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2 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-12 S-12 CHAPTER 1 THE RATIONAL CONSUMER 3. 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. 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, 1, 2, 3, or bagels. a. Calculate Brenda s marginal utility from bagels as she goes from consuming bagel to 1 bagel, from 1 bagel to 2 bagels, from 2 bagels to 3 bagels, and from 3 bagels to bagels. b. Draw Brenda s marginal utility curve of bagels. Does Brenda have increasing, diminishing, or constant marginal utility of bagels? Consumption bundle Quantity of Quantity of Total utility bagels coffee (cups) (utils) 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 Quantity of Total utility Marginal utility bagels coffee (cups) (utils) per bagel (utils)

3 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-13 CHAPTER 1 THE RATIONAL CONSUMER S-13 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) Marginal utility curve Quantity of bagels. Brenda, the consumer in Problem 3, now has to make a decision about how many bagels and how much coffee to have for breakfast. She has \$8 of income to spend on bagels and coffee. Use the information given in the table in Problem 3 to answer the following questions. a. 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? b. The price of bagels increases to \$, 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? c. What do your answers to parts a and b 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.. a. 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 Quantity of Total utility bagels coffee (cups) (utils) 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.

4 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-1 S-1 CHAPTER 1 THE RATIONAL CONSUMER b. 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. 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. c. 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 had 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. 5. Bruno can spend his income on two different goods: Beyoncé CDs and notebooks for his class notes. 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. CDs cost \$1 each, and notebooks cost \$2 each. Bruno has income of \$6. He is considering a consumption bundle containing 3 CDs and 15 notebooks. b. CDs cost \$1 each, and notebooks cost \$5 each. Bruno has income of \$11. He is considering a consumption bundle containing 3 CDs and 1 notebooks. c. CDs cost \$2 each, and notebooks cost \$1 each. Bruno has income of \$5. He is considering a consumption bundle containing 2 CDs and 2 notebooks. Consumption bundle Quantity of Quantity of Total utility bagels coffee (cups) (utils) a. This consumption bundle costs \$1 3 + \$2 15 = \$6, which is exactly equal to Bruno s income of \$6. 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 \$1 3 + \$5 1 = \$8, which is less than Bruno s income of \$11. 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 \$2 2 + \$1 2 = \$6, which is more than Bruno s income of \$5. So the bundle is not within Bruno s consumption possibilities; it lies above his budget line.

5 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-15 CHAPTER 1 THE RATIONAL CONSUMER S Bruno, the consumer in Problem 5, is best friends with Bernie, who shares his love for notebooks and Beyoncé CDs. The accompanying table shows Bernie s utilities from notebooks and Beyoncé CDs. Utility from Utility from Quantity of notebooks Quantity of CDs notebooks (utils) CDs (utils) The price of a notebook is \$5, the price of a CD is \$1, and Bernie has \$5 of income to spend. a. Which consumption bundles of notebooks and CDs can Bernie consume if he spends all his income? Illustrate Bernie s budget line with a diagram, putting notebooks on the horizontal axis and CDs on the vertical axis. b. Calculate the marginal utility of each notebook and the marginal utility of each CD. Then calculate the marginal utility per dollar spent on notebooks and the marginal utility per dollar spent on CDs. c. Draw a diagram like Figure 1- in which both the marginal utility per dollar spent on notebooks and the marginal utility per dollar spent on CDs are illustrated. Using this diagram and the optimal consumption rule, predict which bundle from all the bundles on his budget line Bernie will choose a. Bernie can consume the following bundles if he spends all his income: notebooks, 5 CDs 2 notebooks, CDs notebooks, 3 CDs 6 notebooks, 2 CDs 8 notebooks, 1 CD 1 notebooks, CDs The accompanying diagram shows Bernie s budget line. Quantity of CDs BL Quantity of notebooks

6 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-16 S-16 CHAPTER 1 THE RATIONAL CONSUMER b. The accompanying table shows the marginal utility for each notebook and for each CD, the marginal utility per dollar spent on notebooks, and the marginal utility per dollar spent on CDs. Note that the utility numbers for notebooks are given in increments of 2: for instance, going from notebooks to 6, utility increases by 5 utils (from 13 utils to 18 utils). Per notebook, this is a marginal utility of 25 utils. Utility Marginal Marginal Marginal Marginal Quantity 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) c. The optimal consumption rule 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 notebooks and the marginal utility per dollar spent on CDs. When Bernie consumes notebooks and 3 CDs, the marginal utility per dollar spent on notebooks is the same as the marginal utility per dollar spent on CDs, so this is the optimal consumption bundle. It is also the only bundle from all the bundles he can consume (that is, from all the bundles on his budget line) for which the marginal utility per dollar is equal for the two goods. Marginal utility per dollar (utils) Quantity of notebooks Optimal choice 3 2 Quantity of CDs 1 MU CD /P CD MU N /P 1 N 7. For each of the following situations, decide whether the bundle Lakshani is considering 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 should she spend less on.

8 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-18 S-18 CHAPTER 1 THE RATIONAL CONSUMER b. The price of cell phones falls to \$5 each, but the price of sunglasses remains at \$5 per pair. Which bundles lie on Cal s budget line? Draw a diagram like Figure 1- in which both the marginal utility per dollar spent on cell phones and the marginal utility per dollar spent on sunglasses are illustrated. Use this diagram and 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 phones falls? In words, describe the income effect and the substitution effect of this fall in the price of cell phones, assuming that cell phones are a normal good. Utility from Quantity of Utility from Quantity of cell phones sunglasses sunglasses cell phones (utils) (pairs) (utils) , 7 8. a. The following bundles lie on Cal s budget line: cell phones, pairs of sunglasses 1 cell phone, 2 pairs of sunglasses 2 cell phones, pairs of sunglasses Going from cell phones to 1 cell phone, the marginal utility per cell phone is utils; that is, the marginal utility per dollar spent on cell phones is utils. Going from 1 cell phone to 2 cell phones, the marginal utility per cell phone is 3 utils; that is, the marginal utility per dollar spent on cell phones is 3 utils. Going from pairs of sunglasses to 2 pairs of sunglasses, the marginal utility per pair is 6/2 = 3 utils; that is, the marginal utility per dollar spent on sunglasses is 6 utils. Going from 2 pairs of sunglasses to pairs, the marginal utility per pair is 1/2 = 5 utils; that is, the marginal utility per dollar spent on sunglasses is 1 util. The marginal utility per dollar spent on cell phones and the marginal utility per dollar spent on sunglasses are plotted in the accompanying diagram. Marginal utility per dollar (utils) Optimal choice MU S /P S MU C /P C 1 Quantity of cell phones 2 Quantity of sunglasses (pairs) 2

9 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-19 CHAPTER 1 THE RATIONAL CONSUMER S-19 Of all the possible bundles Cal could consume (that is, from all the bundles on his budget line), the bundle that contains 1 cell phone and 2 pairs of sunglasses is optimal. At that bundle, the marginal utility per dollar spent on cell phones and the marginal utility per dollar spent on sunglasses are equal. By the optimal consumption rule, this is Cal s optimal consumption bundle. b. The bundles that lie on Cal s budget line are: cell phones, pairs of sunglasses 1 cell phone, 3 pairs of sunglasses 2 cell phones, 2 pairs of sunglasses 3 cell phones, 1 pair of sunglasses cell phones, pairs of sunglasses The accompanying table calculates marginal utility per cell phone, marginal utility per pair of sunglasses, marginal utility per dollar spent on cell phones, and marginal utility per dollar spent on sunglasses. 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) , 7 The accompanying diagram plots the marginal utility per dollar spent on cell phones and the marginal utility per dollar spent on sunglasses. Marginal utility per dollar (utils) Optimal choice MU S /P S MU C /P C Quantity of cell phones Quantity of sunglasses (pairs)

10 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-15 S-15 CHAPTER 1 THE RATIONAL CONSUMER From all the bundles on Cal s budget line, the marginal utility per dollar spent on cell phones is the same as the marginal utility per dollar spent on sunglasses at 2 cell phones and 2 pairs of sunglasses. By the optimal consumption rule, this is Cal s optimal consumption bundle. c. Cal s consumption of cell phones increases from 1 to 2 as the price of cell phones falls. This is due to two effects. The substitution effect says that as the price of cell phones falls, their opportunity cost falls: Cal now has to give up fewer pairs of sunglasses for 1 cell phone. This makes cell phones more attractive, and Cal substitutes cell phones in place of sunglasses. The income effect says that as cell phones become cheaper, Cal gets richer in a real sense: his income now buys more goods. Since cell phones are a normal good, when the purchasing power of Cal s income rises, he consumes more cell phones. Both effects contribute to the fact that 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 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 Utility from Quantity of Utility from gym visits gym visits movies per movies per week (utils) week (utils) Damien has 1 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 1- in which both the marginal utility per hour spent at the gym and the marginal utility per hour spent watching movies are illustrated. Use this diagram and the optimal consumption rule to decide how Damien should allocate his time.

11 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S a. Damien can consume the following bundles if he spends all his time going to the gym and watching movies: gym visits, 7 movies 1 gym visit, 6 movies 2 gym visits, 5 movies 3 gym visits, movies gym visits, 3 movies 5 gym visits, 2 movies 6 gym visits, 1 movie 7 gym visits, movies The accompanying diagram illustrates Damien s budget line. CHAPTER 1 THE RATIONAL CONSUMER S-151 Quantity of movies BL 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. 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)

12 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-152 S-152 CHAPTER 1 THE RATIONAL CONSUMER 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 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 dollar (utils) Optimal choice Marginal utility per hour spent on movies Marginal utility per hour spent in the gym Quantity of gym visits Quantity of movies 1. 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 9. 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? 1. 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. 11. 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? 11. 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

14 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-15 S-15 CHAPTER 1 THE RATIONAL CONSUMER 1. 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? 1. 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 \$1 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 \$1 2 = \$2. So an increase in spending on a good as its price rises need not necessarily imply that the good is a Giffen good. 15. Margo s marginal utility of one dance lesson is 1 utils per lesson. Her marginal utility of a new pair of dance shoes is 3 utils per pair. The price of a dance lesson is \$5 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? 15. 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 1 utils per lesson/\$5 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 3 utils per pair, the price of a pair of shoes has to be \$15 per pair, so that 3 utils per pair/\$15 per pair = 2 utils per dollar. 16. According to data from the U.S. Department of Energy, the average retail price of regular gasoline rose from \$.93 in 1985 to \$1.81 in 25, a 95% 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 optimal consumption rule 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 82%. 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 1985 and 25, the typical consumer 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 \$6,326 in 25, an increase of 96%. 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. 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 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

15 S11-S156_Krugman2e_PS_Ch1.qxp 9/16/8 9:21 PM Page S-155 CHAPTER 1 THE RATIONAL CONSUMER S-155 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. 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 (96%) than did overall prices (only 82%). 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 (95%) than did the prices of other goods and services (82%), 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. (If you would like to know, the quantity of regular gasoline bought and sold in the United States has, in fact, increased from 19 million gallons per day in 1985 to 316 million gallons per day in 25, according to data from the U.S. Department of Energy.)

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