.
95
e.
We can’t determine the answer without knowing the price of x.
5. Diana consumes commodities x and y and her utility function is U(x, y) = xy2. Good x costs $2 per unit
and good y costs $1 per unit. If she is endowed with 3 units of x and 6 units of y, how many units of
good y will she consume?
a.
11
b.
3
c.
8
d.
14
e.
None of the above.
6. Holly consumes commodities x and y and her utility function is U(x, y) = xy5. Good x costs $2 per unit
and good y costs $1 per unit. If she is endowed with 7 units of x and 4 units of y, how many units of
good y will she consume?
a.
7
b.
15
c.
19
d.
18
e.
None of the above.
7. Donald consumes goods x and y. His utility function is U(x, y) = xy3. He is endowed with 43 units of x
and 7 units of y. The price of x is $1 and the price of y is $3. Find his net demand for x.
a.
−27
b.
18
c.
−30
d.
−20
e.
59
8. Donald consumes goods x and y. His utility function is U(x, y) = xy3. He is endowed with 10 units of x
and 15 units of y. The price of x is $1 and the price of y is $2. Find his net demand for x.
a.
15
b.
0
c.
12
d.
−3
e.
20
9. Jackie’s net demands for x and y are (6, −6) and her gross demands are (15, 15). What is her initial
endowment of x?
a.
16
b.
13
c.
5
d.
9
e.
None of the above.
10. Holly consumes x and y. The price of x is 4 and the price of y is 4. Holly’s only source of income is her
endowment of 6 units of x and 6 units of y which she can buy or sell at the going prices. She plans to
consume 7 units of x and 5 units of y. If the prices change to $7 for x and $7 for y,
a.
she is better off.
b.
she is worse off.
c.
she is neither better off nor worse off.
d.
she is better off if she has nonconvex preferences.
e.
We can’t tell whether she is better off or worse off unless we know her utility function.
11. Fanny consumes x and y. The price of x is $9 and the price of y is $9. Fanny’s only source of income is
her endowment of 12 units of x and 12 units of y which she can buy or sell at the going prices. She
plans to consume 13 units of x and 11 units of y. If the prices change to $12 for x and $12 for y,
a.
she is better off.
b.
she is worse off.
c.
she is neither better off nor worse off.
d.
she is better off if she has nonconvex preferences.
e.
We can’t tell whether she is better off or worse off unless we know her utility function.
12. Milton consumes two commodities in a perfect market system. The price of x is $5 and the price of y is
$1. His utility function is U(x, y) = xy. He is endowed with 40 units of good x and no y. Find his
consumption of good y.
a.
110
b.
105
c.
50
d.
100
e.
None of the above.
13. Milton consumes two commodities in a perfect market system. The price of x is $4 and the price of y is
$1. His utility function is U(x, y) = xy. He is endowed with 76 units of good x and no y. Find his
consumption of good y.
a.
76
b.
157
c.
152
d.
162
e.
None of the above.
14. Russ Tickman is a dairy farmer. He consumes milk and other goods. His utility function is given by
U(x, y) = y(x + 1), where x is his milk consumption and y is his consumption of other goods. His initial
endowment is 19 units of milk per day and no units of other goods. If the price of milk is $2 and the
price of other goods is $1, how much milk does he consume?
a.
9 gallons
b.
38 gallons
c.
20 gallons
d.
14 gallons
e.
12 gallons
15. Jack earns 5 dollars per hour. He has 100 hours per week which he can use for either labor or leisure.
The government institutes a plan in which each worker receives a $100 grant from the government but
has to pay 50% of his or her labor income in taxes. If Jack’s utility function is U(c, r) = cr, where c is
dollars worth of consumption of goods and r is hours of leisure per week, how many hours per week
will Jack choose to work?
a.
30
b.
40
c.
26
d.
20
e.
None of the above.
16. Aristotle earns 5 dollars per hour. He has 110 hours per week available for either labor or leisure. In
the old days he paid no taxes and received nothing from the government. Now he gets a $200 payment
per week from the government but he must pay half of his labor income in taxes. (His before-tax
wages are the same as they were before, and he has no other source of income than wages and
payments from the government.) He notices that with the government payment and his taxes, he can
exactly afford the combination of leisure and consumption goods that he used to choose. How many
hours per week did he work in the old days?
a.
100
b.
20
c.
45
d.
60
e.
None of the above.
17. Rhoda takes a job with a construction company. She earns $5 an hour for the first 40 hours of each
week and then gets “double–time” for overtime. That is, she is paid $10 an hour for every hour beyond
40 hours a week that she works. Rhoda has 70 hours a week available to divide between construction
work and leisure. She has no other source of income, and her utility function is U = cr, where c is her
income to spend on goods and r is the number of hours of leisure that she has per week. She is allowed
to work as many hours as she wants to. How many hours will she work?
a.
50
b.
30
c.
45
d.
35
e.
None of the above.
18. Wendy and Mac work in fast-food restaurants. Wendy is paid $4 an hour for the first 40 hours a week
that she works and $6 an hour for every hour beyond 40 hours per week. Mac gets $5 an hour no
matter how many hours he works. Each has 110 hours per week to allocate between work and leisure.
Each has a utility function U = cr, where c is expenditure per week on consumption and r is hours of
leisure per week. Each can choose the number of hours to work. If Wendy works W hours and Mac
works M hours, then
a.
W = 1.5M.
b.
W M.
c.
W 2 M = 6.66.
d.
W 2 M = 10.
e.
None of the above.
19. Heather and Myrtle have the same tastes. Heather is paid $10 an hour and chooses to work 9 hours a
day. Myrtle is paid $9 an hour for the first 8 hours she works and $18 an hour for any time she works
beyond 8 hours a day.
a.
Since she has the same tastes as Heather and can earn the same income by working 9
hours a day, she chooses to work 9 hours a day.
b.
Unless her indifference curve is kinked, Heather would be better off facing the same pay
schedule as Myrtle.
c.
Myrtle would prefer Heather’s pay schedule to her own.
d.
Myrtle will work less than 9 hours a day.
e.
None of the above.
20. Mike Teevee likes to watch television and to eat candy. In fact his utility function is U(x, y) = x2y,
where x is the number of hours he spends watching television and y is the number of dollars per week
he spends on candy. Mike’s mother doesn’t like him to watch so much television. She limits his
television watching to 36 hours a week and in addition she pays him $1 an hour for every hour that he
reduces his television watching below 36 hours a week. If this is Mike’s only source of income to buy
candy, how many hours of television does he watch per week?
a.
36
b.
12
c.
24
d.
18
e.
16
21. Georgina earns 6 dollars an hour. She has no nonlabor income. She has 100 hours a week available for
either labor or leisure. Her utility function is U(c, r) = cr3, where c is dollars worth of goods and r is
hours of leisure. How many hours per week will she work?
a.
23
b.
25
c.
28
d.
50
e.
None of the above.
22. Irene earns 8 dollars an hour. She has no nonlabor income. She has 30 hours a week available for
either labor or leisure. Her utility function is U(c, r) = cr2, where c is dollars worth of goods and r is
hours of leisure. How many hours per week will she work?
a.
8
b.
13
c.
15
d.
10
e.
None of the above.
23. Will is paid $10 an hour for the first 40 hours per week that he works. He can also work as many hours
overtime as he wishes to. He is paid $15 an hour for every hour that he works beyond 40 hours a week.
Leisure is a normal good for Will and he is currently working some overtime. If his hourly wage for
the first 40 hours per week that he works rises to $12 and his wages for overtime remain at $15 per
hour, he will choose to work
a.
fewer hours per week.
b.
more hours per week.
c.
the same number of hours per week.
d.
more hours per week if and only if his income exceeds his labor income.
e.
more hours per day if and only if he works less than 20 hours overtime per week.
24. Henri is paid $9 an hour for the first 40 hours per week that he works. He can also work as many hours
overtime as he wishes to. He is paid $15 an hour for every hour that he works beyond 40 hours a week.
Leisure is a normal good for Henri and he is currently working some overtime. If his hourly wage for
the first 40 hours per week that he works rises to $11 and his wages for overtime remain at $15 per
hour, he will choose to work
a.
more hours per week.
b.
more hours per week if and only if his income exceeds his labor income.
c.
the same number of hours per week.
d.
fewer hours per week.
e.
more hours per day if and only if he works less than 20 hours overtime per week.
25. There are no taxes on the first $500 that Debra earns per week, but on income above $500 per week,
she must pay a 60% tax. Debra’s job pays $10 per hour. Her utility function is U(c, r) = rc2, where r is
hours of leisure and c is dollars worth of consumption. She has 100 hours to divide between work and
leisure. How many hours per week will she choose to work?
a.
66.66
b.
50
c.
40
d.
33.33
e.
20
26. Susan’s utility function is U(x, y) = (x + y)R2, where x and y are the quantities of goods X and Y that
she consumes and R is the number of hours of leisure that she has per day. Good X costs 4 dollars per
unit and good Y costs 2 dollars per unit. Her wage rate is 8 dollars per hour and she has 15 hours per
day to allocate between labor and leisure. She will
a.
consume equal amounts of goods X and Y.
b.
consume 10 units of good X.
c.
consume 20 units of good Y.
d.
work 10 hours a day.
e.
consume twice as much of good X as of good Y.
27. George Goodhands is a life insurance agent. He can work 40 hours a week for a large national
insurance company and receive a fixed salary of S dollars per week, or he can work independently, for
as many or as few hours per week as he likes and earn w dollars per hour. (He cannot take both jobs.)
Which of the following responses to an increase in the salary paid by the insurance company would be
inconsistent with the weak axiom of revealed preference?
a.
Leaving independent work for the 40 hour salaried job
b.
Doing exactly what he was doing before
c.
More than one of these options would be inconsistent
d.
Continuing to work independently but working more hours
e.
None of the above.
28. Gladys Goodhands is an insurance agent. She must choose one and only one of two possible
alternative jobs. She can either work for a large national insurance company for which she must work
exactly 40 hours a week and will receive a salary of S dollars per week, or she can work as an
independent insurance agent, in which case she can work exactly as many hours per week as she
wishes and will earn w dollars for every hour that she works. Gladys satisfies the weak axiom of
revealed preference and she cares only about how much money she makes and about how much leisure
time she has.
a.
If S/40 w, she will prefer to work for the large national insurance company.
b.
If S/40 w and she decides to work independently, then it must be that she chooses to
work more than 40 hours a week.
c.
If S/40 w and she decides to work independently, then it must be that she chooses to
work less than 40 hours a week.
d.
If S/40 = w, she will be indifferent between working for the large insurance company and
working independently.
e.
None of the above.
29. Albert consumes only tangerines and bananas. His only source of income is an initial endowment of 30
units of tangerines and 10 units of bananas. Albert insists on consuming tangerines and bananas in
fixed proportions, 1 unit of tangerines per 1 unit of bananas. He initially faces a price of $10 per unit
for each fruit. The price of tangerines rose to $30 per unit while the price of bananas stayed
unchanged. After the price change, he would
a.
increase his consumption of tangerines by exactly 5 units.
b.
decrease his consumption or tangerines by at least 5 units.
c.
increase his consumption of tangerines by exactly 15 units.
d.
decrease his consumption of tangerines by exactly 7 units.
e.
decrease his consumption of bananas by at least 1 unit.
30. Quincy consumes only uglifruits and bananas. His only source of income is an initial endowment of 30
units of uglifruits and 10 units of bananas. Quincy insists on consuming uglifruits and bananas in fixed
proportions, 1 unit of uglifruits per 1 unit of bananas. He initially faces a price of $20 per unit for each
fruit. The price of uglifruits rose to $40 per unit while the price of bananas stayed unchanged. After the
price change, he would
a.
increase his consumption of uglifruits by exactly 3.33 units.
b.
decrease his consumption or uglifruits by at least 3.33 units.
c.
decrease his consumption of uglifruits by exactly 5.33 units.
d.
increase his consumption of uglifruits by exactly 13.33 units.
e.
decrease his consumption of bananas by at least 1 unit.
31. Yolanda receives a lump sum child support payment of $150 per week. She has 80 hours a week to
divide between labor and leisure. She earns $5 an hour. The first $150 per week of her labor income is
untaxed, but all labor income that she earns above $150 is taxed at the rate 30%. If we graph her
budget line with leisure on the horizontal axis and consumption on the vertical axis, her budget line
has
a.
a kink in it at the point where she takes 60 units of leisure.
b.
a kink in it where her income is $300 and her leisure is 50 units.
c.
a slope of −3.50 everywhere.
d.
no kinks in the part that corresponds to positive labor supply.
e.
a piece that is a horizontal straight line.
32. Tomoko receives a lump sum child support payment of $200 per week. She has 80 hours a week to
divide between labor and leisure. She earns $5 an hour. The first $100 per week of her labor income is
untaxed, but all labor income that she earns above $100 is taxed at the rate 50%. If we graph her
budget line with leisure on the horizontal axis and consumption on the vertical axis, her budget line
has
a.
no kinks in the part that corresponds to positive labor supply.
b.
a kink in it where her income is $300 and her leisure is 60 units.
c.
a kink in it at the point where she takes 70 units of leisure.
d.
a slope of −2.50 everywhere.
e.
a piece that is a horizontal straight line.
33. If Abishag owns 16 quinces and 15 kumquats and if the price of kumquats is 4 times the price of
quinces, how many kumquats can she afford if she buys as many kumquats as she can?
a.
38
b.
31
c.
15
d.
19
e.
16
34. If Abishag owns 18 quinces and 5 kumquats and if the price of kumquats is 6 times the price of
quinces, how many kumquats can she afford if she buys as many kumquats as she can?
a.
5
b.
23
c.
16
d.
8
e.
5
35. Mario consumes eggplants and tomatoes in the ratio of 1 bushel of eggplants per 1 bushel of tomatoes.
His garden yields 30 bushels of eggplants and 10 bushels of tomatoes. He initially faced prices of $25
per bushel for each vegetable, but the price of eggplants rose to $100 per bushel, while the price of
tomatoes stayed unchanged. After the price change, he would
a.
increase his eggplant consumption by 6 bushels.
b.
decrease his eggplant consumption by at least 6 bushels.
c.
increase his consumption of eggplants by 8 bushels.
d.
decrease his consumption of eggplants by 8 bushels.
e.
decrease his tomato consumption by at least 1 bushel.
36. Mario consumes eggplants and tomatoes in the ratio of 1 bushel of eggplants per 1 bushel of tomatoes.
His garden yields 30 bushels of eggplants and 10 bushels of tomatoes. He initially faced prices of $10
per bushel for each vegetable, but the price of eggplants rose to $30 per bushel, while the price of
tomatoes stayed unchanged. After the price change, he would
a.
decrease his consumption of eggplants by 7 bushels.
b.
increase his consumption of eggplants by 7 bushels.
c.
decrease his eggplant consumption by at least 5 bushels.
d.
increase his eggplant consumption by 5 bushels.
e.
decrease his tomato consumption by at least 1 bushel.
37. Dr. Johnson receives a lump sum payment of $150 per week. Suppose that the first $150 per week of
labor income is untaxed but all labor income above $150 is taxed at a rate of 10%.
a.
Dr. Johnson’s budget line has a kink in it at the point where he takes 60 units of leisure.
b.
Dr. Johnson’s budget line has a kink where his income is $300 and his leisure is 50 units.
c.
Dr. Johnson’s budget line has slope −4.50 everywhere.
d.
Dr. Johnson’s budget line has no kinks in the part of it that corresponds to a positive labor
supply.
e.
Dr. Johnson’s budget line has a piece that is a horizontal straight line.
38. Dr. Johnson receives a lump sum payment of $100 per week. Suppose that the first $100 per week of
labor income is untaxed but all labor income above $100 is taxed at a rate of 40%.
a.
Dr. Johnson’s budget line has a kink in it at the point where he takes 70 units of leisure.
b.
Dr. Johnson’s budget line has no kinks in the part of it that corresponds to a positive labor
supply.
c.
Dr. Johnson’s budget line has slope 23 everywhere.
d.
Dr. Johnson’s budget line has a kink where his income is $200 and his leisure is 60 units.
e.
Dr. Johnson’s budget line has a piece that is a horizontal straight line.
39. Dudley has a utility function U(C, R) = C − (12 − R)2, where R is leisure and C is consumption per day.
He has 16 hours per day to divide between work and leisure. If Dudley has a nonlabor income of $20
per day and is paid a wage of $0 per hour, how many hours of leisure will he choose per day?
a.
9
b.
10
c.
11
d.
13
e.
12
40. Dudley has a utility function U(C, R) = C − (12 − R)2, where R is leisure and C is consumption per day.
He has 16 hours per day to divide between work and leisure. If Dudley has a nonlabor income of $35
per day and is paid a wage of $6 per hour, how many hours of leisure will he choose per day?
a.
10
b.
8
c.
7
d.
6
e.
9
41. Mr. Cog has 18 hours per day to divide between labor and leisure. His utility function is U(C, R) = CR,
where C is dollars per year spent on consumption and R is hours of leisure. If he has 19 dollars of
nonlabor income per day and gets a wage rate of 15 dollars per hour when he works, his budget
equation, expressing combinations of consumption and leisure that he can afford to have, can be
written as
a.
15R + C = 19.
b.
15R + C = 289.
c.
R + C/15 = 379.
d.
C = 289 + 15R.
e.
C = 346 + 15R.
42. Mr. Cog has 18 hours per day to divide between labor and leisure. His utility function is U(C, R) = CR,
where C is dollars per year spent on consumption and R is hours of leisure. If he has 5 dollars of
nonlabor income per day and gets a wage rate of 11 dollars per hour when he works, his budget
equation, expressing combinations of consumption and leisure that he can afford to have, can be
written as
a.
C = 203 + 11R.
b.
R + C/11 = 269.
c.
11R + C = 5.
d.
11R + C = 203.
e.
C = 218 + 11R.
43. Mr. Cog has 18 hours per day to divide between labor and leisure. His utility function is U(C, R) = CR,
where C is dollars per year spent on consumption and R is hours of leisure. If he has a nonlabor
income of 40 dollars per day and a wage rate of 8 dollars per hour, he will choose a combination of
labor and leisure that allows him to spend
a.
184 dollars per day on consumption.
b.
82 dollars per day on consumption.
c.
112 dollars per day on consumption.
d.
92 dollars per day on consumption.
e.
138 dollars per day on consumption.
44. Mr. Cog has 18 hours per day to divide between labor and leisure. His utility function is U(C, R) = CR,
where C is dollars per year spent on consumption and R is hours of leisure. If he has a nonlabor
income of 32 dollars per day and a wage rate of 13 dollars per hour, he will choose a combination of
labor and leisure that allows him to spend
a.
133 dollars per day on consumption.
b.
149 dollars per day on consumption.
c.
266 dollars per day on consumption.
d.
123 dollars per day on consumption.
e.
199.50 dollars per day on consumption.
45. Ollie South has an endowment of 10 guns and 10 pounds of butter. He can buy or sell butter at $1 a
pound. But the world market for guns is more complicated: he can buy guns for $5 each, but he can
sell guns for only $2. If we graph his budget line with guns on the horizontal axis and butter on the
vertical axis, then Ollie’s budget line is a straight line
a.
joining (12, 0) and (0, 30).
b.
joining (14, 0) and (0, 14).
c.
with slope − 2/5 through the point (10, 10).
d.
with slope − 5/2 going through the point (10, 10).
e.
None of the above.
46. Charlie consumes apples and bananas; his utility function is U(a, b) = ab. Charlie’s fruit farm yielded
5 apples and 10 bananas. In addition, Charlie has $10 that he was given by a secret admirer. Charlie
can buy or sell apples at $2 each and he can buy or sell bananas at $1 each. Charlie will consume
a.
more apples and more bananas than he grows.
b.
more apples and fewer bananas than he grows.
c.
fewer apples and more bananas than he grows.
d.
fewer apples and more bananas than he grows.
e.
exactly as many apples as he grows and more bananas than he grows.
47. A farmer gets 20 eggs and 10 tomatoes every week from her chickens and her tomato plants. She has
no other source of income. She has convex, downward-sloping indifference curves. The current market
prices are $2 per egg and $3 per tomato. At these prices she chooses the same bundle that she is
endowed with (20 eggs and 10 tomatoes).
a.
If relative prices change in any way whatsoever, she will certainly be no worse off and
may be better off than she was before the price change.
b.
An increase in the price of eggs (with the price of tomatoes remaining constant) will
decrease her utility.
c.
An increase in the price of tomatoes (with the price of eggs remaining constant) will make
her worse off.
d.
If both prices rise, she will be worse off, but if only one price rises, she might be made
better off or worse off, depending on her tastes.
e.
Since she earns her income from tomatoes and eggs only, she treats eggs and tomatoes as
perfect substitutes.
PROBLEM
1. Mr. and Mrs. Brauer owned their own home. There was a real estate boom in their town and the price
of houses doubled. Their income and other prices stayed constant. The Brauers complained that “we
are being driven from our home; we can’t afford to live here any more.”
a. Draw a diagram that illustrates what happened to the Brauers’ budget constraint.
b. Could they have been made worse off by the change? Could they have been made better off?
Explain why.
2. Harvey’s net demands for goods 1 and 2 are (2, −3) and his endowment is (6, 5).
a. What are his gross demands?
b. Draw a diagram illustrating his budget line, his endowment, and his consumption. (Put good 1 on
the horizontal axis.)
c. Draw a dotted line to show what his budget line would be if the price of good 1 doubled and the
price of good 2 stayed the same.
3. Is it ever possible that if someone is a net seller of a good, and the price of the good he sells falls, the
consumer could wind up better off than he was before by switching from being a seller to being a
buyer? Draw a graph to justify your answer.
4. Is it ever possible that an increase in the price of a good for which a person is a net seller can make
him worse off? Use a diagram to illustrate your answer.
5. Peter has an endowment of 3 units of good x and 5 units of good y. He can buy and sell x at a price of
$100 and y at a price of $200. He receives an income of $700 as alimony from a former spouse.
a. Draw Peter’s budget line for x and y. Show his initial endowment of x and y on your diagram.
b. Calculate the amount of x that he could afford if he bought only x and the amount of y he could
afford if he bought only y.
c. Write an equation for Peter’s budget.
6. Dudley’s utility function for goods and leisure is U(G, L) = G − (20 − L)(20 − L), where G is
consumption of goods and L is the number of hours of leisure per day. Goods cost $1 per unit.
a. If Dudley had an income from nonlabor sources of $25 per day and could work as much as he chose
to but would get zero wages, how much would he work?
b. Sketch Dudley’s indifference curves on a graph with leisure on the horizontal axis and income on
the vertical axis. If Dudley’s nonlabor income were $25 a day and he could work as much as he
wished for $10 an hour, how many hours a day would he choose to work?
7. Marilyn is a journalist. She is considering two possible jobs. One job is as an editor for a magazine.
The other job is writing freelance articles and selling them to whoever will buy them. If she works for
the magazine, she must spend 10 hours a day at work and commuting. She will be paid $130 a day net
of commuting costs and taxes if she takes this job. If she writes freelance articles, she can work at
home and as many hours a day as she pleases. She estimates that she would earn $10 an hour after
taxes if she does this. Her utility function is U = (R3)C, where R is the number of hours a day she
spends not working or commuting and C is her earnings.
a. If Marilyn chooses to freelance, how many hours will she work?
b. Calculate her utility in each job and identify which job she will choose.
8. Ernie’s wage rate is $10 an hour. He has no earnings other than his labor income. His utility function is
U(C, L) = CR2, where C is the amount of money he spends on consumption, and R is the number of
hours a day he spends not working.
a. Write an equation that describes Ernie’s budget constraint.
b. How many hours does Ernie choose to work per day?
c. How much money does he spend on consumption per day?
9. May’s utility function is U = C + 14D1/22.5(H + J)2, where C is dollars spent on goods other than
housecleaning, D is the number of hours per day that somebody spends cleaning her house, H is the
number of hours per day May spends cleaning her house, and J is the number of hours per day May
spends working at her job. All May’s income comes from her job. She can work as many hours a day
as she wishes at a wage of $7 an hour.
a. If she cannot hire anyone to do her housecleaning, how many hours will she spend on the job and
how many hours will she spend housecleaning?
b. If she can hire a housecleaner at $5 an hour, how many hours will she work on her job, how many
hours of housecleaning will she hire, and how many hours will she clean house?
10. Leo thinks leisure and consuming goods are perfect complements. Goods cost $1 per unit. Leo wants
to consume 5 units of goods per hour of leisure. Leo can work as much as he wants to at the wage rate
of $15 an hour. He has no other source of income.
a. How many hours a day will Leo choose to spend at leisure?
b. Draw a diagram showing Leo’s budget and his choice of goods and leisure.
c. Will Leo work more or less if his wage rate increases?
11. Lucetta changes light bulbs. She is paid $10 an hour. She can work as many hours as she wishes.
Lucetta works only 6 hours a day. But she says she loves her job and is happier working at this job
than she would be if she made the same income without working at all. Though this may sound
strange, Lucetta is perfectly rational. Draw a graph showing leisure on the horizontal axis and income
on the vertical axis. Draw a budget line and some indifference curves for Lucetta that are consistent
with Lucetta’s words and actions. Explain in words what happens.