The Rational Consumer Chapter 10 1. For each of the following situations, decide whether Al has diminishing marginal utility. Explain. a. The more economics classes Al takes, the more he enjoys the subject. And the more classes he takes, the easier each one gets, making him enjoy each additional class even more than the one before. b. Al likes loud music. In fact, according to him, “the louder, the better.” Each time he turns the volume up a notch, he adds 5 utils to his total utility. c. Al enjoys watching reruns of the X Files. He claims that these episodes are always exciting, but he does admit that the more times he sees an episode, the less exciting it gets. d. Al loves toasted marshmallows. The more he eats, however, the fuller he gets and the less he enjoys each additional marshmallow. And there is a point at which he becomes satiated: beyond that point, more marshmallows actually make him feel worse rather than better. 1. a. Al’s marginal utility of economics classes increases as he takes an additional class since he enjoys each class more than the one before. Therefore, he does not have diminishing marginal utility. b. Al’s marginal utility is the same for each additional notch of volume of music, hence he does not have diminishing marginal utility. c. Al has diminishing marginal utility of X Files episodes. Although additional episodes increase 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, additional marshmallows add to his total utility, so total utility increases. But total utility increases by less and less. In fact, total utility eventually begins to decline. In other words, his marginal utility becomes smaller and smaller and eventually becomes negative. 2. Use the concept of marginal utility to explain the following: Newspaper vending machines are designed so that once you have paid for one paper, you could take more than one paper at a time. But soda vending machines, once you have paid for one soda, dispense only one soda at a time. 2. After you have taken the first newspaper, the marginal utility of the second newspaper is zero: you don’t learn any more news by having two copies of the same paper instead of just one. So once you have paid for the vending machine to open, you will take only one paper. For soda, on the other hand, marginal utility is positive: after you have drunk the first soda, the second will still give you more utility. It will give you less additional utility than the first soda—that is, there is diminishing marginal utility—but the marginal utility of the second soda is still positive. If the vending machine allowed you to take more than one soda at a time after paying for only one, you would. So the soda vending machine has to be designed to prevent you from taking more than one soda, and it does so by dispensing only one soda at a time. Chapter 10 3. Bruno can spend his income on two different goods: smoothies and energy bars. For each of the following three situations, decide if the given consumption bundle is within Bruno’s consumption possibilities. Then decide if it lies on the budget line or not. a. Smoothies cost $2 each, and energy bars cost $3 each. Bruno has income of $60. He is considering a consumption bundle containing 15 smoothies and 10 energy bars. b. Smoothies cost $2 each, and energy bars cost $5 each. Bruno has income of $110. He is considering a consumption bundle containing 20 smoothies and 10 energy bars. c. Smoothies cost $3 each, and energy bars cost $10 each. Bruno has income of $50. He is considering a consumption bundle containing 10 smoothies and 3 energy bars. 3. a. This consumption bundle costs $2 × 15 + $3 × 10 = $60, which is exactly equal to Bruno’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 $2 × 20 + $5 × 10 = $90, which is less than Bruno’s income of $110. So the bundle is within Bruno’s consumption possibilities. However, since he does not spend all his money, it does not lie on his budget line; it lies below his budget line. c. This consumption bundle costs $3 × 10 = $10 × 3 = $60, which is more than Bruno’s income of $50. So the bundle is not within Bruno’s consumption possibilities; it lies above his budget line. 4. Bruno, the consumer in Problem 3, is best friends with Bernie, who shares his love for energy bars and smoothies. The accompanying table shows Bernie’s utilities from smoothies and energy bars. Quantity of smoothies 0 Utility from smoothies (utils) 0 Quantity of energy bars Utility from energy bars (utils) 0 0 1 32 2 28 2 60 4 52 3 84 6 72 4 104 8 88 5 120 10 100 The price of an energy bar is $2, the price of a smoothie is $4, and Bernie has $20 of income to spend. a. Which consumption bundles of energy bars and smoothies can Bernie consume if he spends all his income? Illustrate Bernie’s budget line with a diagram, putting smoothies on the horizontal axis and energy bars on the vertical axis. b. Calculate the marginal utility of each energy bar and the marginal utility of each smoothie. Then calculate the marginal utility per dollar spent on energy bars and the marginal utility per dollar spent on smoothies. c. Draw a diagram like Figure 10-4 in which both the marginal utility per dollar spent on energy bars and the marginal utility per dollar spent on smoothies are illustrated. Draw the quantity of energy bars increasing from left to right, and the quantity of smoothies increasing from right to left. Using this diagram and the utility-maximizing principle of marginal analysis, predict which bundle—from all the bundles on his budget line—Bernie will choose. 4. a. Bernie can consume the following bundles if he spends all his income: 0 smoothies, 5 energy bars 2 smoothies, 4 energy bars 4 smoothies, 3 energy bars 6 smoothies, 2 energy bars 8 smoothies, 1 energy bar 10 smoothies, 0 energy bars The accompanying diagram shows Bernie’s budget line. Quantity of energy bars 10 9 8 7 6 5 4 3 2 1 0 BL 1 2 3 4 5 6 7 8 9 10 Quantity of smoothies b. The accompanying table shows the marginal utility for each energy bar and for each smoothie, the marginal utility per dollar spent on energy bars, and the marginal utility per dollar spent on smoothies. Note that the utility numbers for energy bars are given in increments of 2: for instance, going from 4 energy bars to 6, utility increases by 24 utils (from 60 utils to 84 utils). Per energy bar, this is a marginal utility of 12 utils. Marginal Utility Marginal Utility Marginal utility from Marginal utility Quantity from utility per per Quantity energy utility per per of smoothies smoothie dollar of energy bars energy bar dollar smoothies (utils) (utils) (utils/$) bars (utils) (utils) (utils/$) 0 0 32 1 32 2 60 3 84 4 104 5 120 28 24 20 16 0 0 2 28 4 52 6 72 8 88 10 100 8 7 6 5 4 14 7 12 6 10 5 8 4 6 3 c. The utility-maximizing principle of marginal analysis states that the optimal bundle, from all those on a consumer’s budget line, is the one at which the marginal utility per dollar spent on each good is equal. The accompanying diagram shows the marginal utility per dollar spent on energy bars and the marginal utility per dollar spent on smoothies. When Bernie consumes 4 energy bars and 3 smoothies, the marginal utility per dollar spent on energy bars is the same as the marginal utility per dollar spent on smoothies, so this is the optimal consumption bundle. It is also the only bundle—from all the bundles he can consume and that are on his budget line—for which the marginal utility per dollar is equal for the two goods. Marginal utility per dollar (utils/$) 8 Optimal choice 7 MUs /Ps 6 5 4 3 MUr /Pr 2 1 0 2 4 6 8 Quantity of energy bars 10 5 4 3 2 1 Quantity of smoothies 0 5. For each of the following situations, decide whether the bundle Lakshani is considering is optimal or not. If it is not optimal, how could Lakshani improve her overall level of utility? That is, determine which good she should spend more on and which good she should spend less on. 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 and 5 sweaters. She tells her friend that the additional utility she would get from the second pair of sneakers is the same as the additional utility she would get from the fifth sweater. b. Lakshani has $5 to spend on pens and pencils. Each pen costs $0.50 and each pencil costs $0.10. She is thinking about buying 6 pens and 20 pencils. The last pen 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 to soccer games. Each football ticket costs $10 and each soccer ticket costs $5. She is thinking about buying 3 football tickets and 2 soccer tickets. Her marginal utility from the third football ticket is twice as much as her marginal utility from the second soccer ticket. 5. a. This bundle lies on Lakshani’s budget line, but the marginal utility per dollar for sneakers and for sweaters is not equal. The marginal utility per pair of sneakers is equal to her marginal utility per sweater. However, since sneakers cost $50 and sweaters 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 than her marginal utility per dollar spent on sneakers. That is, she would improve her level 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 five times as great as the marginal utility per pencil. However, pens are also five times as expensive as pencils, so her marginal utility per dollar spent on pens is just equal to her marginal utility per dollar spent on pencils. So this is her optimal bundle. c. Although Lakshani’s marginal utility per dollar spent on soccer tickets is equal to her 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 probably will. But for a precise answer about how many football tickets and how many soccer tickets she will actually buy, we would need more information about her utility at other consumption bundles. 6. Cal “Cool” Cooper has $200 to spend on Nikes and sunglasses. a. Each pair of Nikes costs $100 and each pair of sunglasses costs $50. Which bundles lie on Cal’s budget line? Draw a diagram like Figure 10-4 in which both the marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses are illustrated. Draw the quantity of Nikes increasing from left to right, and the quantity of sunglasses increasing from right to left. Use this diagram and the utility-maximizing principle of marginal analysis 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 Nikes and sunglasses. Quantity of Nikes (pairs) Utility from Nikes (utils) Quantity of sunglasses (pairs) Utility from sunglasses (utils) 0 0 0 0 1 400 2 600 2 700 4 700 b. The price of a pair of Nikes falls to $50 each, but the price of sunglasses remains at $50 per pair. Which bundles lie on Cal’s budget line? Draw a diagram like Figure 10-4 in which both the marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses are illustrated. Use this diagram and the utility-maximizing principle of marginal analysis to decide how Cal should allocate his money. That is, from all the bundles on his budget line, which bundle will Cal choose? The accompanying table gives his utility of Nikes and sunglasses. Quantity of Nikes (pairs) Utility from Nikes (utils) Quantity of sunglasses (pairs) 0 Utility from sunglasses (utils) 0 0 0 1 400 1 325 2 700 2 600 3 900 3 825 4 1,000 4 700 c. How does Cal’s consumption of Nikes change as the price of Nikes falls? In words, describe the income effect and the substitution effect of this fall in the price of Nikes, assuming that Nikes are a normal good. 6. a. The following bundles lie on Cal’s budget line: 0 pairs of Nikes, 4 pairs of sunglasses 1 pair of Nikes, 2 pairs of sunglasses 2 pairs of Nikes, 0 pairs of sunglasses Going from 0 pairs of Nikes to 1 pair of Nikes, the marginal utility per pair is 400 utils; that is, the marginal utility per dollar spent on Nikes is 4 utils. Going from 1 pair of Nikes to 2 pairs, the marginal utility per pair is 300 utils; that is, the marginal utility per dollar spent on Nikes is 3 utils. Going from 0 pairs of sunglasses to 2 pairs of sunglasses, the marginal utility per pair is 600/2 = 300 utils; that is, the marginal utility per dollar spent on sunglasses is 6 utils. Going from 2 pairs of sunglasses to 4 pairs, the marginal utility per pair is 100/2 = 50 utils; that is, the marginal utility per dollar spent on sunglasses is 1 util. The marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses are plotted in the accompanying diagram. Marginal utility per dollar (utils/$) Optimal choice 6 5 MUS /PS 4 3 MUN/PN 2 1 0 1 Quantity of Nikes (pairs) 2 4 2 Quantity of sunglasses (pairs) 0 Of all the possible bundles Cal could consume (that is, from all the bundles on his budget line), the bundle that contains 1 pair of Nikes and 2 pairs of sunglasses is optimal. At that bundle, the marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses are equal. By the utility-maximizing principle of marginal analysis this is Cal’s optimal consumption bundle. b. The bundles that lie on Cal’s budget line are: 0 1 2 3 4 pairs of Nikes, 4 pairs of sunglasses pair of Nikes, 3 pairs of sunglasses pairs of Nikes, 2 pairs of sunglasses pairs of Nikes, 1 pair of sunglasses pairs of Nikes, 0 pairs of sunglasses The accompanying table calculates marginal utility per pair of Nikes, marginal utility per pair of sunglasses, marginal utility per dollar spent on Nikes, and marginal utility per dollar spent on sunglasses. Marginal Marginal Utility Marginal utility Marginal utility Quantity from utility per Quantity of Utility from utility per of Nikes Nikes per pair dollar sunglasses sunglasses per pair dollar (pairs) (utils) (utils) (utils/$) (pairs) (utils) (utils) (utils/$) 0 0 400 1 400 2 700 3 900 4 1,000 300 200 100 0 0 1 325 2 600 3 825 4 700 8 6 4 2 325 6.5 275 5.5 225 4.5 -125 -2.5 The accompanying diagram plots the marginal utility per dollar spent on Nikes and the marginal utility per dollar spent on sunglasses. Marginal utility per dollar (utils/$) 8 Optimal choice 7 MUS /PS 6 5 4 3 2 MUN /PN 1 0 –1 –2 –3 0 1 2 3 4 Quantity of Nikes (pairs) 4 3 2 1 0 Quantity of sunglasses (pairs) From all the bundles on Cal’s budget line, the marginal utility per dollar spent on Nikes is the same as the marginal utility per dollar spent on sunglasses at 2 pairs of Nikes and 2 pairs of sunglasses. By the utility-maximizing principle of marginal analysis, this is Cal’s optimal consumption bundle. c. Cal’s consumption of Nikes increases from 1 to 2 as the price of Nikes falls. This is due to two effects. The substitution effect says that as the price of Nikes falls, their opportunity cost falls: Cal now has to give up fewer pairs of sunglasses for 1 Nike. This makes Nikes more attractive, and Cal substitutes Nikes in place of sunglasses. The income effect says that as Nikes become cheaper, Cal gets richer in a real sense: his income now buys more goods. Since Nikes are a normal good, when the purchasing power of Cal’s income rises, he consumes more Nikes. Both effects contribute to the fact that as the price of Nikes falls, Cal’s consumption of Nikes increases. 7. Damien Matthews is a busy actor. He allocates his free time to watching movies and working out at the gym. The accompanying table shows his utility from the number of times per week he watches a movie or goes to the gym. Quantity of gym visits per week Utility from gym visits (utils) Quantity of movies per week Utility from movies (utils) 1 2 3 4 5 6 7 100 180 240 280 310 330 340 1 2 3 4 5 6 7 60 110 150 180 190 195 197 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 free time is analogous to income he can spend. The hours needed for each activity are analogous to the price of that activity.) a. Which bundles of gym visits and movies can Damien consume per week if he spends all his time either going to the gym or watching movies? Draw Damien’s budget line in a diagram with gym visits on the horizontal axis and movies on the vertical axis. b. Calculate the marginal utility of each gym visit and the marginal utility of each movie. Then calculate the marginal utility per hour spent at the gym and the marginal utility per hour spent watching movies. c. Draw a diagram like Figure 10-4 in which both the marginal utility per hour spent at the gym and the marginal utility per hour spent watching movies are illustrated. Draw the quantity of gym visits increasing from left to right, and the quantity of movies increasing from right to left. Use this diagram and the utility-maximizing principle of marginal analysis to decide how Damien should allocate his time. 7. a. Damien can consume the following bundles if he spends all his time going to the gym and watching movies: 0 1 2 3 4 5 6 7 gym gym gym gym gym gym gym gym visits, 7 movies visit, 6 movies visits, 5 movies visits, 4 movies visits, 3 movies visits, 2 movies visits, 1 movie visits, 0 movies The accompanying diagram illustrates Damien’s budget line. Quantity of movies 7 6 5 4 3 2 1 0 BL 1 2 3 4 5 6 7 Quantity of gym visits b. The accompanying table shows Damien’s marginal utility per gym visit, marginal utility per movie, marginal utility per hour spent on gym visits, and marginal utility per hour spent on movies. Marginal Marginal Marginal Quantity Utility utility per utility Utility Marginal utility of gym from gym gym per hour Quantity from utility per per hour visits per visits visits (utils per of movies movies movie (utils week (utils) (utils) hour) per week (utils) (utils) per hour) 1 100 80 2 180 3 240 4 280 5 310 6 330 7 340 1 60 2 110 3 150 4 180 5 190 6 195 7 197 40 60 30 40 20 30 15 20 50 25 40 20 30 15 10 5 5 2.5 2 1 10 10 5 c. The accompanying diagram shows Damien’s marginal utility per hour spent on gym visits and his marginal utility per hour spent watching movies. Of all the bundles on his budget line, the bundle containing 4 gym visits and 3 movies is optimal: this is the bundle at which the marginal utility per hour spent in the gym is equal to the marginal utility per hour spent watching movies. Marginal utility per hour (utils per hour) 40 35 Optimal choice 30 25 20 Marginal utility per hour spent on movies 15 Marginal utility per hour spent in the gym 10 5 0 1 2 3 4 5 Quantity of gym visits 6 7 7 6 5 1 0 4 3 2 Quantity of movies 8. Anna Jenniferson is an actress who currently spends several hours each week watching movies and going to the gym. On the set of a new movie she meets Damien, the consumer in Problem 7. She tells him that she likes watching movies much more than going to the gym. In fact, she says that if she had to give up seeing 1 movie, she would need to go to the gym twice to make up for the loss in utility from not seeing the movie. A movie takes 2 hours, and a gym visit also lasts 2 hours. Damien tells Anna that she is not watching enough movies. Is he right? 8. Damien is right. Since Anna’s marginal utility for the last movie is twice as large as the marginal utility for a gym visit, but gym visits and movies “cost” the same in terms of hours spent, Anna’s marginal utility per hour spent on movies is twice as large as her marginal utility per hour spent on gym visits. So she should spend more of her time going to movies and less going to the gym. 9. Sven is a poor student who covers most of his dietary needs by eating cheap breakfast cereal, since it contains most of the important vitamins. As the price of cereal increases, he decides to buy even less of other foods and even more breakfast cereal to maintain his intake of important nutrients. This makes breakfast cereal a Giffen good for Sven. Describe in words the substitution effect and the income effect from this increase in the price of cereal. In which direction does each effect move, and why? What does this imply for the slope of Sven’s demand curve for cereal? 9. As its price increases, cereal becomes relatively less attractive compared to other goods: its opportunity cost is now higher. As a result, Sven will tend to substitute away 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 Sven buys 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 effect is so strong that it outweighs the substitution effect: with both effects taken together, Sven consumes more cereal. For a Giffen good, the income effect works opposite to and is stronger than the substitution effect. Since Sven’s consumption of cereal rises as the price of cereal rises, his demand curve slopes upward. 10. In each of the following situations, describe the substitution effect and, if it is significant, 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. Because tuition fees rise, one of his children has to withdraw from college. b. Homer spends much of his monthly income on home mortgage payments. The interest 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, she decides to buy less of it. 10. a. As tuition fees rise, college education becomes relatively more expensive compared to other goods. So Ed decides to substitute away from college education and toward other goods. This is the substitution effect. Since tuition takes up a large portion of his income, the income effect will also be significant. As tuition rises, Ed, in a real sense, becomes poorer: the purchasing power of his income falls. As a result, he will buy less of all normal goods. College education is a normal good, so the income effect also moves in the direction of less college education. The effects reinforce each other. b. As mortgage payments decrease, large homes become cheaper compared to other goods. So Homer will substitute toward buying a larger home. This is the substitution effect. Since he spends much of his income on mortgage payments, the fall in mortgage rates also increases his income in a real sense: the purchasing power of his income is now higher. This implies that Homer will now buy more of all normal goods. Housing is a normal good, so the income effect will also move in the direction of more housing. The effects reinforce each other. c. As its price rises, Spam becomes relatively more expensive compared to other goods. So Pam will substitute away from Spam and toward other goods. This is the substitution effect. Spam probably does not account for a large portion of Pam’s income, so the income effect is likely to be negligible. However, we do know that since Spam is an inferior good, the income effect would make Pam want to consume 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 inferior goods—that is, the income effect will lead her to buy more Spam. However, we know that overall she buys less Spam as its price rises, so the substitution effect outweighs the income effect. 11. Restaurant meals and housing (measured in the number of rooms) are the only two goods that Neha buys. She has income of $1,000. Initially, she buys a consumption bundle such that she spends exactly half her income on restaurant meals and the other half of her income on housing. Then her income increases by 50%, but the price of restaurant meals increases by 100% (it doubles). The price of housing remains the same. After these changes, if she wanted to, could Neha still buy the same consumption bundle as before? 11. Yes, she could. If she spends equally as much money on housing as before, she gets the 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 restaurant meals (her income increased by 50%). But the price of restaurant meals has doubled also, so she could still buy the same quantity of restaurant meals as before. 12. Scott finds that the higher the price of orange juice, the more money he spends on orange juice. Does that mean that Scott has discovered a Giffen good? 12. 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, Scott has only found that the amount of money he spends on purchases of orange juice has increased as its price rises. For instance, suppose the price of orange juice were to rise from $5 per half-gallon to $10 per half-gallon, and as a result Scott reduces the quantity of orange juice demanded from 3 half-gallons to 2 half-gallons. This means that orange juice is not a Giffen good, since the quantity demanded decreases as the price 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 need not necessarily imply that the good is a Giffen good. 13. Margo’s marginal utility of one dance lesson is 100 utils per lesson. Her marginal utility of a new pair of dance shoes is 300 utils per pair. The price of a dance lesson is $50 per lesson. She currently spends all her income, and she buys her optimal consumption bundle. What is the price of a pair of dance shoes? 13. Since Margo buys her optimal consumption bundle, the marginal utility per dollar spent on dance lessons must be equal to the marginal utility per dollar spent on dance shoes. Here, the marginal utility per dollar spent on dance lessons is 100 utils per lesson/$50 per lesson = 2 utils per dollar. The marginal utility per dollar spent on dance shoes therefore has to equal 2 utils per dollar. Since the marginal utility of a pair of dance shoes is 300 utils per pair, the price of a pair of shoes has to be $150 per pair, so that 300 utils per pair/$150 per pair = 2 utils per dollar. 14. According to data from the U.S. Department of Energy, the average retail price of regular gasoline rose from $1.16 in 1990 to $2.52 in 2015, a 117% increase. a. Other things equal, describe the effect of this price increase on the quantity of gasoline demanded. In your explanation, make use of the utility-maximizing principle of marginal analysis and describe income and substitution effects. In fact, however, other things were not equal. Over the same time period, the prices of other goods and services rose as well. According to data from the Bureau of Labor Statistics, the overall price of a bundle of goods and services consumed by an average consumer rose by 81%. b. Taking into account the rise in the price of gasoline and in overall prices, other things equal, describe the effect on the quantity of gasoline demanded. However, this is not the end of the story. Between 1990 and 2015, the typical consumer’s nominal income increased, too: the U.S. Census Bureau reports that U.S. median household nominal income rose from $29,943 in 1990 to $56,516 in 2015, an increase of 89%. c. Taking into account the rise in the price of gasoline, in overall prices, and in consumers’ incomes, describe the effect on the quantity of gasoline demanded. 14. a. The utility-maximizing principle of marginal analysis states that, at the optimal consumption bundle, the marginal utility per dollar spent on gasoline is equal to the marginal utility per dollar spent on other goods and services. As the price of gasoline rises, other things equal, the marginal utility per dollar spent on gasoline falls. Now the marginal utility per dollar spent on gasoline is less than the marginal utility per dollar spent 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 goods and services. This raises the marginal utility of gasoline, which raises the marginal utility per dollar spent on gasoline; and it lowers the marginal utility of other goods and services, which lowers the marginal utility per dollar spent on other goods and services. This continues until the marginal utility per dollar spent on gasoline is again equal to the marginal utility per dollar spent on other goods and services. That is, the quantity of gasoline demanded falls. Almost certainly, the whole story is captured by the substitution effect: as the price of gasoline rises, most consumers substitute other goods and services in place of gasoline. Only for consumers for whom spending on gasoline makes up a major portion of their total spending will there be a noticeable income effect: as the price of gasoline rises, they will be made poorer. Since gasoline is a normal good, they will consume less gasoline, further reducing the quantity of gasoline demanded. The income effect reinforces the substitution effect. b. First, if all prices had increased by the same percentage, the effect would be the same as if all prices had remained unchanged but the consumer’s income had fallen. 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 goods and 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 as the prices of all goods and services, then consumers’ optimal consumption bundle would remain unchanged. In fact, however, income increased by more (89%) than did overall prices (only 81%). As a result, consumers would be likely to consume more of all normal goods, including gasoline. Finally, adding in the fact that the price of gasoline increased by more (117%) than did the prices of other goods and services (81%), there would still be some substitution effect at work, leading consumers to substitute other goods and services in place of gasoline. So the overall effect on the quantity of gasoline demanded would, theoretically at least, be inconclusive. WORK IT OUT Interactive step-by-step help with solving this problem can be found online. 15. Brenda likes to have bagels and coffee for breakfast. The accompanying table shows Brenda’s total utility from various consumption bundles of bagels and coffee. Consumption bundle Quantity of bagels Quantity of coffee (cups) 0 0 Total utility (utils) 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 Suppose Brenda knows she will consume 2 cups of coffee for sure. However, she can choose to consume different quantities of bagels: she can choose either 0, 1, 2, 3, or 4 bagels. a. Calculate Brenda’s marginal utility from bagels as she goes from consuming 0 bagels to 1 bagel, from 1 bagel to 2 bagels, from 2 bagels to 3 bagels, and from 3 bagels to 4 bagels. b. Draw Brenda’s marginal utility curve of bagels. Does Brenda have diminishing marginal utility of bagels? Explain. c. Brenda has $8 of income to spend on bagels and coffee. Bagels cost $2 each, and coffee costs $2 per cup. Which bundles are on Brenda’s budget line? For each of these bundles, calculate the level of utility (in utils) that Brenda enjoys. Which bundle is her optimal bundle? d. 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, calculate Brenda’s level of utility (in utils). Which bundle is her optimal bundle? e. What do your answers to parts c and d imply about the slope of Brenda’s demand curve for bagels? Describe the substitution effect and the income effect of this increase in the price of bagels, assuming that bagels are a normal good. 15. a. If Brenda consumes 2 cups of coffee, the consumption bundles that are relevant are those in the accompanying table. The first two columns are the bundles, and the third column shows the total utility of each bundle. The fourth column calculates her marginal utility of bagels. Consumption bundle Quantity of bagels Quantity of coffee (cups) Total utility (utils) 0 2 28 1 2 48 2 2 56 3 2 62 Marginal utility per bagel (utils) 20 8 6 4 4 2 66 b. The accompanying diagram shows Brenda’s marginal utility of bagels. Since Brenda’s marginal utility curve of bagels slopes downward, she has diminishing marginal utility of bagels. Marginal utility per bagel (utils) 20 18 16 14 12 10 8 6 4 2 Marginal utility curve 0 1 2 3 4 Quantity of bagels c. The first two columns in the accompanying table list the bundles that lie on Brenda’s budget line, and the third column shows her total utility from these bundles. Consumption bundle Quantity of bagels Quantity of coffee (cups) Total utility (utils) 0 4 40 1 3 54 2 2 56 3 1 54 4 0 40 Of all the bundles on her budget line, the bundle that contains 2 bagels and 2 cups of coffee gives Brenda the highest total utility. So this is her optimal bundle. d. The first two columns in the accompanying table list the bundles that lie on Brenda’s budget line, and the third column shows her total utility from these bundles. Consumption bundle Quantity of bagels Quantity of coffee (cups) Total utility (utils) 0 4 40 1 2 48 2 0 28 Of all the bundles on her budget line, the bundle that contains 1 bagel and 2 cups of coffee gives Brenda the highest utility. So this is her optimal bundle. e. As the price of bagels increased, Brenda’s consumption fell from 2 bagels to 1 bagel, implying that her demand curve for bagels slopes downward. This happens for two reasons. First, the substitution effect: as the price of bagels increases, bagels become relatively less attractive, so Brenda is likely to substitute coffee in place of bagels. Second, the income effect: as the price of bagels increases, it is as if Brenda has become poorer—her money now buys fewer goods than before. Since bagels are a normal good, a reduction in a consumer’s real income results in a lower quantity of bagels demanded. The two effects move in the same direction. 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. c. Isabella gets utility from consuming two goods: leisure time and income. Both have diminishing marginal utility. Be sure to label the axes of your diagram. Place leisure on the horizontal axis and income on the vertical axis. d. Isabella can consume two goods: skis and bindings. For each ski she wants exactly one binding. Be sure to label and number the axes of your diagram. Place bindings on the horizontal axis and skis on the vertical axis. e. Isabella gets utility from consuming soda. But she gets no utility from consuming water: any more, or any less, water leaves her total utility level unchanged. Be sure to label the axes of your diagram. Place water on the horizontal axis and soda on the vertical axis. 1. Following are Isabella’s indifference curve maps for each of the situations described. a. Quantity of cars 3 I3 2 I2 1 I1 0 4 8 12 Quantity of tires b. Quantity of Valley Dew 3 2 1 I1 0 2 I2 4 I3 6 Quantity of cola 10 Appendix c. Quantity of income I2 I1 Quantity of leisure d. Quantity of skis 3 I3 2 I2 1 I1 0 1 2 3 4 5 6 Quantity of bindings e. Quantity of soda I3 I2 I1 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? Bundle A: 2 movie tickets and 3 cafeteria meals Bundle B: 4 movie tickets and 8 cafeteria meals b. Can you rank the following two bundles? If so, which property of indifference curves helps you rank them? Bundle A: 2 movie tickets and 3 cafeteria meals Bundle B: 4 movie tickets and 3 cafeteria meals c. Can you rank the following two bundles? If so, which property of indifference curves helps you rank them? Bundle A: 12 videos and 4 bags of chips Bundle B: 5 videos and 10 bags of chips d. Suppose you are indifferent between the following two bundles: Bundle A: 10 breakfasts and 4 dinners Bundle B: 4 breakfasts and 10 dinners 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 dinners on the horizontal axis and breakfasts on the vertical axis. And remember that breakfasts and dinners are ordinary goods.) 2. a. Because bundle B has more movie tickets and more cafeteria meals than bundle 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 accompanying 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 get flatter as we move along them to the right), bundle C has to be on a higher indifference curve than bundle A (and bundle B). Since the number of goods in bundle C is exactly the average of the numbers in bundles A and B, sometimes this property of indifference curves is known as “averages are preferred to extremes.” Since bundle C lies on a higher indifference curve than either bundles A or B, you prefer bundle C to bundles A or B. Quantity of breakfasts A 10 C 7 B 4 0 4 I 7 10 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. a. Quantity of Y I2 I1 Quantity of X b. Quantity of Y I Quantity of X c. Quantity of Y I Quantity of X d. Quantity of Y I 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 goods get flatter as you move to the right is a result of the assumption of diminishing marginal utility. So diminishing marginal utility rules out indifference curves like this. 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 X than the other. Because more is better, these two bundles can’t give the consumer the same total utility; the one with more of good X must give the consumer a higher level of total utility than the one with less. So they cannot be on the same indifference curve. 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. 5. Answer the following questions based on two assumptions: (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. b. The prices of all goods have increased by 20%, but Ina’s income has increased by only 10%. Fewer bundles are now within Ina’s consumption possibilities: the budget line has shifted inward. 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. b. Kory is considering buying 2 albums and 15 cups of hot chocolate. Kory’s marginal utility of the second album is 25, and her marginal utility of the fifteenth cup of hot chocolate is 5. c. Kory is considering buying 1 album and 10 cups of hot chocolate. At that bundle, her marginal rate of substitution of albums in place of hot chocolate is 5; that is, she would be just willing to exchange 5 cups of hot chocolate for 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. However, the relative price of 1 album is 5 cups of hot chocolate: she would have to give up 5 cups of hot chocolate for 1 album. Kory values albums less than they cost her, so she should consume fewer albums and more hot chocolate to remain on her budget line. Kory should shift consumption toward hot chocolate until her MRS is the same as the relative price of albums. 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. c. At this bundle, the marginal rate of substitution is equal to the relative price, but the bundle does not lie on Kory’s budget line: she spends only $30 of her $50 income on this bundle. If her income were $30, this would be her optimal consumption bundle. However, her income is $50. At this higher income she will buy more of both goods, since both are normal goods for her. 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 willing 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? c. Suppose Raul has traded baseball cards and after trading still has some of each kind of card. Also, he now no longer wants to make any more trades. What is his marginal rate of substitution of Cal Ripken in place of Nolan Ryan cards now? 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 by selling Cal Ripken cards and buying Nolan Ryan cards until his marginal rate of substitution equals the relative price. c. If Raul can no longer benefit from trade, he must be consuming his optimal consumption bundle. That is, his marginal rate of substitution must be equal to the relative price. The relative price rule—which says that MUCal/MUNolan = PCal/PNolan —applies. Since we know that the relative price is 2, Raul’s marginal rate of substitution must also be 2. 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 consumption 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. b. How should Ralph adjust his consumption so that it is optimal? Illustrate an optimal choice in your diagram. 8. a. Lauren is right. Since Ralph values one more meal twice as much as he values 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, the relative price of a meal is Pmeal/Pgym = 1 (they both cost the same). A in the accompanying diagram illustrates this bundle. Since his marginal rate of substitution is different from the relative price, this cannot be his optimal consumption bundle. Quantity of gym sessions A Optimal bundle Slope: –MUmeal /MUgym = –2 B I1 I2 Slope: –Pmeal /Pgym = –1 BL Quantity of restaurant meals 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 better off. In the diagram, bundle B is the bundle that is optimal: the relative price is equal to Ralph’s marginal rate of substitution. 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? 9. a. If Sabine can’t tell the difference between Coke and Pepsi, the two are perfect substitutes for her. She is always willing to exchange 1 six-pack of Pepsi for 1 sixpack of Coke, so her marginal rate of substitution of Coke in place of Pepsi is 1. b. Sabine’s indifference curves are the lines labeled I1, I2, and I3 in the accompanying diagram. c. Sabine’s budget line is the line labeled BL in the diagram. d. Sabine’s optimal consumption bundle is bundle A in the diagram: she can get onto her highest indifference curve by consuming only Pepsi. (In this special case of perfect substitutes, the relative price rule does not hold. Sabine’s marginal rate of substitution is less than the relative price, so she should want to consume less Coke and more Pepsi. But that is impossible since she is already consuming no Coke!) 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 A 6 4 2 I1 0 I2 2 BL I3 4 6 Quantity of Coke 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 fries on the vertical axis. b. Can you determine definitively whether she consumes more or less french fries? Explain with a diagram, placing nachos on the horizontal axis and french fries on the vertical axis. 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 movement 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 definitively that her consumption of nachos falls in response to the increase in the price of nachos. Quantity of french fries B A C BL2 BLS I1 I2 BL1 Quantity of nachos 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 the size of the income effect on salsa consumption from the price increase of nachos (which makes her poorer) is large enough to dominate the size of the substitution effect on salsa consumption (which makes her want to consume more salsa and fewer nachos). The accompanying diagram shows a case in which her consumption of salsa falls in response to an increase in the price of nachos. At her new consumption bundle D, she consumes fewer nachos and less salsa than she did at A. Quantity of salsa A I2 D I1 BL2 BL1 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 horizontal axis and food on the vertical axis. 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 is, Gus goes from bundle A on his original budget line BL1 to bundle B on his new budget line BL2. In effect, what this policy does is to isolate just the substitution effect of the price change: the income effect is fully compensated for by the increase in Gus’s income, so only the substitution effect remains. Quantity of food B A BL2 I BL1 Quantity of gas 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. a. Draw a diagram of Pam’s budget line, placing Spam on the horizontal axis and bread on the vertical axis. Suppose her optimal consumption bundle is 4 cans of Spam and 6 loaves of bread. Illustrate that bundle and draw the indifference curve on which it lies. b. The price of Spam falls to $1; the price of bread remains the same. Pam now buys 7 loaves of bread and 6 cans of Spam. Illustrate her new budget line and new optimal consumption bundle in your diagram. Also draw the indifference curve on which this bundle lies. c. In your diagram, show the income and substitution effects from this fall in the price of Spam. Remember that Spam is an inferior good for Pam. 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 characteristic 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 indifference curve I2, represents her optimal choice of 7 loaves of bread and 6 cans of Spam. c. Budget line BLS isolates the substitution effect. The move from bundle A to bundle B shows the substitution effect. Because the relative price of Spam is now lower, Pam substitutes more Spam for less bread. The move from bundle B to C illustrates the income effect. Since Spam is an inferior good, the income effect tells us that Pam consumes less Spam at C than at B. For inferior goods, the substitution effect (from A to B) and the income effect (from B to C) move in opposite directions. Quantity of bread 10 7 6 C A I2 B BL1 0 4 6 BLS 10 I1 BL2 20 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 ordinary 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 indifference curve that illustrates her optimal consumption bundle after the price of public transport has fallen. Is Katya consuming more or less public transport? d. Show the income and substitution effects from this fall in the price of public transport. 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 consumption of a good fall as its price falls.) d. Budget line BLS in the diagram isolates the substitution effect. The move from bundle A to bundle B shows the substitution effect. It tells you that Katya will substitute more public transport in place of fewer car rides since the relative price of public transport has fallen. The move from bundle B to bundle C shows the income effect. Since public transport is an inferior good, the income effect tells us that Katya will consume less public transport as her income rises. For inferior goods, the income and substitution effects work in opposite directions. Quantity of car travel A C I2 B BL1 BLS I1 BL2 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? c. Show the income and substitution effects from this price rise. 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 budget 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 BL2 in the diagram, and his optimal consumption bundle is B. He consumes 6 cheese cubes and 6 crackers. c. To isolate the substitution effect of this price rise, we run through the following thought experiment: Give Crandall just enough extra income to bring him onto the same indifference curve that he was on before the price rise. The budget line that does this is BLS in the diagram, where Crandall would consume the same bundle that he consumed to begin with (bundle A). So in this special case there is no substitution effect. The move from bundle A to bundle B is entirely accounted for by the income effect. Of course this is intuitive: since the two goods are perfect complements, they are not substitutable—and so it makes sense that there is no substitution effect. Quantity of cheese cubes 16 14 12 10 8 6 4 2 0 A I2 I1 B BL2 BLS BL1 2 4 6 8 10 12 14 16 18 20 22 24 26 Quantity of crackers 15. Carmen consumes nothing but cafeteria meals and music albums. Her indifference 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 optimal 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 consumption 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 Carmen’s consumption of cafeteria meals. This increase in income causes a pure income effect, and for inferior goods the income effect of an increase in income is to reduce consumption. c. It is not possible to draw an indifference curve for which all goods are inferior goods. This is because as your income increases, you have more money to spend, and you will always spend all your money (because of the “more is better” assumption). If, as a result of this income increase, you buy less of one good (an inferior good), you must spend more on the other—making the other good a normal good. Quantity of albums 10 B I2 5 BL1 A I1 0 BL2 10 20 Quantity of cafeteria meals 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 number 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 diagram, draw the average Japanese household’s budget line in 2013 and in 2015. Place the quantity of eggs on the y-axis and the quantity of tuna on the x-axis. b. Calculate the relative price of eggs in terms of tuna for each year. Use the relative price rule to determine how the average household’s consumption of eggs and tuna would have changed between 2013 and 2015. 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 consumed a maximum of only ¥524,585/¥231 = 2,271 packs of eggs and a maximum of ¥524,585/¥390 = 1,345 portions of tuna. The accompanying diagram shows the budget lines in 2003 and 2005. Quantity of eggs (packs of 10) 2,806 Budget line in 2013 2,271 Budget line in 2015 0 1,339 1,345 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 increased, the marginal rate of substitution of eggs in place of tuna must have increased, too. This means that consumers must have reallocated their consumption to increase their marginal utility of eggs (by reducing their consumption of eggs) and to decrease their marginal utility of tuna (by increasing their consumption of tuna). 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 budget 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? (Hint: Determine whether Tyrone can afford to buy his original consumption bundle of 16 meals and 10 notepads with the lower income and new prices.) Illustrate your answer using an indifference curve and label it I2. d. Give an intuitive explanation of your answer to part c. 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 horizontal intercept (the quantity of cafeteria meals he can buy if he spends all his income on meals, equal to $100/$5 = 20) and its vertical intercept (the quantity of notepads he can buy if he spends all his income on notepads, equal to $100/$2 = 50). Quantity of notepads BL H 100 90 BL2 B 50 BL1 I1 10 0 A I2 16 18 20 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). 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 ($90/$5 = 18). Note that Tyrone can indeed buy his original consumption bundle of 16 meals and 10 notepads at the new prices and lower income: (16 × $5) + (10 × $1) = $90. So he cannot be any worse off than he was originally. But, in fact, he is better off: as can be seen from the diagram, BL2 allows him to reach a higher indifference curve, I2, than he achieved before. 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. The fall in the price of notepads has been sufficiently large so that once he re-allocates his consumption toward more notepads and fewer meals, he is more than compensated for the fall in his income level. Solution Manual for Microeconomics Paul Krugman, Robin Wells 9781319098780
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