Krugman2e Solutions CH10

Solution

Solution

The Rational Consumer1. For each of the following situations, decide whether Al has increasing, constant, or

diminishing marginal utility.

a. The more economics classes Al takes, the more he enjoys the subject. And themore classes he takes, the easier each one gets, making him enjoy each additionalclass even more than the one before.

b. Al likes loud music. In fact, according to him, “the louder, the better.” Each timehe turns the volume up a notch, he adds 5 utils to his total utility.

c. Al enjoys watching reruns of the old sitcom Friends. He claims that these episodesare always funny, but he does admit that the more he sees an episode, the lessfunny it gets.

d. Al loves toasted marshmallows. The more he eats, however, the fuller he gets andthe less he enjoys each additional marshmallow. And there is a point at which hebecomes satiated: beyond that point, more marshmallows actually make him feelworse rather than better.

1. a. Al has increasing marginal utility of economics classes. Each additional class addsmore to his total utility than the previous class.

b. Al has constant marginal utility of volume of music. His total utility increases by5 utils for each additional notch of volume, so his marginal utility is constant at 5 utils.

c. Al has diminishing marginal utility of Friends episodes. Although additional episodesincrease his total utility, they do so less and less. That is, his marginal utility declines.

d. Al has diminishing marginal utility of marshmallows. For a certain range, addi-tional marshmallows add to his total utility, so total utility increases. But totalutility increases by less and less. In fact, total utility eventually begins to decline.In other words, his marginal utility becomes smaller and smaller and eventuallybecomes negative.

2. Use the concept of marginal utility to explain the following: Newspaper vendingmachines are designed so that once you have paid for one paper, you could takemore than one paper at a time. But soda vending machines, once you have paid forone soda, dispense only one soda at a time.

2. After you have taken the first newspaper, the marginal utility of the second newspa-per is zero: you don’t learn any more news by having two copies of the same paperinstead of just one. So once you have paid for the vending machine to open, you willtake only one paper. For soda, on the other hand, marginal utility is positive: afteryou have drunk the first soda, the second will still give you more utility. It will giveyou less utility than the first soda—that is, there is diminishing marginal utility—butthe marginal utility of the second soda is still positive. If the vending machineallowed you to take more than one soda at a time after paying for only one, youwould. So the soda vending machine has to be designed to prevent you from takingmore than one soda, and it does so by dispensing only one soda at a time.

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S-142 C H A P T E R 1 0 T H E R AT I O N A L C O N S U M E R

3. Brenda likes to have bagels and coffee for breakfast. The accompanying table showsBrenda’s total utility from various consumption bundles of bagels and coffee.

Suppose Brenda knows she will consume 2 cups of coffee for sure. However, she canchoose to consume different quantities of bagels: she can choose either 0, 1, 2, 3, or4 bagels.

a. Calculate Brenda’s marginal utility from bagels as she goes from consuming 0bagel to 1 bagel, from 1 bagel to 2 bagels, from 2 bagels to 3 bagels, and from 3bagels to 4 bagels.

b. Draw Brenda’s marginal utility curve of bagels. Does Brenda have increasing,diminishing, or constant marginal utility of bagels?

3. a. If Brenda consumes 2 cups of coffee, the consumption bundles that are relevantare those in the accompanying table. The first two columns are the bundles, andthe third column shows the total utility of each bundle. The fourth column calcu-lates her marginal utility of bagels.

Consumption bundleQuantity of Quantity of Total utility Marginal utility

bagels coffee (cups) (utils) per bagel (utils)

0 2 2820

1 2 488

2 2 566

3 2 624

4 2 66

Consumption bundleQuantity of Quantity of Total utility

bagels coffee (cups) (utils)

0 0 0

0 2 28

0 4 40

1 2 48

1 3 54

2 0 28

2 2 56

3 1 54

3 2 62

4 0 40

4 2 66


Solution

b. The accompanying diagram shows Brenda’s marginal utility of bagels. SinceBrenda’s marginal utility curve of bagels slopes downward, she has diminishingmarginal utility of bagels.

4. Brenda, the consumer in Problem 3, now has to make a decision about how manybagels and how much coffee to have for breakfast. She has $8 of income to spend onbagels and coffee. Use the information given in the table in Problem 3 to answer thefollowing questions.

a. Bagels cost $2 each, and coffee costs $2 per cup. Which bundles are on Brenda’sbudget line? For each of these bundles, calculate the level of utility (in utils) thatBrenda enjoys. Which bundle is her optimal bundle?

b. The price of bagels increases to $4, but the price of coffee remains at $2 per cup.Which bundles are now on Brenda’s budget line? For each bundle, calculateBrenda’s level of utility (in utils). Which bundle is her optimal bundle?

c. What do your answers to parts a and b imply about the slope of Brenda’s demandcurve for bagels? Describe the substitution effect and the income effect of thisincrease in the price of bagels, assuming that bagels are a normal good.

4. a. The first two columns in the accompanying table list the bundles that lie onBrenda’s budget line, and the third column shows her total utility from these bun-dles.

Of all the bundles on her budget line, the bundle that contains 2 bagels and 2cups of coffee gives Brenda the highest total utility. So this is her optimal bundle.



0 4 40

1 3 54

2 2 56

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C H A P T E R 1 0 T H E R AT I O N A L C O N S U M E R S-143


Solution

b. The first two columns in the accompanying table list the bundles that lie onBrenda’s budget line, and the third column shows her total utility from these bun-dles.

Of all the bundles on her budget line, the bundle that contains 1 bagel and 2 cupsof coffee gives Brenda the highest utility. So this is her optimal bundle.

c. As the price of bagels increased, Brenda’s consumption fell from 2 bagels to 1bagel, implying that her demand curve for bagels slopes downward. This happensfor two reasons. First, the substitution effect: as the price of bagels increases,bagels become relatively less attractive, so Brenda is likely to substitute coffee inplace of bagels. Second, the income effect: as the price of bagels increases, it is asif Brenda had become poorer—her money now buys fewer goods than before. Sincebagels are a normal good, a reduction in a consumer’s real income results in alower quantity of bagels demanded. The two effects move in the same direction.

5. Bruno can spend his income on two different goods: Beyoncé CDs and notebooks forhis class notes. For each of the following three situations, decide if the given con-sumption bundle is within Bruno’s consumption possibilities. Then decide if it lies onthe budget line or not.

a. CDs cost $10 each, and notebooks cost $2 each. Bruno has income of $60. He isconsidering a consumption bundle containing 3 CDs and 15 notebooks.

b. CDs cost $10 each, and notebooks cost $5 each. Bruno has income of $110. He isconsidering a consumption bundle containing 3 CDs and 10 notebooks.

c. CDs cost $20 each, and notebooks cost $10 each. Bruno has income of $50. He isconsidering a consumption bundle containing 2 CDs and 2 notebooks.

5. a. This consumption bundle costs $10 × 3 + $2 × 15 = $60, which is exactly equal toBruno’s income of $60. So the bundle is within Bruno’s consumption possibilities.And, since he spends all his money, it lies on his budget line.

b. This consumption bundle costs $10 × 3 + $5 × 10 = $80, which is less thanBruno’s income of $110. So the bundle is within Bruno’s consumption possibili-ties. However, since he does not spend all his money, it does not lie on his budgetline; it lies below his budget line.

c. This consumption bundle costs $20 × 2 + $10 × 2 = $60, which is more thanBruno’s income of $50. So the bundle is not within Bruno’s consumption possi-bilities; it lies above his budget line.



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Solution

6. Bruno, the consumer in Problem 5, is best friends with Bernie, who shares his lovefor notebooks and Beyoncé CDs. The accompanying table shows Bernie’s utilitiesfrom notebooks and Beyoncé CDs.

The price of a notebook is $5, the price of a CD is $10, and Bernie has $50 ofincome to spend.

a. Which consumption bundles of notebooks and CDs can Bernie consume if hespends all his income? Illustrate Bernie’s budget line with a diagram, putting note-books on the horizontal axis and CDs on the vertical axis.

b. Calculate the marginal utility of each notebook and the marginal utility of eachCD. Then calculate the marginal utility per dollar spent on notebooks and themarginal utility per dollar spent on CDs.

c. Draw a diagram like Figure 10-4 in which both the marginal utility per dollarspent on notebooks and the marginal utility per dollar spent on CDs are illustrat-ed. Using this diagram and the optimal consumption rule, predict which bundle—from all the bundles on his budget line—Bernie will choose.

6. a. Bernie can consume the following bundles if he spends all his income:

0 notebooks, 5 CDs2 notebooks, 4 CDs4 notebooks, 3 CDs6 notebooks, 2 CDs8 notebooks, 1 CD10 notebooks, 0 CDs

The accompanying diagram shows Bernie’s budget line.

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Utility from Utility from Quantity of notebooks Quantity of CDs notebooks (utils) CDs (utils)

0 0 0 0

2 70 1 80

4 130 2 150

6 180 3 210

8 220 4 260

10 250 5 300



b. The accompanying table shows the marginal utility for each notebook and foreach CD, the marginal utility per dollar spent on notebooks, and the marginalutility per dollar spent on CDs. Note that the utility numbers for notebooks aregiven in increments of 2: for instance, going from 4 notebooks to 6, utilityincreases by 50 utils (from 130 utils to 180 utils). Per notebook, this is a marginalutility of 25 utils.

c. The optimal consumption rule states that the optimal bundle, from all those on aconsumer’s budget line, is the one at which the marginal utility per dollar spenton each good is equal. The accompanying diagram shows the marginal utility perdollar spent on notebooks and the marginal utility per dollar spent on CDs. WhenBernie consumes 4 notebooks and 3 CDs, the marginal utility per dollar spent onnotebooks is the same as the marginal utility per dollar spent on CDs, so this isthe optimal consumption bundle. It is also the only bundle—from all the bundleshe can consume (that is, from all the bundles on his budget line)—for which themarginal utility per dollar is equal for the two goods.

7. For each of the following situations, decide whether the bundle Lakshani is consider-ing optimal or not. If it is not optimal, how could Lakshani improve her overall levelof utility? That is, determine which good she should spend more on and which goodshould she spend less on.

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Utility Marginal Marginal Marginal MarginalQuantity from utility per utility Utility utility utility

of notebooks notebook per dollar Quantity from CDs per CD per dollar notebooks (utils) (utils) (utils) of CDs (utils) (utils) (utils)

0 0 0 035 7 80 8

2 70 1 8030 6 70 7

4 130 2 15025 5 60 6

6 180 3 21020 4 50 5

8 220 4 26015 3 40 4

10 250 5 300



Solution

a. Lakshani has $200 to spend on sneakers and sweaters. Sneakers cost $50 per pair,and sweaters cost $20 each. She is thinking about buying 2 pairs of sneakers and5 sweaters. She tells her friend that the additional utility she would get from thesecond pair of sneakers is the same as the additional utility she would get fromthe fifth sweater.

b. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and eachpencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The lastpen would add five times as much to her total utility as the last pencil.

c. Lakshani has $50 per season to spend on tickets to football games and tickets tosoccer games. Each football ticket costs $10 and each soccer ticket costs $5. She isthinking about buying 3 football tickets and 2 soccer tickets. Her marginal utilityfrom the third football ticket is twice as much as her marginal utility from thesecond soccer ticket.

7. a. This bundle lies on Lakshani’s budget line, but the marginal utility per dollar forsneakers and for sweaters is not equal. The marginal utility per pair of sneakers isequal to her marginal utility per sweater. However, since sneakers cost $50 andsweaters cost only $20 (that is, sneakers are 2.5 times as expensive as sweaters),Lakshani’s marginal utility per dollar spent on sweaters is 2.5 times greater thanher marginal utility per dollar spent on sneakers. That is, she would improve herlevel of utility if she spent more money on sweaters and less on sneakers.

b. This bundle lies on Lakshani’s budget line. The marginal utility per pen is fivetimes as great as the marginal utility per pencil. However, pens are also five timesas expensive as pencils, so her marginal utility per dollar spent on pens is justequal to her marginal utility per dollar spent on pencils. So this is her optimalbundle.

c. Although Lakshani’s marginal utility per dollar spent on soccer tickets is equal toher marginal utility per dollar spent on football tickets, this bundle is not optimal:it does not lie on her budget line. She could buy more of both goods and probablywill. But for a precise answer about how many football tickets and how many soc-cer tickets she will actually buy, we would need more information about her utilityat other consumption bundles.

8. Cal “Cool” Cooper has $200 to spend on cell phones and sunglasses.

a. Each cell phone costs $100 and each pair of sunglasses costs $50. Which bundleslie on Cal’s budget line? Draw a diagram like Figure 10-4 in which both the mar-ginal utility per dollar spent on cell phones and the marginal utility per dollarspent on sunglasses are illustrated. Use this diagram and the optimal consumptionrule to decide how Cal should allocate his money. That is, from all the bundles onhis budget line, which bundle will Cal choose? The accompanying table gives hisutility of cell phones and sunglasses.

Utility from Quantity of Utility from Quantity of cell phones sunglasses sunglasses cell phones (utils) (pairs) (utils)

0 0 0 0

1 400 2 600

2 700 4 700



Solution

b. The price of cell phones falls to $50 each, but the price of sunglasses remains at$50 per pair. Which bundles lie on Cal’s budget line? Draw a diagram like Figure10-4 in which both the marginal utility per dollar spent on cell phones and themarginal utility per dollar spent on sunglasses are illustrated. Use this diagramand the optimal consumption rule to decide how Cal should allocate his money.That is, from all the bundles on his budget line, which bundle will Cal choose?The accompanying table gives his utility of cell phones and sunglasses.

c. How does Cal’s consumption of cell phones change as the price of cell phonesfalls? In words, describe the income effect and the substitution effect of this fallin the price of cell phones, assuming that cell phones are a normal good.

8. a. The following bundles lie on Cal’s budget line:

0 cell phones, 4 pairs of sunglasses1 cell phone, 2 pairs of sunglasses2 cell phones, 0 pairs of sunglasses

Going from 0 cell phones to 1 cell phone, the marginal utility per cell phone is400 utils; that is, the marginal utility per dollar spent on cell phones is 4 utils.Going from 1 cell phone to 2 cell phones, the marginal utility per cell phone is300 utils; that is, the marginal utility per dollar spent on cell phones is 3 utils.

Going from 0 pairs of sunglasses to 2 pairs of sunglasses, the marginal utility perpair is 600/2 = 300 utils; that is, the marginal utility per dollar spent on sunglass-es is 6 utils. Going from 2 pairs of sunglasses to 4 pairs, the marginal utility perpair is 100/2 = 50 utils; that is, the marginal utility per dollar spent on sunglassesis 1 util. The marginal utility per dollar spent on cell phones and the marginalutility per dollar spent on sunglasses are plotted in the accompanying diagram.

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Utility from Quantity of Utility from Quantity of cell phones sunglasses sunglasses cell phones (utils) (pairs) (utils)

0 0 0 0

1 400 1 325

2 700 2 600

3 900 3 825

4 1,000 4 700



Of all the possible bundles Cal could consume (that is, from all the bundles onhis budget line), the bundle that contains 1 cell phone and 2 pairs of sunglasses isoptimal. At that bundle, the marginal utility per dollar spent on cell phones andthe marginal utility per dollar spent on sunglasses are equal. By the optimal con-sumption rule, this is Cal’s optimal consumption bundle.

b. The bundles that lie on Cal’s budget line are:

0 cell phones, 4 pairs of sunglasses1 cell phone, 3 pairs of sunglasses2 cell phones, 2 pairs of sunglasses3 cell phones, 1 pair of sunglasses4 cell phones, 0 pairs of sunglasses

The accompanying table calculates marginal utility per cell phone, marginal utilityper pair of sunglasses, marginal utility per dollar spent on cell phones, and mar-ginal utility per dollar spent on sunglasses.

The accompanying diagram plots the marginal utility per dollar spent on cellphones and the marginal utility per dollar spent on sunglasses.

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Marginal Marginal Marginal Utility utility utility Quantity Utility Marginal utility

Quantity from cell per cell per of from utility per of cell phones phone dollar sunglasses sunglasses per pair dollar phones (utils) (utils) (utils) (pairs) (utils) (utils) (utils)

0 0 0 0400 8 325 6.5

1 400 1 325300 6 275 5.5

2 700 2 600200 4 225 4.5

3 900 3 825100 2 −125 −2.5

4 1,000 4 700



From all the bundles on Cal’s budget line, the marginal utility per dollar spent oncell phones is the same as the marginal utility per dollar spent on sunglasses at 2cell phones and 2 pairs of sunglasses. By the optimal consumption rule, this isCal’s optimal consumption bundle.

c. Cal’s consumption of cell phones increases from 1 to 2 as the price of cell phonesfalls. This is due to two effects. The substitution effect says that as the price of cellphones falls, their opportunity cost falls: Cal now has to give up fewer pairs ofsunglasses for 1 cell phone. This makes cell phones more attractive, and Cal sub-stitutes cell phones in place of sunglasses. The income effect says that as cellphones become cheaper, Cal gets richer in a real sense: his income now buys moregoods. Since cell phones are a normal good, when the purchasing power of Cal’sincome rises, he consumes more cell phones. Both effects contribute to the factthat as the price of cell phones falls, Cal’s consumption of cell phones increases.

9. Damien Matthews is a busy actor. He allocates his free time to watching movies andworking out at the gym. The accompanying table shows his utility from the numberof times per week he watches a movie or goes to the gym.

Damien has 14 hours per week to spend on watching movies and going to the gym.Each movie takes 2 hours and each gym visit takes 2 hours. (Hint: Damien’s freetime is analogous to income he can spend. The hours needed for each activity areanalogous to the price of that activity.)

a. Which bundles of gym visits and movies can Damien consume per week if hespends all his time either going to the gym or watching movies? Draw Damien’sbudget line in a diagram with gym visits on the horizontal axis and movies on thevertical axis.

b. Calculate the marginal utility of each gym visit and the marginal utility of eachmovie. Then calculate the marginal utility per hour spent at the gym and the mar-ginal utility per hour spent watching movies.

c. Draw a diagram like Figure 10-4 in which both the marginal utility per hour spentat the gym and the marginal utility per hour spent watching movies are illustrat-ed. Use this diagram and the optimal consumption rule to decide how Damienshould allocate his time.

Quantity of Utility from Quantity of Utility from gym visits gym visits movies per movies per week (utils) week (utils)

1 100 1 60

2 180 2 110

3 240 3 150

4 280 4 180

5 310 5 190

6 330 6 195

7 340 7 197



Solution9. a. Damien can consume the following bundles if he spends all his time going to thegym and watching movies:

0 gym visits, 7 movies1 gym visit, 6 movies2 gym visits, 5 movies3 gym visits, 4 movies4 gym visits, 3 movies5 gym visits, 2 movies6 gym visits, 1 movie7 gym visits, 0 movies

The accompanying diagram illustrates Damien’s budget line.

b. The accompanying table shows Damien’s marginal utility per gym visit, marginalutility per movie, marginal utility per hour spent on gym visits, and marginal utili-ty per hour spent on movies.

Quantity Utility Marginal Marginal Utility Marginal Marginal of gym from gym utility per utility Quantity from utility utility

visits per visits gym visit per hour of movies movies per movie per hour week (utils) (utils) (utils) per week (utils) (utils) (utils)

1 100 1 6080 40 50 25

2 180 2 11060 30 40 20

3 240 3 15040 20 30 15

4 280 4 18030 15 10 5

5 310 5 19020 10 5 2.5

6 330 6 19510 5 2 1

7 340 7 197

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Solution

Solution

c. The accompanying diagram shows Damien’s marginal utility per hour spent ongym visits and his marginal utility per hour spent watching movies. Of all thebundles on his budget line, the bundle containing 4 gym visits and 3 movies isoptimal: this is the bundle at which the marginal utility per hour spent in the gymis equal to the marginal utility per hour spent watching movies.

10. Anna Jenniferson is an actress, who currently spends several hours each week watchingmovies and going to the gym. On the set of a new movie she meets Damien, the con-sumer in Problem 9. She tells him that she likes watching movies much more thangoing to the gym. In fact, she says that if she had to give up seeing 1 movie, she wouldneed to go to the gym twice to make up for the loss in utility from not seeing themovie. A movie takes 2 hours, and a gym visit also lasts 2 hours. Damien tells Annathat she is not watching enough movies. Is he right?

10. Damien is right. Since Anna’s marginal utility for the last movie is twice as large asthe marginal utility for a gym visit, but gym visits and movies “cost” the same interms of hours spent, Anna’s marginal utility per hour spent on movies is twice aslarge as her marginal utility per hour spent on gym visits. So she should spend moreof her time going to movies and less going to the gym.

11. Sven is a poor student who covers most of his dietary needs by eating cheap breakfastcereal, since it contains most of the important vitamins. As the price of cerealincreases, he decides to buy even less of other foods and even more breakfast cerealto maintain his intake of important nutrients. This makes breakfast cereal a Giffengood for Sven. Describe in words the substitution effect and the income effect fromthis increase in the price of cereal. In which direction does each effect move, andwhy? What does this imply for the slope of Sven’s demand curve for cereal?

11. As its price increases, cereal becomes relatively less attractive compared to othergoods: its opportunity cost is now higher. As a result, Sven will tend to substituteaway from cereal. This is the substitution effect. But as the price of cereal increases,the purchasing power of Sven’s income falls: in a real sense, Sven is now poorer.Since he spends a large fraction of his income on cereal, this effect is large. So Svenbuys less of other foods, since they are normal goods. However, he buys more cereal,so cereal must be an inferior good for him. This is the income effect. In fact, this

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Solution

Solution

effect is so strong that it outweighs the substitution effect: with both effects takentogether, Sven consumes more cereal. For a Giffen good, the income effect worksopposite to and is stronger than the substitution effect. Since Sven’s consumption ofcereal rises as the price of cereal rises, his demand curve slopes upward.

12. In each of the following situations, describe the substitution effect and, if it is signif-icant, the income effect. In which direction does each of these effects move? Why?

a. Ed spends a large portion of his income on his children’s education. Becausetuition fees rise, one of his children has to withdraw from college.

b. Homer spends much of his monthly income on home mortgage payments. Theinterest on his adjustable-rate mortgage falls, lowering his mortgage payments,and Homer decides to move to a larger house.

c. Pam thinks that Spam is an inferior good. Yet as the price of Spam rises, shedecides to buy less of it.

12. a. As tuition fees rise, college education becomes relatively more expensive compared toother goods. So Ed decides to substitute away from college education and towardother goods. This is the substitution effect. Since tuition takes up a large portion ofhis income, the income effect will also be significant. As tuition rises, Ed, in a realsense, becomes poorer: the purchasing power of his income falls. As a result, he willbuy less of all normal goods. College education is a normal good, so the income effectalso moves in the direction of less college education. The effects reinforce each other.

b. As mortgage payments decrease, large homes become cheaper compared to othergoods. So Homer will substitute toward buying a larger home. This is the substitu-tion effect. Since he spends much of his income on mortgage payments, the fall inmortgage rates also increases his income in a real sense: the purchasing power ofhis income is now higher. This implies that Homer will now buy more of all nor-mal goods. Housing is a normal good, so the income effect will also move in thedirection of more housing. The effects reinforce each other.

c. As its price rises, Spam becomes relatively more expensive compared to othergoods. So Pam will substitute away from Spam and toward other goods. This is thesubstitution effect. Spam probably does not account for a large portion of Pam’sincome, so the income effect is likely to be negligible. However, we do know thatsince Spam is an inferior good, the income effect would make Pam want to con-sume more of it. As the price of Spam rises, Pam is now, in a real sense, poorer:her income buys fewer goods. Since she is now poorer, she will buy more inferiorgoods—that is, the income effect will lead her to buy more Spam. However, weknow that overall she buys less Spam as its price rises, so the substitution effectoutweighs the income effect.

13. Restaurant meals and housing (measured in the number of rooms) are the only twogoods that Neha buys. She has income of $1,000. Initially, she buys a consumptionbundle such that she spends exactly half her income on restaurant meals and theother half of her income on housing. Then her income increases by 50%, but theprice of restaurant meals increases by 100% (it doubles). The price of housingremains the same. After these changes, if she wanted to, could Neha still buy thesame consumption bundle as before?

13. Yes, she could. If she spends equally as much money on housing as before, she getsthe same number of rooms as before (the price of housing has not changed).However, she now has twice as much money left over as before to spend on restau-rant meals (her income increased by 50%). But the price of restaurant meals hasdoubled also, so she could still buy the same quantity of restaurant meals as before.



Solution

Solution

Solution

14. Scott finds that the higher the price of orange juice, the more money he spends onorange juice. Does that mean that Scott has discovered a Giffen good?

14. Scott has not necessarily discovered a Giffen good. For a good to be a Giffen good,the quantity demanded of the good has to increase as its price rises. However, Scotthas only found that the amount of money he spends on purchases of orange juicehas increased as its price rises. For instance, suppose the price of orange juice were torise from $5 per half-gallon to $10 per half-gallon, and as a result Scott reduces thequantity of orange juice demanded from 3 half-gallons to 2 half-gallons. This meansthat orange juice is not a Giffen good, since the quantity demanded decreases as theprice rises. However, Scott’s spending on orange juice would have increased from $5 ×3 = $15 to $10 × 2 = $20. So an increase in spending on a good as its price rises neednot necessarily imply that the good is a Giffen good.

15. Margo’s marginal utility of one dance lesson is 100 utils per lesson. Her marginalutility of a new pair of dance shoes is 300 utils per pair. The price of a dance lessonis $50 per lesson. She currently spends all her income, and she buys her optimal con-sumption bundle. What is the price of a pair of dance shoes?

15. Since Margo buys her optimal consumption bundle, the marginal utility per dollarspent on dance lessons must be equal to the marginal utility per dollar spent ondance shoes. Here, the marginal utility per dollar spent on dance lessons is 100 utilsper lesson/$50 per lesson = 2 utils per dollar. The marginal utility per dollar spent ondance shoes therefore has to equal 2 utils per dollar. Since the marginal utility of apair of dance shoes is 300 utils per pair, the price of a pair of shoes has to be $150per pair, so that 300 utils per pair/$150 per pair = 2 utils per dollar.

16. According to data from the U.S. Department of Energy, the average retail price ofregular gasoline rose from $0.93 in 1985 to $1.81 in 2005, a 95% increase.

a. Other things equal, describe the effect of this price increase on the quantity ofgasoline demanded. In your explanation, make use of the optimal consumptionrule and describe income and substitution effects.

In fact, however, other things were not equal. Over the same time period, the pricesof other goods and services rose as well. According to data from the Bureau of LaborStatistics, the overall price of a bundle of goods and services consumed by an averageconsumer rose by 82%.

b. Taking into account the rise in the price of gasoline and in overall prices, otherthings equal, describe the effect on the quantity of gasoline demanded.

However, this is not the end of the story. Between 1985 and 2005, the typical con-sumer’s nominal income increased, too: the U.S. Census Bureau reports that U.S.median household nominal income rose from $23,618 in 1985 to $46,326 in 2005,an increase of 96%.

c. Taking into account the rise in the price of gasoline, in overall prices, and in con-sumers’ incomes, describe the effect on the quantity of gasoline demanded.

16. a. The optimal consumption rule states that, at the optimal consumption bundle,the marginal utility per dollar spent on gasoline is equal to the marginal utility perdollar spent on other goods and services. As the price of gasoline rises, otherthings equal, the marginal utility per dollar spent on gasoline falls. Now the mar-ginal utility per dollar spent on gasoline is less than the marginal utility per dollarspent on other goods and services. But there is a simple way for the consumer to



make him- or herself better off: spend less on gasoline and more on other goodsand services. This raises the marginal utility of gasoline, which raises the marginalutility per dollar spent on gasoline; and it lowers the marginal utility of othergoods and services, which lowers the marginal utility per dollar spent on othergoods and services. This continues until the marginal utility per dollar spent ongasoline is again equal to the marginal utility per dollar spent on other goods andservices. That is, the quantity of gasoline demanded falls.

Almost certainly, the whole story is captured by the substitution effect: as theprice of gasoline rises, most consumers substitute other goods and services inplace of gasoline. Only for consumers for whom spending on gasoline makes up amajor portion of their total spending will there be a noticeable income effect: asthe price of gasoline rises, they will be made poorer. Since gasoline is a normalgood, they will consume less gasoline, further reducing the quantity of gasolinedemanded.

b. First, if all prices had increased by the same percentage, the effect would be thesame as if all prices had remained unchanged but the consumer’s income had fall-en. In other words, the quantity demanded of all normal goods, such as gasoline,would fall.

However, the price of gasoline rose slightly more than the prices of other goodsand services. So it is likely that there would still be a substitution effect at work,leading consumers to consume less gasoline.

c. First, consider the following: If income had increased by the same percentage asthe prices of all goods and services, then consumers’ optimal consumption bundlewould remain unchanged. In fact, however, income increased by more (96%)than did overall prices (only 82%). As a result, consumers would be likely to con-sume more of all normal goods, including gasoline. Finally, adding in the fact thatthe price of gasoline increased by more (95%) than did the prices of other goodsand services (82%), there would still be some substitution effect at work, leadingconsumers to substitute other goods and services in place of gasoline. So the over-all effect on the quantity of gasoline demanded would, theoretically at least, beinconclusive.

(If you would like to know, the quantity of regular gasoline bought and sold inthe United States has, in fact, increased from 149 million gallons per day in 1985to 316 million gallons per day in 2005, according to data from the U.S.Department of Energy.)



Krugman2e Solutions CH10

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