Download chapter 5 consumer choice answers to online review questions

CHAPTER 5
CONSUMER CHOICE
ANSWERS TO ONLINE REVIEW QUESTIONS
1. The prices of the two goods and the consumer’s income are always assumed constant
along a budget line.
2. A change in income will shift the budget line in a parallel fashion—increases in
income shift the budget line outward and away from the origin, decreases shift it
inward and nearer the origin. Changes in income alone do not affect the budget line’s
slope.
A change in one or both prices will rotate the budget line and change its slope. For
example, a decrease in the price of the good measured on the horizontal axis will
cause a rotation of the budget line around its vertical axis intercept; the rotation will
result in a horizontal intercept farther to the right.
3. [Using the Marginal Utility Approach] Total and marginal are often confused.
However, marginal always refers to the change in the total that results from one more
of something, e.g., one more unit of consumption or production. Marginal utility, for
example, represents the change in total utility from the consumption of one more unit
of a good.
4. [Using the Marginal Utility Approach] The law of diminishing marginal utility states
that marginal utility declines as more of a good is consumed. It is a reasonable
assumption for most goods: The more of a good one consumes, the less additional
satisfaction is derived from each additional unit.
There are, indeed, exceptions to the law. One example might be found among
collectors. As the collection becomes more complete, the marginal utility of additional
paintings might actually increase.
Marginal utility would be negative for any good that a consumer dislikes. An
additional unit consumed in this case would decrease utility. One example is garbage.
5. “Logically consistent” preferences are transitive. For example, if A is preferred to B,
and B to C, then A should be preferred to C. In addition, economists assume that a
consumer can make choices, i.e., she can look at two alternatives and compare them to
see whether one is preferred to another, or whether she is completely indifferent
between them. When a consumer can make comparisons, and when all comparisons
are logically consistent, the consumer’s preferences are said to be rational. Finally,
two assumptions in addition to rationality are (1) that marginal utility is positive
(“more is better”) and (2) that marginal utility diminishes as more of a good is
consumed.
6. The statement makes an error. Rationality does not mean that individuals make
choices that are “sensible” to others. Preferences are called rational if (1) they satisfy
the logical consistency requirement detailed in question 5, and if (2) the consumer can
compare any two combinations of goods and state either that he/she is indifferent
between them or that he/she prefers one of them.
7. [Marginal Utility Analysis answer] A consumer maximizes utility subject to a budget
constraint when she or he consumes that combination of goods at which marginal
utility per dollar is the same for all goods consumed. Hence, for any two goods X and
Y,
MU X
MU Y
=
.
PX
PY
[Indifference Curve Analysis answer] A consumer maximizes utility subject to a
budget constraint when she or he consumes that combination of goods at which the
marginal rate of substitution between those goods equals the slope of the budget line at
that combination. Hence, for any two goods X and Y,
MRSY,X = Px/Py
8. A change in the price of one good relative to another gives rise to the substitution
effect—the tendency of consumers to substitute more of the good made relatively
cheaper by the price decline for the good that is now relatively more expensive.
Hence, the substitution effect always works to increase the quantity demanded of a
good whose price has decreased. In this sense, the substitution effect is always
consistent with the law of demand.
The income effect is the change in quantity demanded that arises because of the
change in purchasing power caused by a price change. For example, if the price of a
good declines, a given income will “go farther”—as if the consumer has more income.
Any given price change sets in motion both income and substitution effects. If a
good is normal, these effects reinforce each other to increase quantity demanded, in
the case of a price decrease, or decrease quantity demanded when price increases.
When a good is inferior, the income and substitution effects work in opposite
directions. The question then becomes, Which effect is stronger? If the substitution
effect dominates, the law of demand will still hold; but if the income effect is stronger,
a price increase will actually cause quantity demanded to increase, in violation of the
law of demand.
9. False. As explained in the answer to Question 8, as long as the substitution effect is
stronger than the income effect, the demand curve for an inferior good will still be
downward sloping. Only when the good is inferior and the income effect dominates
will the demand curve have a positive slope.
10. The market demand curve for a particular good is found as the horizontal sum of the
demand curves of all consumers in the market for the good. Each individual demand is
found by varying the price of the good and observing how the optimal quantity of a
good changes as the consumer’s budget line rotates outward or inward.
PROBLEM SET
Novels
1. a.
Original budget line
15
Budget line after
PCD ↑ to $10
12
20
CDs
b.
2. [Using the Marginal Utility Approach] No, he is not maximizing utility. For each dollar
spent on novels, Parvez gets 5 units of utility; for each dollar’s worth of CDs, only 4.
He should spend less of his budget on CDs and more on novels. As he does so, the
marginal utility of CDs will rise and the marginal utility of novels will fall, until the
ratio of marginal utility to price is the same for both goods.
3. [Using the Marginal Utility Approach] Anita’s utility is maximized where
MU pizza MU Pepsi
=
,
Ppizza
PPepsi
or, given the prices in the problem, she should consume slices and cans such that
MU pizza = 2MU Pepsi . This will be satisfied at 8 cans of Pepsi (the eighth can gives her
additional utility of 10) and 5 slices of pizza (the marginal utility of the fifth slice is
20).
4. a. Recall that the market demand curve is simply the horizontal sum (summed over
quantities at each price) of the individual demand curves. In this case, then, the
market demand schedule is:
Price
$5.00
$4.00
$3.00
D
$2.00
$1.00
3
5
7
Price
$5.00
$4.50
$4.00
$3.50
9
Quantity
Qty. Demanded
3
5
7
9
b. The three consumers have different demand schedules because they have different
preferences for the cereal.
5.
a. 75,000 bottles. This is 1000 × (100 – 25($1)) = 1000 × 75.
b. 50,000 bottles. This is 1000 × (100 – 25($2)) = 1000 × 50.
c. QD = 100,000 – 25,000P
6. An increase in income always decreases demand for an inferior good. Hence, the
demand curve would behave as below, with new (post-income increase) demand
shown by D2.
Price
S1
P1
P2
D1
D2
Q2
Q1
Quantity
7. a. Since the price of inputs is a determinant of the supply curve, an increase in paper
prices will shift the firm’s supply curve to the left, increasing the equilibrium price
for its books to P2 as shown below:
Price
S2
S1
P2
P1
D1
Q2
Q1
Quantity
b. By the substitution effect, the increased price for Pulp Fiction’s books will cause
consumers to substitute other goods (perhaps the publications of other publishers)
for Pulp’s books, decreasing quantity demanded. Assuming Pulp’s novels are
normal goods for most consumers, the income effect acts to reinforce the
substitution effect, decreasing quantity demanded. (If Pulp’s novels are inferior
goods, then the income effect will work against the substitution effect—tending to
increase quantity demanded while the substitution effect decreases quantity
demanded.)
8. False. The price increase generates both income and substitution effects. With an
inferior good, both effects work against each other. While it is possible for the income
effect to dominate (a case that would, indeed, violate the law of demand), this would
be extremely rare. More commonly, the substitution effect dominates, so the good
would obey the law of demand.
9.
a. Violates the assumption of rational preferences, since the condition that Joseph
will be able to state that he prefers one choice over the other, or that he is
indifferent between the two, is not fulfilled.
b. Does not violate the assumption of rational preferences. Brenda can state her
preference for mustard.
c. Violates the assumption of rational preferences, since the condition that Brewster’s
preferences are logically consistent is not fulfilled.
10. [Using the Indifference Curve Approach]
a.
b.
c.
11.
[Using the Marginal Utility Approach]
Income = $300|
Concerts at $30 each
Movies at $10 each
(1)
(2)
(3)
(4)
(5)
(6)
Marginal
Marginal
Number of Marginal
Marginal
Number of
Utility from
Utility per
Movies
Utility
Utility per
Concerts per
Last
Dollar Spent per Month from Last
Dollar
Month
Concert
on Last
Movie
Spent on
Concert
Last
Movie
3
600
20
21
4
0.4
4
450
15
18
6
0.6
5
360
12
15
10
1
6
300
10
12
20
2
7
180
6
9
30
3
8
150
5
6
35
3.5
9
120
4
3
40
4
Max’s utility maximizing combination is 9 concerts and 3 movies. This corresponds to
point H’ in Figure 5.
12. [Using the Marginal Utility Approach]
Income = $300 per month|
Concerts at $30 each
Movies at $10 each
(1)
(2)
(3)
(4)
(5)
(6)
Number of
Marginal
Marginal
Number of Marginal
Marginal
Concerts per Utility from
Utility per
Movies
Utility
Utility per
Month
Last
Dollar Spent per Month from Last
Dollar
Concert
on Last
Movie
Spent on
Concert
Last
Movie
1
450
15
27
150
15
2
390
13
24
175
17.5
3
300
10
21
200
20
4
225
7.5
18
225
22.5
5
180
6
15
250
25
6
150
5
12
275
27.5
7
90
3
9
300
30
8
75
2.5
6
325
32.5
9
60
2
3
350
35
Max’s utility maximizing combination is 1 concert and 27 movies. This corresponds to
point H” in Figure 5.
13. [Using the Indifference Curve Approach]
a.
The original equilibrium is at point A.
b. The new budget line is BL2. The new tangency must occur at a point with MORE
THAN 25 pounds of potatoes, for instance, at point B. If potatoes are inferior, then
Cameron will consume more potatoes and fewer steaks than at his original
position.
14. [Using the Indifference Curve Approach]
a.
The original equilibrium is at point A.
b. The new budget line is BL2. The new tangency must occur at a point where
Rafaella is consuming MORE THAN 4 pounds of chicken, and LESS than 10
eggs, for instance, at point B.
15.
[Using the Indifference Curve Approach]
a.
The original equilibrium is at point A.
b. A new tangency will occur at a point where she consumes more clothes and less
food, such as point B.
c. A new tangency will occur at a point where she consumes fewer clothes and more
food, such as point C.
16.
Income = $150 per month
Concerts at $5 each
Movies at $10 each
Number of
Marginal
Marginal
Number of
Marginal
Marginal
concerts per utility from
utility per
movies per
utility from
utility per
month
last concert
dollar spent
month
last movie
dollar spent
on last
on last
concert
movie
3
600
120
4
450
90
5
360
72
6
300
60
7
180
36
8
150
30
12
100
10
9
100
20
11
120
12
10
67.5
13.50
10
135
13.50
From this table, the marginal utility per dollar spent on last concert is equal to the
marginal utility per dollar spend on the last movie when Max consumes 10 concerts
and 10 movies per month. This does, indeed, demonstrate that point K on Figure 6 is
optimal.
MORE CHALLENGING QUESTIONS
17. a. Current consumption is at A, where 2,500 units of food and 5,000 units of shelter
are consumed. The Smiths spend $5000 = $2 x 2500 on food and $5000 = $1 x
5000 on shelter.
Food (in units)
7,500
B''
5,000
A
2,500
B'
5,000
10,000
7,500
Shelter
(in sq ft/ year)
b. When the price of housing rises to $2 per square foot, the new budget line is given
by the line marked B′ in the figure above. The Smiths cannot continue to consume
at point A.
c. The income supplement shifts the budget constraint rightward to the line marked
B′′. The original consumption levels, represented by point A, is again affordable.
d. No, the family will not necessarily return to point A. The utility-maximizing
consumption choice will be somewhere on the new budget line, B′′. But all the
points on this budget line below A could have been reached with the original prices
and income, and were not chosen before, so they must be less preferred than point
A. They will not be chosen now. All the points above point A are newly available.
Any of these points might be preferred to point A, and could be chosen. (If you use
the indifference curve approach, you can actually show that point A will never be
chosen after the cash grant. To do so, draw an indifference curve tangent to point
A, reflecting the best initial choice before the price change and the cash grant.
Then, after the price change and the cash grant, the best choice is the point of
tangency between some new indifference curve and budget line B”. This new
tangency cannot occur at point A, as you can see by trying to draw it.)
18. Nothing would happen to consumer choices in this situation. If prices alone were
increasing, then the budget line would shift towards the origin. However, in this example,
wages are increasing by enough to keep the combination of goods and services the
consumer can afford unchanged.
19. [Using the Indifference Curve Approach]
a.
b.
c.
20.
[Using the Indifference Curve Approach]