3
Consumer CHAPTER Behavior
MULTIPLE CHOICE
Section 3.1
easy
1. Gary Franklin is a movie critic. He invented the Franklin Scale with which he rates movies
from 1 to 10 (10 being best). When asked about his scale, Mr. Franklin explained "that it is a
subjective measure of movie quality. A movie with a ranking of 10 is not necessarily 10 times
better than a movie with a ranking of 1, but it is better. A movie with a ranking of 5 is better
than a movie with a ranking of 1, but is not as good a movie with a ranking of 10. That's all it
really tells you." Based on Mr. Franklin's description, his scale is:
a.
b.
c.
d.
easy
2. Which of the following is NOT an assumption regarding people's preferences in the theory of
consumer behavior?
a.
b.
c.
d.
easy
complete.
transitive.
intransitive.
both (a) and (b) are correct.
both (a) and (c) are correct.
4. The assumption of transitive preferences implies that indifference curves must:
a.
b.
c.
d.
e.
easy
preferences are complete.
preferences are transitive.
consumers prefer more of a good to less.
none of the above.
3. The theory of consumer behavior is based on certain assumptions. It includes at least the
assumption(s) that preferences are:
a.
b.
c.
d.
e.
easy
ordinal but not cardinal.
cardinal but not ordinal.
an objective standard to judge movies.
neither cardinal nor ordinal.
not cross one another.
have a positive slope.
be L-shaped.
be convex to the origin.
all of the above.
5. If a market basket is changed by adding more of at least one good, then rational consumers will:
a.
b.
c.
d.
rank the market basket more highly after the change.
more likely prefer a different market basket.
rank the market basket as being just as desirable as before.
be unable to decide whether the first market basket is preferred to the
second or vice versa.
e. have indifference curves that cross.
42
CHAPTER 3
CONSUMER BEHAVIOR
easy
TEST BANK
SIXTH EDITION
6. A consumer prefers market basket A to market basket B, and prefers market basket B to market
basket C. Therefore, A is preferred to C. The assumption that leads to this conclusion is:
a. transitivity.
b. completeness.
c. all goods are good.
43
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
d. diminishing MRS.
e. assumption of rationality.
easy
7. The assumption that preferences are complete:
a. means that a consumer will spend her entire income.
b. is unnecessary, as long as transitivity is assumed.
c. recognizes that there may be pairs of market baskets that cannot be
compared.
d. means that between any two market baskets of goods, the consumer
can determine that either one is preferred to the other or that she
is indifferent between them.
easy
8. A curve that represents all combinations of market baskets that provide the same level of utility
to a consumer is called:
a.
b.
c.
d.
e.
easy
a budget line.
an isoquant.
an indifference curve.
a demand curve.
none of the above.
9. An upward sloping indifference curve defined over two goods violates which of the following
assumptions from the theory of consumer behavior?
a.
b.
c.
d.
transitivity.
preferences are complete.
more is preferred to less.
all of the above.
44
CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
e. none of the above.
easy
10. The slope of an indifference curve reveals:
a.
b.
c.
d.
e.
moderate
11. Zoe is an executive at Dell Computer Company who is in charge of designing the next version of
laptop computers. She will consider such features as screen size, weight, processor speed, and
CD and DVD drives. Given the fact that it is costly to include more features in new products,
why might Zoe be interested in data on how much consumers paid for a range of laptops with
different attributes?
a.
b.
c.
d.
e.
easy
in order to estimate willingness to pay for each feature.
in order to set an optimal price for the laptops.
in order to determine the best features to include.
in order to estimate willingness to trade off one feature for another.
all of the above.
12. In what ways can economists help auto manufacturers estimate the marginal rate of substitution
between features such as vehicle interior size and acceleration?
a.
b.
c.
d.
e.
easy
examining cost data
conducting consumer surveys
solving the standard consumer model
statistically analyzing data on historical purchases
(b) and (d) only
13. Indifference curves are convex to the origin because of:
a.
b.
c.
d.
e.
easy
transitivity of consumer preferences.
the assumption of a diminishing marginal rate of substitution.
the assumption that more is preferred to less.
the assumption of completeness.
none of the above.
14. Suppose that a market basket of two goods is changed by adding more of one of the goods and
subtracting one unit of the other. The consumer will:
a.
b.
c.
d.
easy
that preferences are complete.
the marginal rate of substitution of one good for another good.
the ratio of market prices.
that preferences are transitive.
none of the above.
rank the market basket more highly after the change.
rank the market basket more highly before the change.
rank the market basket just as desirable as before.
any one of the above statements may be true.
15. If indifference curves cross, then:
a. the assumption of a diminishing marginal rate of substitution is
violated.
b. the assumption of transitivity is violated.
c. the assumption of completeness is violated.
d. consumers minimize their satisfaction.
e. all of the above.
45
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
Alvin's preferences for good X and good Y are shown in the diagram below.
Figure 3.1
easy
16. Based on Figure 3.1, it can be inferred that:
a.
b.
c.
d.
e.
easy
17. Refer to Figure 3.1. Which of the following is true concerning Alvin's marginal rate of
substitution?
a.
b.
c.
d.
easy
Alvin does not consider good X as "good."
Alvin will never purchase any of good Y.
Alvin regards good X and good Y as perfect substitutes.
Alvin regards good X and good Y as perfect complements.
none of the above.
It is diminishing.
It is positive.
It is constant.
It is zero.
18. Refer to Figure 3.1. Which assumption concerning preferences do Alvin's indifference curves
violate?
a.
b.
c.
d.
Diminishing marginal rates of substitution.
Transitivity of preferences.
More is preferred to less.
Completeness.
46
CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
Alvin's preferences for good X and good Y are shown in the diagram below.
Good Y
45
A
Figure 3.2
easy
19. Based on Figure 3.2, it can be inferred that:
a.
b.
c.
d.
e.
easy
moderate
diminishing.
positive.
constant and positive.
zero.
21. Refer to Figure 3.2. Which assumption concerning preferences do Alvin's indifference curves
violate?
a.
b.
c.
d.
e.
easy
Alvin does not consider good X as "good."
Alvin will never purchase any of good Y.
Alvin regards good X and good Y as perfect substitutes.
Alvin regards good X and good Y as perfect complements.
none of the above.
20. Refer to Figure 3.2. At any consumption bundle with the quantity of good X exceeding the
quantity of good Y (that is, a bundle located below the 45 degree line, like point A), Alvins
marginal rate of substitution of good X for good Y is
a.
b.
c.
d.
easy
Good X
Diminishing marginal rates of substitution.
Transitivity of preferences.
More is preferred to less.
Completeness.
Both (a) and (c).
22. Which of the following is true about the indifference curve where one commodity (such as
pollution) is "bad"?
a. It has a negative slope.
b. It has a positive slope.
c. It is horizontal.
d. It is vertical.
23. If indifference curves are concave to the origin, which assumption on preferences is violated?
a. Diminishing marginal rates of substitution.
47
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
b. Transitivity of preferences.
c. More is preferred to less.
d. Completeness.
moderate
24. Envision a graph with meat on the horizontal axis and vegetables on the vertical axis. A strict
vegetarian would have indifference curves that are:
a.
b.
c.
d.
e.
vertical.
horizontal.
diagonal straight lines.
right angles.
upward sloping.
Consider the following three market baskets:
A
B
C
moderate
A is on the same indifference curve as B.
B is on the same indifference curve as C.
A is preferred to C.
B is preferred to A
both (a) and (b) are correct.
26. Refer to Table 3.1. Which of the following cannot be true?
a.
b.
c.
d.
moderate
Clot
hing
3
5
8
25. Refer to Table 3.1. If preferences satisfy all four of the usual assumptions:
a.
b.
c.
d.
e.
easy
Table 3.1
Foo
d
6
8
5
the consumer could be indifferent between A and B.
A and C could be on the same indifference curves.
the consumer could be indifferent between B and C.
A and C could be on different indifference curves.
27. Consider the following three market baskets:
Foo
Clot
d
hing
A
15
18
B
13
19
C
14
17
If baskets B and C are on the same indifference curve, and if preferences satisfy all four of the
usual assumptions, then:
a.
b.
c.
d.
A is preferred to C.
A is preferred to B.
both (a) and (b) are correct.
none of the above.
48
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
28. Mikey is very picky and insists that his mom make his breakfast with equal parts of cereal and
apple juice any other combination and it ends up on the floor. Cereal costs 4 cents per
tablespoon and apple juice costs 6 cents per tablespoon. If Mikeys mom budgets $8 per month
for Mikeys breakfast, how much cereal and juice does she buy?
a.
b.
c.
d.
moderate
29. Jane is trying to decide which courses to take next semester. She has narrowed down her choice
to two courses Econ 1 and Econ 2. Now she is having trouble. She just cannot decide which of
the two courses to take. Its not that she is indifferent between the two courses, she just cannot
decide. An economist would say that this is an example of preferences that:
a.
b.
c.
d.
moderate
impulse purchases
following fads and fashions instead of ones own preferences
complexity of making choices
all of the above
31. What is a good argument for using the model of the consumer despite the fact that it requires making
many simplifying assumptions?
a.
b.
c.
d.
49
are not transitive.
are incomplete.
violate the assumption that more is preferred to less.
all of the above.
30. Which of the following are examples of situations in which the standard model of the consumer
may not be realistic?
a.
b.
c.
d.
easy
40 tablespoons each of cereal and juice.
80 tablespoons each of cereal and juice.
40 tablespoons of cereal and 75 tablespoons of juice.
100 tablespoons of cereal and 67 tablespoons of juice.
it is complex to solve
the assumptions are sometimes realistic
it explains observed patterns of behavior
it is used in many scholarly fields
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
Good B
Increasing
utility
Good A
Figure 3.3
moderate
32. Refer to the indifference curve in Figure 3.3. Which of the following statements is correct?
a.
b.
c.
d.
easy
33. Refer to the indifference curve in Figure 3.3. Which of the following statements is correct?
a.
b.
c.
d.
easy
MU(a) =0.
MU(b) =0.
MU(a) is negative.
MU(B) is negative.
34. Refer to the indifference curve in Figure 3.3. Which of the following is true about the MRS?
a.
b.
c.
d.
difficult
This individual receives no satisfaction from Good A.
This individual receives no satisfaction from Good B.
This individual will only consume A and B in fixed proportions.
None of the above.
It is negative.
It is positive.
It is equal to zero.
It is undefined.
35. The magnitude of the slope of an indifference curve is:
a.
b.
c.
d.
e.
called the marginal rate of substitution.
equal to the ratio of the total utility of the goods.
always equal to the ratio of the prices of the goods.
all of the above.
(a) and (c) only.
50
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
36. Use the following two statements to answer this question:
I.
If utility is ordinal, a market basket that provides 30 utils provides twice the satisfaction of a
market basket that provides 15 utils.
II. When economists first studied utility it was believed that utility was cardinal, but it was
later discovered that ordinal preferences are sufficient to explain how most individual
decisions are made.
a.
b.
c.
d.
moderate
37. If X and Y are perfect substitutes, which of the following assumptions about indifference curves
is not satisfied?
a.
b.
c.
d.
e.
difficult
Both I and II are true.
I is true, and II is false.
I is false, and II is true.
Both I and II are false.
completeness.
transitivity.
more is preferred to less.
diminishing MRS.
none of the above (All of the above assumptions are satisfied).
38. If a consumer is always indifferent between an additional one grapefruit or an additional two
oranges, then when oranges are on the horizontal axis the indifference curves:
a.
b.
c.
d.
will be straight lines with a slope of -1/2.
will be straight lines with a slope of -1.
will be straight lines with a slope of +1/2.
will be right angles whose corners occur on a ray from the origin with
a slope of +2.
e. none of the above.
difficult
39. Consider the following three market baskets:
A
B
C
Ch
ees
e
5
15
10
Crac
kers
8
6
7
If baskets A and B are on the same indifference curve and if indifference curves exhibit
diminishing MRS:
a.
b.
c.
d.
51
C is preferred to both A and B.
A and B are both preferred to C.
C is on the same indifference curve as A and B.
There is not enough information to determine preferences for C
relative to the other goods.
TEST BANK
SIXTH EDITION
difficult
CHAPTER 3
CONSUMER BEHAVIOR
40. Use the following two statements to answer this question:
I.
According to the three basic assumptions regarding people's preferences, a person will
always prefer to earn a living through honest work rather than a life of crime.
II. When we say that preferences are complete, we mean that if a consumer prefers market
basket A to market basket B, and prefers market basket B to market basket C, then the
consumer prefers market basket A to market basket C.
a.
b.
c.
d.
difficult
Both I and II are true.
I is true and II is false.
I is false and II is true.
Both I and II are false.
41. Use the following two statements to answer this question:
I
Consumer theory can determine whether giving an individual a more preferred basket of
goods doubles her overall level of satisfaction, less than doubles her satisfaction, or more
than doubles her satisfaction.
II
There is not much empirical evidence to support the assumption that higher incomes result
in higher levels of satisfaction.
a.
b.
c.
d.
moderate
42. Which of the following statements concerning utility as a measure for well being are false?
b.
c.
d.
moderate
Both I and II are true.
I is true and II is false.
I is false and II is true.
Both I and II are false.
a. There is generally a positive relationship between income and utility.
It is possible to determine which of two individuals is made happier by consuming a
particular market basket.
Utility is an abstract representation of an individuals degree of happiness.
Cross country studies suggest that citizens in wealthier countries are happier than citizens
in poorer countries.
43. If Jill's MRS of popcorn for candy is 2 (popcorn is on the horizontal axis), Jill would willingly
give up:
a. 2, but no more than 2, units of popcorn for an additional unit of
candy.
b. 2, but no more than 2, units of candy for an additional unit of
popcorn.
c. 1, but no more than 1, unit of candy for an additional 2 units of
popcorn.
d. 2, but no more than 2, units of popcorn for an additional 2 units of
candy.
52
CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
Section 3.2
easy
44. A consumer has $100 per day to spend on product A, which has a unit price of $7, and product
B, which has a unit price of $15. What is the slope of the budget line if good A is on the
horizontal axis and good B is on the vertical axis?
a.
b.
c.
d.
easy
45. Suppose that the prices of good a and good b were to suddenly double. If good a is plotted along
the horizontal axis,
a.
b.
c.
d.
easy
the budget line will become steeper.
the budget line will become flatter.
the slope of the budget line will not change.
the slope of the budget line will change, but in an indeterminate way.
46. Theodore's budget line has changed from A to B. Which of the following explains the change in
Theodore's budget line?
a.
b.
c.
d.
e.
53
-7/15.
-7/100.
-15/7.
7/15.
The price of food and the price of clothing increased.
The price of food increased, and the price of clothing decreased.
The price of food decreased, and the price of clothing increased.
The price of food and the price of clothing decreased.
None of the above.
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
47. If the quantity of good a (Qa) is plotted along the horizontal axis, the quantity of good b (Qb) is
plotted along the vertical axis, the price of good a is Pa, the price of good b is Pb and the
consumer's income is I, then the slope of the consumer's budget constraint is:
a.
b.
c.
d.
e.
easy
-Qa/Qb
-Qb/Qa
-Pa/Pb
-Pb/Pa
I/Pa or I/Pb
48. The endpoints (horizontal and vertical intercepts) of the budget line:
a. measure its slope.
b. measure the rate at which one good can be substituted for another.
c. measure the rate at which a consumer is willing to trade one good for
another.
d. represent the quantity of each good that could be purchased if all of
the budget were allocated to that good.
e. indicate the highest level of satisfaction the consumer can achieve.
easy
49. An increase in income, holding prices constant, can be represented as:
a.
b.
c.
d.
easy
50. Assume that food is measured on the horizontal axis and clothing on the vertical axis. If the
price of food falls relative to that of clothing, the budget line will:
a.
b.
c.
d.
easy
become flatter.
become steeper.
shift outward.
become steeper or flatter depending on the relationship between
prices and income.
51. Which of the following will result in a decrease in a consumer's purchasing power?
a.
b.
c.
d.
moderate
a change in the slope of the budget line.
a parallel outward shift in the budget line.
an outward shift in the budget line with its slope becoming flatter.
a parallel inward shift in the budget line.
A decrease in the consumer's income.
An increase in the price of the good on the vertical axis.
An increase in the price of the good on the horizontal axis.
All of the above.
52. If prices and income in a two-good society double, what will happen to the budget line?
a.
b.
c.
d.
The intercepts of the budget line will increase.
The intercepts of the budget line will decrease.
The slope of the budget line may either increase or decrease.
Insufficient information is given to determine what effect the change
will have on the budget line but we know society is worse-off.
e. There will be no effect on the budget line.
Section 3.3
54
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
53. A consumer maximizes satisfaction at the point where his valuation of good X, measured as the
amount of good Y he would willingly give up to obtain an additional unit of X, equals:
a. the magnitude of the slope of the indifference curve through that
point.
b. one over the magnitude of the slope of the indifference curve through
that point.
c. Px/Py
d. Py/Px
difficult
54. Which of the following is true about a consumer's optimum when indifference curves are
concave?
a.
b.
c.
d.
moderate
Both goods are consumed.
No goods are consumed.
Only one of the goods is consumed.
It occurs at the point of tangency with the budget line.
55. Pencils sell for 10 cents and pens sell for 50 cents. Suppose Jack, whose preferences satisfy all
of the usual assumptions, buys 5 pens and one pencil each semester. With this consumption
bundle, his MRS of pencils for pens is 3. Which of the following is true?
a. Jack could increase his utility by buying more pens and fewer pencils.
b. Jack could increase his utility by buying more pencils and fewer
pens.
c. Jack could increase his utility by buying more pencils and more pens.
d. Jack could increase his utility by buying fewer pencils and fewer
pens.
e. Jack is at a corner solution and is maximizing his utility.
moderate
56. An individual consumes only two goods, X and Y. Which of the following expressions
represents the utility maximizing market basket?
a.
b.
c.
d.
e.
difficult
57. The fact that Alice spends no money on travel:
a.
b.
c.
d.
moderate
implies that she does not derive any satisfaction from travel.
implies that she is at a corner solution.
implies that her MRS does not equal the price ratio.
any of the above are possible.
58. The price of lemonade is $0.50; the price of popcorn is $1.00. If Fred has maximized his utility
by purchasing lemonade and popcorn, his marginal rate of substitution will be:
a.
b.
c.
d.
55
MRSxy is at a maximum.
Px/Py = money income.
MRSxy = money income.
MRSxy = Px/Py.
All of the above.
2 lemonades for each popcorn.
1 lemonades for each popcorn.
1/2 lemonade for each popcorn.
indeterminate unless more information on Fred's marginal utilities is
provided.
TEST BANK
SIXTH EDITION
difficult
CHAPTER 3
CONSUMER BEHAVIOR
59. When Joe maximizes utility, he finds that his MRS of X for Y is greater than Px/Py. It is most
likely that:
a.
b.
c.
d.
Joe's preferences are incomplete.
Joe's preferences are irrational.
Joe is not consuming good X.
Joe is not consuming good Y.
Section 3.4
moderate 60. The principle of revealed preference would say that if Xavier chooses market basket A over market
basket B then:
a.
b.
c.
d.
easy
if A is more expensive than B, then Xavier must prefer A over B.
if A is more expensive than B, then Xavier must prefer B over A.
if A is less expensive than B, then Xavier must prefer A over B.
if A is less expensive than B, then Xavier must prefer B over A.
61. Denise is shopping for lobsters and eclairs. When she faces budget line b1, she chooses market
basket A over market basket B. When she faces budget line b2, she chooses basket B over
basket C. Which assumption of consumer theory helps us determine Denises preference
ordering over basket A and basket C?
a.
b.
c.
d.
completeness
more is better than less
transitivity
convexity
Section 3.5
difficult
62. If a consumer must spend her entire income on some combination of two commodities and
chooses to spend it all on just one of the commodities then:
a. the other commodity is an economic bad.
b. the other commodity must have zero marginal utility.
c. the other commodity generates less utility per dollar spent on the
good.
d. the two commodities must be perfect substitutes.
easy
63. Marginal utility measures:
a.
b.
c.
d.
e.
the slope of the indifference curve.
the additional satisfaction from consuming one more unit of a good.
the slope of the budget line.
the marginal rate of substitution.
none of the above.
56
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
64. Oscar consumes only two goods, X and Y. Assume that Oscar is not at a corner solution, but he
is maximizing utility. Which of the following is NOT necessarily true?
a.
b.
c.
d.
e.
MRSxy = Px/Py.
MUx/MUy = Px/Py.
Px/Py = money income.
Px/Py = slope of the indifference curve at the optimal choice.
MUx/Px = MUy/Py.
Scenario 1:
Andy derives utility from two goods, potato chips (Qp) and Cola (Qc). Andy receives zero
utility unless he consumes some of at least one good. The marginal utility that he receives from
the two goods is given as follows:
Qp
1
2
3
4
5
6
7
8
easy
1
2
3
4
5
6
7
8
24
22
20
18
16
14
12
10
4 utils.
10 utils.
30 utils.
40 utils.
none of the above.
5
6
7
8
none of the above
67. Refer to Scenario 1. If the price of potato chips is $0.50 and the price of Cola is $4.00, and
Andy has an income of $14.50, how many units of potato chips will he consume?
a.
b.
c.
d.
e.
57
MUc
66. Refer to Scenario 1. If the price of potato chips is $0.50 and the price of Cola is $4.00, and
Andy has an unlimited income, how many units of potato chips will he consume?
a.
b.
c.
d.
e.
difficult
Qc
65. Refer to Scenario 1. What is the total utility that Andy will receive if he consumes 5 units of
potato chips (Qp) and no Cola drink (Qc)?
a.
b.
c.
d.
e.
moderate
MU
p
12
10
8
6
4
2
-2
-4
5
6
7
8
none of the above
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
68. When a person consumes two goods (A and B), that person's utility is maximized when the
budget is allocated such that:
a. the marginal utility of A equals the marginal utility of B.
b. the marginal utility of A times the price of A equals the marginal
utility of B times the price of B
c. the ratio of total utility of A to the price of A equals the ratio of the
marginal utility of B to the price of A.
d. the ratio of the marginal utility of A to the price of A equals the
ratio of the marginal utility of B to the price of B.
moderate
69. If Px = Py, then when the consumer maximizes utility,
a.
b.
c.
d.
moderate
70. Monica consumes only goods A and B. Suppose that her marginal utility from consuming good
A is equal to 1/Qa, and her marginal utility from consuming good B is 1/Qb. If the price of A is
$0.50, the price of B is $4.00, and the Monicas income is $120.00, how much of good A will
she purchase?
a.
b.
c.
d.
e.
moderate
0
12
24
48
120
71. Jane is attempting to maximize utility by selecting a market basket of goods. For each of the
goods in the market basket the marginal utility per dollar spent is equal. There are some goods
which are affordable but do not appear in the Jane's market basket. If Jane has maximized
utility, the marginal utility per dollar spent on each of the goods that does not appear in the
market basket is:
a.
b.
c.
d.
e.
difficult
X must equal Y.
MU(X) must equal MU(Y).
MU(X) may equal MU(Y), but it is not necessarily so.
X and Y must be substitutes.
too high.
too low.
zero.
infinite.
none of the above.
72. Alfred derives utility from consuming iced tea and lemonade. The marginal utility he receives
from iced tea is 16 utils, and the marginal utility he receives from lemonade is 8 utils. Instead of
consuming this bundle, Alfred should:
a.
b.
c.
d.
e.
buy more iced tea and less lemonade.
buy more lemonade and less iced tea.
buy more iced tea and lemonade.
buy less iced tea and lemonade.
none of the above is necessarily correct.
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moderate 73. A team of researchers has conducted a study of the well being of the citizens of the island nation of
Zarasa. Using a scale from 1 (least happy) to 10 (most happy), the researchers find that citizens
who earn 100 Zarutas per year have a mean happiness of 2.0, those who earn 200 Zarutas per
year have a mean happiness of 6.0, and those who earn 300 Zarutas per year have a mean
happiness of 7.0. The researchers should make which of the following conclusions?
a.
b.
c.
d.
e.
The utility of Zarasians increases with income
The marginal utility of Zarasians increases with income
The marginal utility of Zarasians decreases with income
Both a. and b.
Both a. and c.
SHORT-ANSWER PROBLEMS
SECTION 3.1
easy
74. Match the following descriptions of preferences to the indifference curve diagrams that follow.
___ Ann does not care whether she has more diet soft drinks or fewer diet soft drinks.
___ Peter is very picky about his buttered popcorn. He tops every quart of popped corn with
exactly one quarter cup of melted butter.
___ Amy likes M&M's, plain and peanut. For Amy, the marginal rate of substitution between
plain and peanut M&M's does not vary with the quantities of plain and peanut M&M's she
consumes.
___ George dislikes broccoli and would be willing to pay something to not have to eat it.
___ Natalya likes rap and rock music. Natalya's preferences exhibit a diminishing marginal rate
of substitution between the two types of music.
___ Matthew knows his limit. He likes beer up to a point, but if he drinks too much he gets sick.
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Solution: b, f, d, a, c, e
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easy
TEST BANK
SIXTH EDITION
75. Each of the following consumers exhibit behavior that violates one of the basic assumptions of
consumer preferences. Identify the assumption that is violated for each individual.
Art says that he can watch 2 movies a week but couldn't be paid to watch another movie
after that.
Alex says that he prefers going to a movie over hiking. He also indicates that he prefers
hiking to swimming. Alex then states that he would rather go swimming than go to a
movie.
Alicia says that she prefers hiking to watching a movie but can't determine her preferences
for swimming.
Solution:
Art violates the assumption that consumers desire more of a good to less. Alex's preferences
violate transitivity. Alicia violates the completeness assumption.
easy
76. An island economy produces only two goods, coconuts and pineapples. There are five people
(A,B, C, D, and E) living on the island with these preferences:
A
has a strong preference for pineapples.
B
has a strong preference for coconuts.
C
doesn't care for pineapples (assigns no value to them).
D
doesn't care for coconuts (assigns no value to them)
E
will only consume pineapples and coconuts in the fixed proportion of one pineapple to one
coconut.
For each of these five individuals, construct a representative indifference curve with pineapples
on the vertical axis and coconuts on the horizontal axis. Discuss the shape of the indifference
curves and relate them to the MRS.
Solution:
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Individual A has relatively flat indifference curves, since A requires relatively large numbers of
coconuts to compensate for the loss of pineapples that she values highly.
Individual B has relatively steep indifference curves, since B requires relatively few coconuts to
compensate for the loss of pineapples that he does not value highly.
C's indifference curves are vertical; the level of satisfaction is affected only by coconuts.
D's indifference curves are horizontal; the level of satisfaction is affected only by pineapples.
E's indifference curves are L-shaped.
MRS measures (at the margin) the maximum number of pineapples that the consumer will be
willing to give up in order to get one more unit of coconuts.
A's MRS is low. A is willing to relinquish few pineapples relative to coconuts since pineapples
are dear to A. B's MRS is high, for the opposite reason.
C's MRS is infinite. Since C's utility is not affected by pineapples, she is willing to relinquish
all pineapples (an infinite number) to obtain additional coconuts.
D's MRS is zero. D is not willing to give up any pineapples to obtain additional coconuts.
E's MRS is infinite when Qp> Qc, zero when Qc > Qp, and undefined when Qc = Qp.
moderate
77. The following combinations of goods X and Y represent various market baskets. Consumption
is measured in pounds per month.
Market Basket
Units of X
Units of Y
A
4
6
B
16
7
C
15
3
D
3
2
Explain which market basket(s) is(are) preferred to other(s), and if there is any uncertainty over
which is preferable, point this out as well.
Solution:
Since more of each good is preferred to less, we can conclude that a market basket is preferred
to an alternative basket if it lies above and to the right of the alternative basket.
Combination B is preferred to all others. A and C cannot be compared without additional
information. A and C are both preferred over D.
moderate
78. Consider Garys utility function: U(X,Y) = 5 XY, where X and Y are two goods. If the
individual consumed 10 units of X and received 250 units of utility, how many units of Y must
the individual consume? Would a market basket of X=15 and Y=3 be preferred to the above
combination? Explain.
Solution:
Given that U(X,Y) = 5XY = 5(10)Y, then 250 = 50Y, or Y = 5.
Since this individual receives 250 units of satisfaction with (X = 10, Y = 5), would (Y = 3 and X
= 15) be a preferred combination? At these values, U = 5(15)(3) = 225. So, the first
combination would be preferred.
moderate
79. In the theory of consumer behavior, several assumptions are made about the nature of
preferences. What are these assumptions? Illustrate the significance of these assumptions using
indifference curves.
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Solution:
Please see the text, Section 3.1.
moderate
80. In the theory of consumer behavior, certain axioms about the nature of preferences imply that
indifference curves cannot cross. Which axioms imply this? Explain your answer using a
diagram and using words.
Solution:
Transitivity and More is Better together imply that indifference curves cannot cross. If two
indifference curves did cross, then by choosing three points, A, B, and C in the following way.
A lies on the first indifference curve, B is the intersection point, C lies on the second curve, and
A lies to the left and below point C. It is easily shown that the two axioms cannot both be
satisfied. A is at least as preferred as B, and B is at least as preferred as C. By transitivity A is
at least as preferred as C, contradicting More is Better. See figure below.
Y
B
C
A
X
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TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
81. In the field of financial management it has been observed that there is a trade-off between the
rate of return that one earns on investments and the amount of risk that one must bear to earn
that return.
Solution:
a. Draw a set of indifference curves between risk and return for a person
that is risk averse (a person that does not like risk).
b. Draw a set of indifference curves for a person that is risk neutral (a
person that does not care about risk one way or the other).
c. Draw a set of indifference curves for a person that likes risk.
a.
b.
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c.
difficult
82. Draw a set of indifference curves for the following pairs of goods:
a. Hamburgers and carrots for a vegetarian who neither likes nor dislikes
meat. (vegetarians do not eat meat)
b. Peanut butter and jelly for an individual that will not eat peanut butter
sandwiches or jelly sandwiches, but loves peanut butter and jelly
sandwiches made with two parts peanut butter and one part jelly.
c. Tickets for Knott's Berry Farm (KBF) and Universal Studios (US) for
a tourist that believes that KBF and US are perfect substitutes.
d. Ice cream and pie if these are goods that you like, but if you consume
enough of either, you get sick of them. If you are sick of a good,
consuming more of it lowers your utility.
Solution:
a.
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TEST BANK
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b.
c.
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SIXTH EDITION
d.
SECTION 3.3
moderate
83. The local farmer's market sells corn for 20 cents an ear. At this price, Sam buys 6 ears each
Thursday. What would happen to Sam's consumption of corn if the market offered corn at 20
cents an ear for the first 6 ears, but 10 cents an ear for each additional ear? Explain your
answer.
Solution:
Sam would buy more corn.
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SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
84. George has a fixed income and can afford at most 7 units of Y if he spends his entire income on
Y. Alternatively, if he spends all his income on X, he can afford at most 6 units of X. Draw
George's budget line and an indifference curve such that George chooses to buy 4 pieces of X.
Martha has the same income and faces the same prices, yet she chooses to buy 2 pieces of X. In
equilibrium, what is George's subjective value of X in terms of Y? What is Martha's?
Solution:
In equilibrium, one unit of X will be worth 6/7 units of Y for both George and Martha. The
reason is that each consumer choices a consumption bundle so that MRS is equal to the
price ratio.
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moderate
TEST BANK
SIXTH EDITION
85. Hulk goes to the gym 20 times a month. His income is $1,000 per month and his visits to the
gym cost $4 per visit.
a. Draw Hulk's budget line for visits to the gym and all other goods,
show the consumption bundle that maximizes his satisfaction, and
draw the indifference curve through that point.
b. Recently, a new health club opened which offers identical facilities
but which charges a flat fee of $60 per month plus an additional $1
per visit. Draw Hulk's budget line if he were to join this new club.
c. Would Hulk continue to work out at the gym or would he join the new
health club. Why?
Solution:
a.
b.
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c.
He would join the new health club. Although his current consumption bundle is on both
budget lines, the health clubs pricing structure makes other, more preferred, bundles
affordable.
moderate
86. A consumer decides not to buy a VCR when her income is $20,000. However, when her income
rises to $30,000, she decides to buy one. In a single diagram, draw the budget lines and
indifference curves to illustrate this situation (assume the VCR costs $300 in both time periods).
Be sure to label your diagram completely.
Solution:
At the lower budget constraint, the consumer is at a corner solution. is, That she purchases no
VCRs. The consumer has sufficient income to afford a VCR. However, given her preferences it
is optimal to exhaust her budget on other goods. With her increase in income, the budget
constraint shifts out. The consumer now has expanded consumption opportunities. In this case,
the consumer chooses to purchase a VCR given the higher budget constraint. Purchasing one
VCR is optimal as the indifference curve is just tangent to the budget constraint at the
consumption bundle consisting of 1 VCR.
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moderate
TEST BANK
SIXTH EDITION
87. Suppose that the government subsidizes housing expenditures of low-income families by
providing a dollar-for-dollar subsidy to a familys housing expenditure. The Cunninghams
qualify for this subsidy and spend a total of $500 per month on housing: they spend $250 of their
own and receive a government subsidy of $250. Recently, a new policy has been proposed that
would provide each low income family with a lump sum transfer of $250 which can be used for
housing or other goods. Using a graph, demonstrate whether the Cunninghams would prefer the
current program, the proposed program, or would be indifferent between the two.
Solution:
A ll other
goods ($)
I +250
I
O
I- 250
O
500
2I
Housing
(in dollars)
The current program yields the flatter budget constraint for the Cunninghams. The flatter budget
constraint implies that the relative cost of housing is cheaper. This is due to the 50%
government subsidy. Currently, the Cunninghams spend $250 on housing with the government
matching with another $250. The utility maximizing choice is indicated in the diagram by point
O. The proposed program would eliminate the government housing price subsidy. Thus, the
relative price of housing would increase. This shifts the horizontal axis intercept in towards the
origin. However, the proposed plan would pay a cash payment of $250 to the Cunninghams.
This payment shifts the vertical axis intercept up. The Cunninghams may still choose to
consume at point O as it is available with the proposed plan. However, the MRS at point O is
less than the ratio of prices under the proposed plan. This implies the Cunninghams may
increase utility by spending less on housing and purchasing more of all other goods. This is
reflected by a movement to O' which corresponds with higher utility. Thus, the Cunninghams
are better off with the proposed lump sum transfer policy.
71
I+250
TEST BANK
SIXTH EDITION
difficult
CHAPTER 3
CONSUMER BEHAVIOR
88. Sheila can watch as many television programs as she wants for free, but she must pay $2 for
each video she rents. Draw Sheila's budget line for t.v. shows (T) and videos (V), and identify
the set of affordable bundles (be sure to label the axes). At a particular point on Sheila's budget
line, her MRS is 1T/2V. Illustrate this situation on your diagram. Has Sheila maximized her
satisfaction at this point? If not, identify a change in consumption that will make her better off.
Describe her preferences when satisfaction is maximized.
Solution:
Sheila would be better off if she consumed more television. In fact, she should consume
television until the value of an extra television show is zero.
difficult
89. Evelyn Lips preferences are depicted by the set of indifference curves in the diagram below.
Her budget line is also shown in the diagram. Use the information in the diagram to answer the
following questions.
Clothing
25
a. Which of the basic assumptions of consumer preferences are violated
20 Food
by E. Lips' indifference curves? Explain.
b. The price of food is $5 per unit. What is E. Lips' income and what is
the price of clothing?
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c. Show the market basket of food and clothing that maximizes E. Lips'
satisfaction. When satisfaction is maximized, has E. Lips equated
the marginal rate of substitution (of food for clothing) to the ratio of
the prices (of food to clothing)? If so, explain why. If not, explain
why not.
Solution:
a.
The assumption that consumers always prefer more to less is violated.
b.
E. Lips income is $100, the price of clothing is $4.
c.
The point in the diagram indicated above is E. Lips' utility maximizing bundle. At this point, E.
Lips has no marginal rate of substitution. Since this is the best point for E. Lips,
she is
unwilling to substitute either good regardless of the price ratio. Any movement from this point
will make E. Lips worse off.
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TEST BANK
SIXTH EDITION
difficult
CHAPTER 3
CONSUMER BEHAVIOR
90. Lisa's budget line and her satisfaction maximizing market basket, A, are shown in the diagram
below.
a. Suppose that Lisa is given $50 worth of coupons that must be spent on
food. How will the coupons alter Lisa's budget line?
b. Suppose that Lisa is given $50 in cash instead of $50 in coupons.
How will this alter Lisa's budget line?
c. Is Lisa indifferent between the food coupon and cash program, or does
she prefer one program over the other? Draw an indifference curve
to illustrate your answer.
Solution:
Refer to the following diagram with the answers.
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SIXTH EDITION
a.
With the coupons, Lisas budget is abc.
b.
With cash, Lisas budget line is dbc.
c.
If Lisas preferences are as shown, she is indifferent between the two programs. However,
if her preferences were such that an indifference curve was tangent to the db portion of dbc,
she would prefer cash.
difficult
91. Amy is currently spending her income to maximize her satisfaction. She is renting an apartment
for $900 per month as shown in the diagram below (Assume each dollar spent on housing buys 1
unit of housing. H1 represents her $900 per month apartment).
All other
goods
H1
Housing
a. Suppose that Amy qualifies for a government housing assistance
program that will provide her with a $600 per month apartment at
no charge. If she accepts the apartment, she cannot augment her
expenditure on housing (for example, she cannot add $300 of her
income to the $600 per month provided by the government program,
and rent the $900 per month apartment), nor can she exchange the
apartment for cash or other goods. How does the government
program alter Amy's budget line?
b. Suppose that Amy is given $600 in cash instead of the $600 per
month apartment. How will this alter Amy's budget line?
c. Is Amy indifferent between the housing assistance program and cash
program, or does she prefer one program over the other? Draw an
indifference curve to illustrate your answer.
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Solution:
a.
Amy's budget constraint becomes discontinuous at $600 on housing. If she wishes to spend
more or less on housing than $600, she has her original constraints. However, if she
chooses to spend $600, then the government pays the entire amount of her housing costs.
This allows her to use her complete income to spend solely on other goods. Thus, at
housing of $600, her budget constraint jumps up to allow her to use her entire income to
purchase other goods.
b.
The cash payment is another source of income that Amy may spend at her discretion. Thus, the
cash payment is analogous to an increase in income.
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c.
Amy would almost always strictly prefer the cash, since it gives her more choices than the
free apartment. (If housing is inferior and if her point of tangency on the new budget line is
exactly at 600 dollars worth of housing, then Amy would be indifferent between the two
programs.)
difficult
92. Sally consumes two goods, X and Y. Her utility function is given by the expression
U = 3 XY 2 . The current market price for X is $10, while the market price for Y is $5.00.
Sally's current income is $500.
a. Sketch a set of two indifference curves for Sally in her consumption
of X and Y.
b. Write the expression for Sally's budget constraint. Graph the budget
constraint and determine its slope.
c. Determine the X,Y combination which maximizes Sally's utility,
given her budget constraint. Show her optimum point on a graph.
(Partial quantities are possible.) (Note: MUY = 6XY and MUX =
3Y2.)
d. Calculate the impact on Sally's optimum market basket of an increase
in the price of X to 15. What would happen to her utility as a result
of the price increase?
Solution:
a.
To draw indifference curves, pick 2 levels of utility and find the values of x and y that hold
the total utility constant:
Let U = 60
for Y = 2
60 = 3 x ( 2 )
60 = 3 x 4
60
=x
12
77
2
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
x=5
y = 2, x = 5
y=3
60 = 3 x ( 3)
2
60 = 3 x 9
60
=x
27
x = 2.2
y = 3, x = 2.2
y=4
60 = 3 x ( 4 ) 2
60 = 3 x 16
60
=x
48
x = 1.25
y = 4, x = 1.25
Let U = 72
for y = 2
72 = 3 x ( 2 ) 2
72 = 3 x 4
72
=x
12
x=6
y = 2, x = 6
y=3
72 = 3 x ( 3) 2
72 = 3 x 9
72
=x
27
x = 2.67
y=3, x=2.67
y=4
72 = 3 x ( 4 ) 2
72 = 3 x 16
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TEST BANK
SIXTH EDITION
72
=x
48
x = 1.5
b.
I = Pxx + Pyy
500 = 10x + 5y
Slope =
79
rise 100
=
= 2
run
50
y=4, x=1.5
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
c.
To maximize utility, Sally must find the point where
MRS is equal to
MRS =
PX
.
PY
MU X
MU Y
recall: MU Y = 6XY, MU X = 3Y 2
MRS =
3Y 2
Y
=
6XY 2X
PX 10
=
=2
PY
5
set MRS =
Px
Py
Y
=2
2X
Y = 4X
Sally should consume four times as much Y as X.
To determine exact quantities, substitute Y = 4X into
I = PXX + PYY
500 = 10X + 5Y
500 = 10X + 5(4X)
500 = 30X
X = 16.67
Y = 4(16.67)
Y = 66.67
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TEST BANK
SIXTH EDITION
d.
MRS remains
Y PX
15
,
becomes
=3
2X PY
5
Equating MRS to
PX Y
,
= 3, Y = 6X
PY 2X
Substitute Y = 6X into the equation
500 = 15X + 5Y
500 = 15X +5(6X)
500 = 45X
X = 11.11
Y = 6(11.11)
Y = 66.67
Before price change:
U = 3(16.67)(66.67)2 = 222,289.
After price change:
U = 3(11.11)(66.67)2 = 148,148.
Utility fell due to the price change. Sally is on a lower indifference curve. (Note: Answers
may be slightly different due to rounding.)
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TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
93. The food stamp program provides low income households with coupons which can be
exchanged for some specified dollar value worth of food. Many economists argue that this
program is an inefficient means of increasing the well being of low income families. Proponents
of this view argue that an equivalent cash subsidy would bring about a greater increase in the
well being of the low income families receiving aid. Although many economists hold this view,
not all policy analysts agree with the advocates of cash payments instead of food stamps.
Advocates of the existing program argue that food stamps provide an incentive for low income
families to increase the nutritional quality of their diets.
a. Carefully analyze the arguments regarding increases in well being
under cash payments and food stamp programs. Use graphical
analysis to present your arguments.
b. Critically evaluate the pros and cons of the food stamp program. Do
food stamps ensure that low income families increase their
consumption of food?
Solution:
a.
Answers will vary depending on the way the indifference map is drawn. One type of answer
would have a consumer begin in equilibrium at a point like 0. The initial budget constraint
is AB.
The government decides to subsidize the low income family an amount equal to AC. If the
subsidy is an unrestricted increase in cash, the family's budget constraint will increase to
DO''C, and the family may choose a new equilibrium at point 0 (Depending on the exact
shape of the indifference curve, the new point of tangency may be anywhere on DOC.).
From the consumer's standpoint, this is the maximum increase in utility that is possible with
a subsidy of AC. If food stamps are used instead of a cash subsidy, the entire increase
would be spent on food.
Families move to point O'' on a lower indifference curve than 0. It is clear in this particular
instance that a cash subsidy would make families better off. However, the food stamp
program ensures that at least the value of the non-redeemable stamps are spent on food.
This implies in this instance that the nutritional levels of families are likely higher with the
food stamp program.
However, if the initial point of tangency on AB were to the right of O, then the food stamps
would actually decrease food consumption. Therefore, the effect of food stamps on food
consumption depends on the shape of individuals indifference maps.
All other
goods
D
O
B
O
O
A
C
Food
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SIXTH EDITION
b.
Students should balance subjective factors such as the desirability of improving diet for low
income families and the imposition of preferences upon members of low income
communities (i.e., the government knows low-income needs better than the families do).
It should be made clear, however, that food stamps may not increase expenditures on food
by low income families. The families could shift the income spent on food to other goods
or sell the food stamps. At point O'', the families' MRS and price ratio are not equal. We
would expect families to take steps to reach equilibrium.
moderate
94. Suppose that the price of gasoline has risen by 50%. What happens to a consumer's level of
well-being given he spends some of his income on gasoline? Diagram the impact of the increase
in gas prices in a commodity space diagram, and show the relevant indifference curves.
Now, if the individual's income rises just enough so that his original consumption bundle exactly
exhausts his income, will the individual purchase more or less gasoline (this level of income
implies the consumer can afford his original consumption bundle)? Is the individual better-off at
the higher price level of gasoline with the higher income level or the original price of gas and
income?
Solution:
Initially, the consumer is on budget constraint BC1, consuming g1 units of gasoline on
indifference curve I1, where M is the individual's income level and P1 is the price of
gasoline. If only the price of gasoline changes to P2, the horizontal axis intercept of the
budget constraint moves towards the origin. This is illustrated above by a movement to the
budget constraint BC2. On indifference I2, his level of satisfaction is lower than before.
Now, if the individual's income increases just enough so that his original consumption
bundle exactly exhausts his new budget. However, the slope of the budget constraint (BC3)
that runs through his original consumption bundle is steeper due to the higher price of gas.
This also implies that his MRS is less than the ratio of prices. Thus, the individual can
attain a higher level of utility by purchasing less gasoline than g1. The individual is betteroff at higher prices and income than at original levels.
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TEST BANK
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moderate
CHAPTER 3
CONSUMER BEHAVIOR
95. Bobby is a college student who has $500 of income to spend each semester on books and pizzas.
The price of a pizza is $10 and the price of a book is $50. Diagram Bobby's budget constraint.
Now, suppose Bobby's parents buy him a $300 gift certificate each semester that can only be
used to buy books. Diagram Bobby's budget constraint when he has the gift certificate in
addition to his $500 income. Is Bobby better-off with the gift certificates?
Solution:
Without the gift certificate, Bobby's budget constraint is indicated by the line segment from 10
books and 0 pizza to 0 books and 50 pizzas (labeled BC1). With the gift certificate that can only
be used for book purchases, Bobby still cannot afford anymore than 50 pizzas. However, he is
guaranteed 6 books even if he spends all his money on pizza. Since the price of books and pizza
hasn't changed, the slope of his new budget constraint is the same as the slope of the old budget
constraint. The new budget constraint is drawn above as BC2. Note that with the gift certificate,
Bobby has an expanded opportunity set and is guaranteed more of both goods no matter what his
original consumption choice on BC1 was. This implies that Bobby is strictly better-off with the
gift certificate.
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moderate
96. Larry lives with his parents and enjoys listening to jazz. Because of his living arrangements, his
only expense is on jazz music. To earn money to buy new albums, Larry must work. Larry has
16 hours per day he could spend listening to jazz or working. Each hour he works he earns $6.
Each album costs him $12. Diagram Larry's budget constraint for new jazz albums and time
spent listening to jazz. If Larry's parents require him to spend two hours per day doing chores
around the house, what happens to his budget constraint? Does the requirement to do chores
make Larry worse off?
Solution:
85
TEST BANK
SIXTH EDITION
Larry's budget constraints are indicated on the following diagram. Before his parents require
him to do chores, his budget constraint is BC1. After the requirement to do chores, his budget
constraint becomes BC2. Since the requirement to do chores contracts his opportunity set and
we see he no longer may choose an optimal bundle on BC1, we know Larry is strictly worse off.
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
97. Roberta lives alone on a deserted island. She can spend her time gathering coconuts or bananas.
She has 16 hours available each day and can gather 4 coconuts in an hour or 8 bananas in an
hour. Diagram Roberta's budget constraint. Given that Roberta's Marginal Utility of bananas is
always 25 and her Marginal utility of coconuts is always 100, what is her optimal consumption?
One day an individual from a neighboring island arrives by boat and offers to exchange any
number of fruits at a rate of 1 coconut for 1 banana. Diagram Roberta's budget constraint at this
exchange rate assuming she will now spend all her time gathering bananas. Is Roberta better
off? What does she consume?
Solution:
Roberta's initial budget constraint is BC1 on the diagram below. Since Roberta's indifference
curves are always flatter than her budget constraint, Roberta will consume all coconuts. Thus,
she gathers and consumes 64 coconuts. When her neighbor arrives and offers the exchange, her
budget constraint becomes BC2. It is now optimal for her to gather all bananas and exchange
them 1 for 1 with her neighbor for coconuts. This gives her 128 coconuts to consume. This
brings her to the higher indifference curve I2. Roberta is better off.
SECTION 3.4
86
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
98. Tammy and Tad's father has given each of them a debit card and allows each of them to use the
card to spend $500 each month. Tammy and Tad use their $500 to buy only CDs and gasoline.
In February, the price of a CD was $10 and the price of gasoline was $1 per gallon. At these
prices, Tammy purchased 45 CDs and 50 gallons of gas. Ted consumed 20 CDs and 300 gallons
of gas. For the month of March, Tammy and Tad's father lost the records indicating who had
which debit card. From the bank statement in March, their father learned that the price of a CD
was $12 and a gallon of gas cost $0.80. The first debit card was used to purchase 235 gallons of
gas and 26 CDs. The second debit card was used to purchase 265 gallons of gas and 24 CDs.
Using revealed preference theory, identify which card Tammy must possess.
Solution:
From the diagram, we see that point D is revealed preferred to point B. This
implies that Tad would not choose to consume at point B. Thus, we know that Tad
must have consumed at point C and has the second debit card. This means Tammy
has the first debit card.
SECTION 3.5
87
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
99. Jane lives in a dormitory that offers soft drinks and chips for sale in vending machines. Her
utility function is U = 3SC (where S is the number of soft drinks per week and C the number of
bags of chips per week), so her marginal utility of S is 3C and her marginal utility of C is 3S.
Soft drinks are priced at $0.50 each, chips $0.25 per bag.
a. Write an expression for Jane's marginal rate of substitution between
soft drinks and chips.
b. Use the expression generated in part (a) to determine Jane's optimal
mix of soft drinks and chips.
c. If Jane has $5.00 per week to spend on chips and soft drinks, how
many of each should she purchase per week?
Solution:
a.
MRS =
MU S
MU C
MRS =
3C C
=
3S S
b.
The optimal market basket is where
MRS =
PS
PC
Requires =
C .5
=
S .25
C
= 2, C = 2S
S
Jane should buy twice as many chips as soft drinks.
c.
Jane must satisfy her budget constraint as well as optimal mix.
Her budget constraint is:
I = PSS + PCC
where I = income
5.00 = .5S + .25C
But she must also satisfy C = 2S, the optimal mix. Substitute 2S for C into budget constraint
5.00 = .5S + .25(2S)
5 = .5S + .5S
5=S
Buy 5 soft drinks.
Substitute into either expression to obtain C
C = 2S
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CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
C = 2(5)
C = 10
Jane should spend her $5.00 to buy 5 soft drinks and 10 bags of chips.
moderate 100. An individual consumes products X and Y and spends $25 per time period. The prices of the
two goods are $3 per unit for X and $2 per unit for Y. The consumer in this case has a utility
function expressed as:
U(X,Y) = .5XY
MUX = .5Y
MUY = .5X.
a. Express the budget equation mathematically.
b. Determine the values of X and Y that will maximize utility in the
consumption of X and Y.
c. Determine the total utility that will be generated per unit of time for
this individual.
Solution:
a.
The budget line can be expressed as:
I = PXX + PYY
25 = 3X + 2Y
b.
In equilibrium, maximizing utility, the following relationship must hold:
MU X MU Y
=
PX
PY
In equilibrium
(0.5 Y)/3 = (0.5 X)/2
2Y = 3X, Y = (3/2)X
Thus the amount of Y to consume is 3/2 of the amount of X that is consumed. On the budget
line
25 = 3X + 2(
3
X)
2
25 = 3X + 3X = 6X
X = 4.17 units per time period.
Y=
89
3
(4.17) = 6.25 units per time period.
2
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
c.
The total utility is
U(x,y)
= 0.5(4.17)(6.25)
= 13.03 units of utility per time period.
difficult
101. Janice Doe consumes two goods, X and Y. Janice has a utility function given by the
expression:
U = 4X.5Y.5.
So,
MU X =
2Y 0.5
2 X 0.5
and MU Y =
. The current prices of X and Y are 25 and 50,
X 0.5
Y 0.5
respectively. Janice currently has an income of 750 per time period.
a. Write an expression for Janice's budget constraint.
b. Calculate the optimal quantities of X and Y that Janice should choose,
given her budget constraint. Graph your answer.
c. Suppose that the government rations purchases of good X such that
Janice is limited to 10 units of X per time period. Assuming that
Janice chooses to spend her entire income, how much Y will Janice
consume? Construct a diagram that shows the impact of the limited
availability of X. Is Janice satisfying the usual conditions of
consumer equilibrium while the restriction is in effect?
d. Calculate the impact of the ration restriction on Janice's utility.
Solution:
a.
I = PxX + PyY
750 = 25X + 50Y
b.
Optimal Combination:
MRS =
MRS =
PX
PY
MU X 2
=
MU Y 2
Y .5
X .5
X .5
Y .5
Y
X
PX 25 1
=
=
PY 50 2
MRS =
Equating MRS to
PX
:
PY
Y1
1
= , Y= X
X2
2
90
CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
Janice should buy 1/2 as much Y as X.
Recall 750 = 25X + 50Y
Substitute ()X for Y
750 = 25 X + 50(1/2)X
750 = 25X + 25X
750 = 50X
X = 15
Y=(1/2)X
Y = (1/2)(15)
Y = 7.5
Janice should consume 7.5 units of Y and 15 units of X.
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TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
c.
750 = 25X + 50Y
X = 10
750 = 25(10) + 50Y
500 = 50Y
Y = 10
As indicated in the graph below, at Janice's optimal bundle with the restriction,
MU X MU Y
>
. This implies Janice should consume more X to increase utility.
PX
PY
However, the ration restriction prevents her from doing so. Given the restriction,
this is the best Janice can do.
d. Janice's utility without the restriction is: U ( x = 15, y = 7.5 ) = 4 ( 15 )
( 7.5) = 42.43.
0.5
0.5
Janice's utility with the restriction is: U ( x = 10, y = 10 ) = 4 ( 10 ) ( 10 ) = 40. The ration
0.5
0.5
restriction results in a utility loss of 2.43 utils for Janice.
92
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
102. Define the marginal rate of substitution. Using this concept, explain why market basket A is not
utility maximizing while market basket B is utility maximizing.
Solution:
The marginal rate of substitution is the magnitude of the slope of an indifference curve. It is
the maximum amount of one good (clothing) that a consumer is willing to give up to get
another unit of another good (food). In an indifference curve diagram, MRS measures the
subjective value of the good on the horizontal axis in terms of the good on the vertical axis.
In this example, if the slope of the indifference curve through A were, say, 5, the consumer
would be willing to exchange 1 unit of food for 5 units of clothing.
The slope of the budget line, on the other hand, measures the market value of the good on
the horizontal axis in terms of the good on the vertical axis. In this example, the
indifference curve through A is steeper than the budget line, so the consumer's value of
good is greater than the market price. He would be better off if he bought more food.
93
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
103. The local mall has a make-your-own sundae shop. They charge customers 35 cents for each
fresh fruit topping and 25 cents for each processed topping. Barbara is going to make herself a
sundae. The total utility that she receives from each quantity of topping is given by the
following table:
Fresh Fruit Topping
Processed Topping
# of Units Total Utility
# of Units Total Utility
1
10
1
10
2
18
2
20
3
24
3
10
4
28
4
0
5
30
5
-10
6
28
6
-20
7
24
7
-30
8
18
8
-40
9
10
9
-50
10
-6
10
-60
a. What is the marginal utility of the 6th fresh fruit topping?
b. Of the two toppings, which would Barbara purchase first? Explain.
c. If Barbara has $1.55 to spend on her sundae, how many fresh fruit
toppings and processed toppings will she purchase to maximize
utility?
d. If money is no object, how many fresh fruit toppings and processed
toppings will Barbara purchase to maximize utility?
e. Which of the basic assumptions of preferences are violated by
preferences shown in the table above?
Solution:
a.
The marginal utility of the 6th fresh fruit topping is -2 utils (28 utils - 30 utils).
b.
Barbara will purchase the topping that provides the largest marginal utility per dollar spent.
The marginal utility divided by price for the first unit of fresh fruit topping is 10/.35. The
marginal utility divided by price for the first unit of processed topping is 10/.25. Thus the
first topping purchased will be processed (because 10/.25 > 10/.35).
c.
Barbara will continue to purchase toppings, one at a time, until she spends $1.55, by always
selecting the topping that provides the largest marginal utility per dollar spent. Barbara will
purchase 2 processed toppings first, followed by 3 fresh fruit toppings.
d.
If money is no object, Barbara will purchase an additional unit of each topping as long as
the topping provides a positive marginal utility. In this case, 2 processed toppings and 5
fresh fruit toppings.
e.
94
CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
The preferences used in this problem violate the assumption that consumers always prefer
more of a good to less.
moderate
104. If MUa/Pa is greater than MUb/Pb, and the consumer is consuming both goods, the consumer is
not maximizing utility. True or false. Explain.
Solution:
True, when the consumer has maximized utility, the marginal utility per dollar spent on
each good purchased will be equal, and the consumer will be on her budget line. In this
case, the consumer should consume more a and less b.
moderate
105. John consumes two goods, X and Y. The marginal utility of X and the marginal utility of Y
satisfy the following equations:
MUX = Y
MUY = X.
The price of X is $9, and the price of Y is $12.
a. Write an expression for John's MRS.
b. What is the optimal mix between X and Y in John's market basket?
c. John is currently consuming 15 X and 10 Y per time period. Is he
consuming an optimal mix of X and Y?
Solution:
a.
MRS =
MU x Y
=
MU y X
b.
Optimal mix of X and Y:
MRS =
Px
Py
Y9
=
=.75
X 12
John should consume 0.75 times as much Y as X
c.
John's current mix is not optimal. He should consume 0.75 times as much Y as X, rather than
his current 0.67 Y for each X.
95
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
106. Natasha derives utility from attending rock concerts (r) and from colas (c) as follows:
U(c,r) = c.9r.1
The marginal utility of cola (MUc) and the marginal utility of rock concerts (MUr) are given as
follows:
MUc = .9c-.1r.1
MUr = .1c.9r-.9
a. If the price of cola (Pc) is $1 and the price of concert tickets (Pr) is
$30 and Natasha's income is $300, how many colas and tickets
should Natasha buy to maximize utility?
b. Suppose that the promoters of rock concerts require each fan to buy 4
tickets or none at all. Under this constraint and given the prices and
income in (a), how many colas and tickets should Natasha buy to
maximize utility?
c. Is Natasha better off under the conditions in (a) or (b)? Explain your
answer.
Solution:
a.
To maximize utility, Natasha (1) must be on her budget line, and (2) the marginal rate of
substitution must equal the ratio of the prices of the goods. The marginal rate of
substitution is equal to the ratio of the marginal utilities of the goods. Thus:
(1)
(2)
c + 30r = 300
MUc/MUr = (.9c-.1r.1)/(.1c.9r-.9) = Pc/Pr = 1/30
Solving these equations simultaneously for c and r yields c = 270 and r = 1.
b.
Without the 4 ticket constraint, Natasha would prefer to buy just 1 ticket. If required to buy
4 tickets, Natasha would maximize utility by either buying 4 tickets and consuming 180
colas, or by buying zero tickets and consuming 300 colas. The utility function may be used
to determine which is preferred. In this case, Natasha will buy zero tickets and 300 colas.
c.
Natasha prefers (a). Constraining choice never leaves one better off. At best it has no
effect. Otherwise, the addition of a constraint leaves one worse off.
96
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
107. The following table presents Alfred's marginal utility for each good while exhausting his
income. Fill in the remaining column in the table. If the price of tuna is twice the price of
peanut butter, at what consumption bundle in the table is Alfred maximizing his level of
satisfaction? Which commodity bundle entails the largest level of tuna fish consumption?
Bundle
MU of peanut
butter
MU of tuna
A
0.25
2.41
B
0.31
1.50
C
0.42
0.84
D
0.66
Marginal Rate of
Substitution
0.33
Solution:
Bundle
MRS =
MU pb
MU t
MRS =
MU t
MU pb
A
0.10
9.64
B
0.21
4.84
C
0.5
2
D
2
0.5
MU t
P
= t = 2. This implies that commodity
MU pb Ppb
bundle C is the optimal bundle. The bundle that has the highest level of tuna fish
consumption is bundle D as the marginal utility of tuna is the lowest. (Alternatively, the
student could have defined MRS with the two goods reversed. In that case the optimal
bundle occurs where
The optimal bundle occurs where MRS =
MRS = MUpb/MUt = Ppb/Pt = . In either case, the answer is the same.)
97
TEST BANK
SIXTH EDITION
moderate
CHAPTER 3
CONSUMER BEHAVIOR
108. The following table presents Mary's marginal utility for each of the four goods she consumes to
exhaust her income. The price of Good 1 is $1, the price of Good 2 is $2, the price of Good 3 is
$3 and the price of Good 4 is $4. Indicate the consumption bundle in the table that maximizes
Mary's level of utility.
Bundles
Marginal Utilities
Good 1
Good 2
Good 3
Good 4
A
0.21
0.06
1.76
0.59
B
0.22
0.54
0.56
0.18
C
0.17
0.34
0.51
0.68
D
0.20
0.46
0.61
0.27
Solution: In equilibrium, we know that
MU1 MU 2 MU 3 MU 4
=
=
=
. Since P2 = 2 P , we know we need
1
P
P2
P3
P4
1
a bundle such that MU 2 = 2 MU1 . This only occurs at bundle C. In fact, the marginal utility per
dollar across all goods are equivalent for bundle C. Bundle C is the optimal choice.
moderate
109. At commodity bundle A, which consists of only apples and oranges, Annette's marginal utility
per dollar spent on apples is 10 and her marginal utility per dollar spent on oranges is 8.
Diagram a representative budget constraint and indifference curve that that passes through
bundle A given Annette's budget is exhausted at bundle A. Is Annette maximizing utility? Why
or why not? If she is not, what could she do to increase her level of satisfaction?
Solution:
Annette should buy more apples and fewer oranges to increase her level of satisfaction.
98
CHAPTER 3
CONSUMER BEHAVIOR
moderate
TEST BANK
SIXTH EDITION
110. May enjoys spending her free time with her friends at the mall and solving problems from her
microeconomics text. She has 16 hours per week of free time. Diagram May's time constraint.
1
3
4
4
If MU F = 3 P and MU P = 1 F where F is her time spent with friends at the mall and P
4 F
4 P
is her time spent working problems, how much time should May spend at each activity?
Solution:
The time constraint is 16 = F + P.
Since the price of each activity is equivalent, May's optimal choice will be to set the
marginal utilities of each activity to be equal. Doing so will allow us to solve for time spent
with friends as a function of time spent working problems.
1
3
3 P 4 1 F 4
MU F = = = MU P F = 3P. From May's time constraint, we know that
4 F
4 P
16 = F + P. Substituting the optimal choice of F as a function of P into the time constraint
P=4
.
gives us 16 = 4 P
F = 12
SECTION 3.6
moderate
99
111. Suppose the table below lists the price and consumption levels of food and clothing during 1990
and 2000. Calculate a Laspeyres and Paasche index using 1990 as the base year.
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
Prices
Consumption
100
CHAPTER 3
CONSUMER BEHAVIOR
101
TEST BANK
SIXTH EDITION
TEST BANK
SIXTH EDITION
CHAPTER 3
CONSUMER BEHAVIOR
Solution:
The Laspeyres Index is calculated as follows:
C
P F F + P2000 C1990 ( 6.25 ) 100 + (3.35)75 876.25
LI = 2000 1990
=
=
= 1.209.
P F F1990 + P C C1990
725
( 5) 100 + ( 3) 75
1990
1990
The Paasche Index is calculated as follows:
C
P F F + P2000C2000 ( 6.25) 110 + (3.35)87 978.95
PI = 2000 2000
=
=
= 1.207.
P F F2000 + P C C2000
811
( 5) 110 + ( 3) 87
1990
1990
moderate
112. Suppose that a consumer's increase in nominal income from the base year exceeds the inflation
level given by a Laspeyres cost of living index for their level of purchases
Pt F Fb + Pt C Cb Pt F Ft + Pt C Ct
<F
F
. Show that this information implies that the consumer is
C
C
Pb Fb + Pb Cb Pb Fb + Pb Cb
strictly better-off as compared to the base year. (HINT: Use a revealed preference argument)
Solution:
The information given above implies that
P F F + Pt C Cb Pt F Ft + Pt C Ct
I
LI = t F b
<F
= t Pt F Fb + Pt C Cb < Pt F Ft + Pt C Ct . This expression
C
C
Pb Fb + Pb Cb Pb Fb + Pb Cb I b
says that the commodity bundle purchased in the base period is affordable in the new
period. However, the consumer selected a more expensive bundle. Thus, the new
commodity bundle is revealed preferred to the base year commodity bundle.
moderate
113. Suppose that a consumer's increase in nominal income from the base year is exceeded by the
inflation level given by a Paashe cost of living index for their level of purchases
Pt F Ft + Pt C Ct Pt F Ft + Pt C Ct
>F
F
. Show that this information implies that the consumer is strictly
C
C
Pb Ft + Pb Ct Pb Fb + Pb Cb
worse-off as compared to the base year. (HINT: Use a revealed preference argument)
Solution:
The information given above implies that
P F F + Pt C Ct Pt F Ft + Pt C Ct
I
PI = t F t
>F
= t PbF Fb + PbC Cb > PbF Ft + PbC Ct . This expression
C
C
Pb Ft + Pb Ct Pb Fb + Pb Cb I b
says that the commodity bundle purchased in the new period was affordable in the base
period. However, the consumer selected a more expensive bundle in the base year. Thus,
the base year commodity bundle is revealed preferred to the new commodity bundle.
difficult
114. Suppose that a consumer's increase in nominal income from the base year exceeds the inflation
level given by a Paasche cost of living index for their level of purchases
Pt F Ft + Pt C Ct Pt F Ft + Pt C Ct
<F
F
. Is this information enough to imply how the consumer's level
C
C
Pb Ft + Pb Ct Pb Fb + Pb Cb
of well-being has changed? (HINT: Use a revealed preference argument)
102
CHAPTER 3
CONSUMER BEHAVIOR
TEST BANK
SIXTH EDITION
Solution:
There is not enough information to determine the effect on the individual's level of satisfaction.
This can be shown as follows:
PI =
Pt F Ft + Pt C Ct Pt F Ft + Pt C Ct
I
<F
= t PbF Fb + PbC Cb < PbF Ft + PbC Ct .
F
C
C
Pb Ft + Pb Ct Pb Fb + Pb Cb I b
The base year consumption bundle is not revealed preferred to the new commodity bundle.
103