Economics Chapter 10a For Each Of The Following Situations Draw A Diagram Containing Three Of Isabella’s Indifference Curves

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S-159

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Appendix

Consumer Preferences

and Consumer Choice

1. For each of the following situations, draw a diagram containing three of

Isabella’s indifference curves.

a. For Isabella, cars and tires are perfect complements, but in a ratio of 1:4; that

is, for each car, Isabella wants exactly four tires. Be sure to label and number

the axes of your diagram. Place tires on the horizontal axis and cars on the

vertical axis.

b. Isabella gets utility only from her caffeine intake. She can consume Valley

Dew or cola, and Valley Dew contains twice as much caffeine as cola. Be sure

to label and number the axes of your diagram. Place cola on the horizontal

axis and Valley Dew on the vertical axis.

1. Following are Isabella’s indifference curve maps for each of the situations

described.

48120

Quantity

of cars

Quantity of tires

Quantity of

Valley Dew

Quantity of cola

I1I2I3

Solution

S-160 10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE

Quantity

income

Quantity of leisure

1234560

Quantity

Quantity of bindings

Quantity

of soda

Quantity of water

2. Use the four properties of indifference curves for ordinary goods illustrated in

Figure 10–4 to answer the following questions.

a. Can you rank the following two bundles? If so, which property of indifference

curves helps you rank them?

b. Can you rank the following two bundles? If so, which property of indifference

curves helps you rank them?

c. Can you rank the following two bundles? If so, which property of indifference

curves helps you rank them?

d. Suppose you are indifferent between the following two bundles:

10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE S-161

Now compare bundle A and the following bundle:

Bundle C: 7 breakfasts and 7 dinners

Can you rank bundle A and bundle C? If so, which property of indifference

curves helps you rank them? (Hint: It may help if you draw this, placing din-

2. a. Because bundle B has more movie tickets and more cafeteria meals than bun-

dle A, it is preferred. The reason is that more is better.

b. Compared to bundle A, bundle B has the same number of cafeteria meals but

more movie tickets. Again, because more is better, bundle B is preferred.

c. Bundle A has more videos than bundle B, but bundle B has more bags of chips

than bundle A. The “more is better” principle does not help us rank these two

bundles. Without more information, they cannot be ranked.

d. Since we know that you are indifferent between bundle A and bundle B, we

know that they lie on the same indifference curve. Note in the accompany-

ing diagram that bundle C lies on a straight line between bundles A and B.

Since we know that indifference curves for ordinary goods are convex (they

040

Quantity of

breakfasts

Quantity of dinners

3. The four properties of indifference curves for ordinary goods illustrated in

Figure 10–4 rule out certain indifference curves. Determine whether those

general properties allow each of the following indifference curves. If not, state

which of the general principles rules out the curves.

Quantity

of Y

Quantity of X

Solution

S-162 10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE

Quantity

of Y

Quantity of X

Quantity

of Y

Quantity of X

Quantity

of Y

Quantity of X

3. a. These indifference curves cross. One of the properties of indifference curves is

that they never cross. This rules out indifference curves like these.

b. This indifference curve does not get flatter as you move along it to the right;

instead, it gets steeper. The property that indifference curves for ordinary

c. This indifference curve satisfies all four properties of indifference curves for

ordinary goods.

d. This curve has an upward-sloping segment. But such a curve is ruled out by

the principle that more is better. On this indifference curve, there are at least

two bundles that have the same amount of good Y, but one has more of good

Solution

4. Restaurant meals and housing (measured by the number of rooms) are the only

two goods that Neha can buy. She has income of $1,000, and the price of each

room is $100. The relative price of 1 room in terms of restaurant meals is 5.

How many restaurant meals can she buy if she spends all her money on them?

4. The relative price of one room in terms of restaurant meals is the number of

restaurant meals that must be forgone to obtain 1 room. Since 5 restaurant

meals must be forgone to obtain 1 room, the price of a restaurant meal has to be

$100/5 = $20. If Neha spends all of her income on restaurant meals, she can buy

$1,000/$20 = 50 restaurant meals.

(1) Inflation increases the prices of all goods by 20%.

(2) Ina’s income increases from $50,000 to $55,000.

a. Has Ina’s budget line become steeper, less steep, or equally as steep?

b. Has Ina’s budget line shifted outward, inward, or not at all?

5. a. Ina’s budget line is equally as steep. The slope of the budget line is minus the

relative price of one good in terms of another. The relative prices of goods have

not changed: all goods just cost 20% more.

6. Kory has an income of $50, which she can spend on two goods: music albums

and cups of hot chocolate. Both are normal goods for her. Each album costs

$10, and each cup of hot chocolate costs $2. For each of the following situations,

decide whether this is Kory’s optimal consumption bundle. If not, what should

Kory do to achieve her optimal consumption bundle?

a. Kory is considering buying 4 albums and 5 cups of hot chocolate. At that

bundle, her marginal rate of substitution of albums in place of hot chocolate

is 1; that is, she would be willing to forgo only 1 cup of hot chocolate to

acquire 1 album.

6. The relative price of albums in terms of cups of hot chocolate is Palbum/Phot chocolate =

$10/$2 = 5. That is, to get 1 more album, Kory has to give up 5 cups of hot chocolate.

a. This bundle lies on Kory’s budget line: it is a bundle at which she spends all

her income. Kory’s marginal rate of substitution is less than the relative price

of albums. She is willing to exchange only 1 cup of hot chocolate for 1 album.

b. This bundle lies on Kory’s budget line: it is a bundle at which she spends all her

income. Kory’s marginal rate of substitution is MUalbum/MUhot chocolate = 25/5 = 5.

That is, she is willing to exchange 5 cups of hot chocolate for 1 album. Because

the relative price of 1 album is 5 cups of hot chocolate, Kory values albums

equally as much as they cost her. So this is her optimal consumption bundle.

Solution

S-164 10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE

c. At this bundle, the marginal rate of substitution is equal to the relative price,

7. Raul has 4 Cal Ripken and 2 Nolan Ryan baseball cards. The prices of these

baseball cards are $24 for Cal and $12 for Nolan. Raul, however, would be will-

ing to exchange 1 Cal card for 1 Nolan card.

a. What is Raul’s marginal rate of substitution of Cal Ripken in place of Nolan

Ryan baseball cards?

b. Can Raul buy and sell baseball cards to make himself better off? How?

7. a. Raul’s marginal rate of substitution is 1: he is willing to trade only 1 Nolan

Ryan for 1 more Cal Ripken card.

b. Raul’s marginal rate of substitution is MUCal/MUNolan = 1. However, the relative

price of a Cal Ripken card is PCal/PNolan = $24/$12 = 2. Since the marginal rate

of substitution is less than the relative price, Raul can make himself better off

8. Ralph and Lauren are talking about how much they like going to the gym and

how much they like eating out at their favorite restaurant and they regularly do

some of each. A session at the gym costs the same as a meal at the restaurant.

Ralph says that, for his current consumption of gym sessions and restaurant

meals, he values 1 more meal twice as much as he values 1 more session at the

gym. Lauren is studying economics, and she tells him that his current consump–

tion bundle cannot be optimal.

a. Is Lauren right? Why or why not? Draw a diagram of Ralph’s budget line

and the indifference curve that he is on by making his current consumption

choice. Place restaurant meals on the horizontal axis and gym sessions on the

vertical axis.

Solution

8. a. Lauren is right. Since Ralph values one more meal twice as much as he val–

ues one more session at the gym, his marginal utility for meals is twice as

much as his marginal utility for gym sessions. That is, his marginal rate of

substitution of meals in place of gym sessions is MUmeal/MUgym = 2. However,

Quantity

of gym

sessions

Quantity of restaurant meals

Optimal

Slope:

–Pmeal/Pgym = –1

b. Since Ralph’s marginal rate of substitution is greater than the relative price of

a meal, he should consume more meals and fewer gym visits to make himself

9. Sabine can’t tell the difference between Coke and Pepsi—the two taste exactly

the same to her.

a. What is Sabine’s marginal rate of substitution of Coke in place of Pepsi?

b. Draw a few of Sabine’s indifference curves for Coke and Pepsi. Place Coke on

the horizontal axis and Pepsi on the vertical axis.

c. Sabine has $6 to spend on cola this week. Coke costs $1.50 per bottle and Pepsi

costs $1.00. Draw Sabine’s budget line for Coke and Pepsi on the same diagram.

d. What is Sabine’s optimal consumption bundle? Show this on your diagram.

e. If the price of Coke and Pepsi is the same, what combination of Coke and

Pepsi will Sabine buy?

Solution

S-166 10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE

e. If the price of Pepsi and Coke is the same, then the budget line has the same

slope as Sabine’s indifference curves. That is, at any bundle on the budget line,

the relative price rule is true! In that case, we cannot predict what Sabine will

do: any bundle on her budget line would be an optimal choice.

Quantity

of Pepsi

Quantity of Coke

I1I2

BL I3

10. For Norma, both nachos and french fries are normal goods. They are also ordinary

goods for Norma. The price of nachos rises, but the price of french fries remains

unchanged.

a. Can you determine definitively whether she consumes more or fewer nachos?

Explain with a diagram, placing nachos on the horizontal axis and french

10. a. In the accompanying diagram, BL1 is Norma’s original budget line and A is her

optimal consumption bundle. After the increase in the price of nachos, BL2

is her new budget line and C is her new consumption bundle. The movement

from A to B isolates the pure substitution effect of the rise in the relative price

of nachos: at B she consumes fewer nachos and more french fries. The move–

ment from B to C isolates the income effect: she has been made poorer by the

rise in the price of nachos, so she consumes fewer nachos at C than at B. Since

nachos are a normal good, and the income and substitution effect run in the

same direction when the price changes for a normal good, we can say defini-

tively that her consumption of nachos falls in response to the increase in the

price of nachos.

BL2

BLSBL1

Quantity of

ench fries

Quantity of nachos

Solution

10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE S-167

b. We cannot say definitively whether Norma’s consumption of salsa rises or

falls. In the diagram from part a, Norma’s consumption of salsa rises in

response to the increase in the price of nachos: she consumes more salsa at

bundle C than she did at bundle A. Depending on her preferences, however,

it is possible that her consumption of salsa falls as well. This will occur if

BL2BL1

Quantity

of salsa

Quantity of nachos

11. Gus spends his income on gas for his car and food. The government raises the

tax on gas, thereby raising the price of gas. But the government also lowers the

income tax, thereby increasing Gus’s income. And this rise in income is just

enough to place Gus on the same indifference curve as the one he was on before

the price of gas rose. Will Gus buy more, less, or the same amount of gas as

before these changes? Illustrate your answer with a diagram, placing gas on the

11. Gus will buy less gas. As shown in the accompanying diagram, the increase in

the price of gas makes his budget line steeper (the relative price of gas is now

higher). The increase in income shifts his budget line outward so that it is just

tangent to the indifference curve that he was on before the gas price rose. That

BL1

BL2

Quantity of gas

Solution

12. Pam spends her money on bread and Spam, and her indifference curves obey

the four properties of indifference curves for ordinary goods. Suppose that, for

Pam, Spam is an inferior, but not a Giffen, good; bread is a normal good. Bread

costs $2 per loaf, and Spam costs $2 per can. Pam has $20 to spend.

12. a. BL1 in the accompanying diagram is Pam’s budget line. Bundle A, her optimal

choice, lies on indifference curve I1, which slopes downward, has the charac–

teristic convex shape, and does not cross any other indifference curves.

b. Budget line BL2 in the accompanying diagram represents Pam’s budget line

when the price of Spam falls to $1 per can. Point C, which lies on indiffer-

ence curve I2, represents her optimal choice of 7 loaves of bread and 6 cans of

Spam.

Quantity of Spam

13. Katya commutes to work. She can either use public transport or her own car.

Her indifference curves obey the four properties of indifference curves for ordi–

nary goods.

a. Draw Katya’s budget line with car travel on the vertical axis and public transport

on the horizontal axis. Suppose that Katya consumes some of both goods. Draw

an indifference curve that helps you illustrate her optimal consumption bundle.

b. Now the price of public transport falls. Draw Katya’s new budget line.

c. For Katya, public transport is an inferior, but not a Giffen, good. Draw an indif–

ference curve that illustrates her optimal consumption bundle after the price of

public transport has fallen. Is Katya consuming more or less public transport?

Solution

13. a. BL1 in the accompanying diagram shows Katya’s budget line, and the optimal

consumption bundle is labeled A.

b. Katya’s budget line after the price of public transport has fallen is labeled BL2

in the diagram.

c. Katya’s optimal consumption bundle is C. Since public transport is not a

Giffen good, we know that as a result of the price fall, Katya’s consumption of

public transport will increase. (Only if it were a Giffen good would consump–

tion of a good fall as its price falls.)

BL1BLSBL2

Quantity of public transport

14. For Crandall, cheese cubes and crackers are perfect complements: he wants

to consume exactly 1 cheese cube with each cracker. He has $2.40 to spend on

cheese and crackers. One cheese cube costs 20 cents, and 1 cracker costs

10 cents. Draw a diagram, with crackers on the horizontal axis and cheese cubes

on the vertical axis, to answer the following questions.

a. Which bundle will Crandall consume?

b. The price of crackers rises to 20 cents. How many cheese cubes and how many

crackers will Crandall consume?

14. a. Bundle A in the accompanying diagram is Crandall’s optimal consumption

bundle. When cheese cubes cost 20 cents and crackers cost 10 cents, his bud-

get line is BL1. He consumes 8 cheese cubes and 8 crackers.

b. When the price of crackers rises to 20 cents, Crandall’s budget line becomes

Solution

S-170 10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE

goods are perfect complements, they are not substitutable—and so it makes

sense that there is no substitution effect.

Quantity of

cheese cubes

Quantity of crackers

15. Carmen consumes nothing but cafeteria meals and music albums. Her indiffer-

ence curves exhibit the four general properties of indifference curves. Cafeteria

meals cost $5 each, and albums cost $10. Carmen has $50 to spend.

a. Draw Carmen’s budget line and an indifference curve that illustrates her opti-

mal consumption bundle. Place cafeteria meals on the horizontal axis and

albums on the vertical axis. You do not have enough information to know the

specific tangency point, so choose one arbitrarily.

b. Now Carmen’s income rises to $100. Draw her new budget line on the same

diagram, as well as an indifference curve that illustrates her optimal con-

sumption bundle. Assume that cafeteria meals are an inferior good.

c. Can you draw an indifference curve showing that cafeteria meals and albums

are both inferior goods?

15. a. Carmen’s budget line when she has $50 to spend is BL1 in the accompanying

diagram. Her optimal consumption bundle is A, lying on indifference curve I1.

b. Carmen’s budget line when she has $100 to spend is BL2 in the diagram. Her

optimal consumption bundle is bundle B, lying on indifference curve I2. Since

cafeteria meals are an inferior good, this increase in income must reduce

c. It is not possible to draw an indifference curve for which all goods are infe–

rior goods. This is because as your income increases, you have more money

Quantity of cafeteria meals

Solution

16. The Japanese Ministry of Internal Affairs and Communications collects data on

the prices of goods and services in the Ku-area of Tokyo, as well as data on the

average Japanese household’s monthly income. The accompanying table shows

some of this data. (¥ denotes the Japanese currency the yen.)

Year

Price of eggs

(per pack of 10)

Price of tuna

(per 100–gram

portion)

Average

monthly

income

2013 ¥187 ¥392 ¥524,810

2015 231 390 524,585

a. For each of the two years for which you have data, what is the maximum num-

ber of packs of eggs that an average Japanese household could have consumed

each month? The maximum number of 100-gram portions of tuna? In one dia-

16. a. In 2013, the average Japanese household could have consumed a maximum of

¥524,810/¥187 = 2,806 packs of eggs or a maximum of ¥524,810/¥392 = 1,339

portions of tuna. In 2015, the average Japanese household could have con-

Quantity of

tuna

(100-gram portions)

b. In 2013, the relative price of eggs in terms of tuna was ¥187/¥392 = 0.48. In

2015, the relative price of eggs in terms of tuna was ¥231/¥390 = 0.59. In order

for the relative price rule to hold, as the relative price of eggs in terms of tuna

Solution

S-172 10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE

WORK IT OUT Interactive step-by-step help with solving this

problem can be found online.

17. Tyrone is a utility maximizer. His income is $100, which he can spend on

cafeteria meals and on notepads. Each meal costs $5, and each notepad

costs $2. At these prices Tyrone chooses to buy 16 cafeteria meals and

10 notepads.

a. Draw a diagram that shows Tyrone’s choice using an indifference curve

and his budget line, placing notepads on the vertical axis and cafeteria

meals on the horizontal axis. Label the indifference curve I1 and the bud-

get line BL1.

b. The price of notepads falls to $1; the price of cafeteria meals remains

the same. On the same diagram, draw Tyrone’s budget line with the new

prices and label it BLH.

c. Lastly, Tyrone’s income falls to $90. On the same diagram, draw his

budget line with this income and the new prices and label it BL2. Is he

worse off, better off, or equally as well off with these new prices and

lower income than compared to the original prices and higher income?

17. a. Tyrone’s initial optimal bundle of 16 meals and 10 notepads is given by point

A, the point at which I1 and BL1 are tangent. BL1 is found by calculating its

BL1

Quantity of cafeteria meals

b. Given that the price of notepads falls to $1 and the price of meals stays

unchanged at $5, Tyrone’s budget line, BLH, is given by its vertical intercept

($100/$1 = 100) and its horizontal intercept ($100/$5 = 20).

Solution

10 APPENDIX CONSUMER PREFERENCES AND CONSUMER CHOICE S-173

c. Given that the price of notepads drops to $1, the price of meals stays

unchanged at $5, and his income drops to $90, Tyrone’s budget line is BL2.

It is given by its vertical intercept ($90/$1 = 90) and its horizontal intercept

d. Despite having a lower income ($90 instead of $100), Tyrone is better off

because the fall in the price of notepads has made him richer in a real sense.