# Why are hockey tickets so expensive

89 10 The Rational Consumer Exercise 1 Use the marginal utility principle to explain the following observation: Newspaper machines are designed so that once you have paid you can take out more than one newspaper. Vending machines, on the other hand, are designed in such a way that they only eject a bottle when you have paid. Solution The second (and every additional) newspaper has a marginal utility of zero: if you already have a newspaper, another newspaper does not provide any additional utility. Beverages show a decreasing but positive marginal utility. If another drink is available free of charge in addition to the first, you will be tempted to take that extra drink with you. Task 2 Bruno can spend his income on two different goods: Beyoncé MP3s and notebooks for his lecture notes. For each of the following situations, determine whether he can consume the respective consumption bundle with the given income and prices and whether the consumption bundle is on his budget line. a. MP3s cost 2 euros each and notebooks cost 3 euros each. Bruno has an income of 60 euros. He is considering a consumption bundle of 15 MP3s and 10 notebooks. b. MP3s cost 2 euros each and notebooks cost 5 euros each. Bruno has an income of 110 euros. He is considering a consumption bundle of 20 MP3s and 10 notebooks. c. MP3s cost 3 euros each and notebooks cost 10 euros each. Bruno has an income of 50 euros. He is considering a consumption bundle of 10 MP3s and 3 notebooks. Solution a. The consumption bundle of 15 MP3s and 10 notebooks costs him: € 2 × 15 + € 3 × 10 = € 60. That corresponds exactly to his income. This bundle of consumption is thus exactly on its budget line. He can afford it. b. The consumption bundle of 20 MP3s and 10 notebooks costs him: € 2 × 20 + € 5 × 10 = € 90. That is less than his income of 110 euros. The rational consumer 90 10 can afford this bundle of consumption. However, it is below its budget line and therefore cannot be an optimal bundle of consumption. c. The consumption bundle of 10 MP3s and 3 notebooks costs him: 3 € × 10 + 10 € × 3 = 60 €. That is more than his income of 50 euros. Bruno cannot afford the bundle of consumption. It is above its budget line. Task 3 Bruno is a close friend of Bernie, who shares his preference for Beyoncé notebooks and MP3s. The table shows the benefits Bernie gets from Beyoncé notebooks and MP3s. The price of a notebook is 4 euros, the price of an MP3 is 2 euros and Bernie can spend an income of 20 euros. a. What bundle of notebooks and MP3s can Bernie consume when he is spending all of his income? Draw Bernie's budget line, with the MP3s on the horizontal axis and the notebooks on the vertical axis. b. Find the marginal utility for each notebook and for each MP3. Then calculate the marginal utility of a euro spent on notebooks and the marginal utility of a euro spent on MP3s. c. Create a drawing analogous to Figure 10-4 (in Krugman / Wells, Volkswirtschaftslehre, 2nd edition) in which both the marginal utility of a euro spent on notebooks and the marginal utility of a euro spent on MP3s are shown in a diagram. Using this drawing and the Optimal Consumption Rule, determine which Bundle Bernie will choose on their budget line. Amount of notebooks Use from notebooks (Utile) Amount of MP3s Use from MP3s (Utile) 0 0 0 0 1 32 2 28 2 60 4 52 3 84 6 72 4 104 8 88 5 120 10 100 Tab. 10 1 The rational consumer 91 10 Solution a. Bernie can afford the following consumption bundles: (0 MP3s and 5 notebooks), (2 MP3s and 4 notebooks), (4 MP3s and 3 notebooks), (6 MP3s and 2 notebooks), (8 MP3s and 1 notebook), and (10 MP3s and 0 notebooks). b. Fig. 10 1 0 1 2 3 4 5 6 0 2 4 6 8 10 12 Note books MP3s Quantity of notebooks Marginal utility per notebook (Utile) Marginal utility of a euro spent on notebooks Quantity of MP3s Marginal utility of an MP3 (Utile) Marginal utility of a euro spent on MP3s 0 0 32 8 14 7 1 2 28 7 12 6 2 4 24 6 10 5 3 6 20 5 8 4 4 8 16 4 6 3 5 10 Tab. 10 2 The rational consumer 92 10 c. The rule of optimal consumption is: With the optimal consumption bundle, the marginal utility per euro is the same for every good. With a quantity of 3 notebooks, the marginal utility is 6 utiles per euro spent on a notebook. With a quantity of 4 MP3s, the marginal utility is 6 utiles per euro spent on MP3s. Bernie will choose the bundle of 3 notebooks and 4 MP3s. This means that he uses exactly his budget of 20 euros: 3 × 4 euros + 4 × 2 euros = 20 euros. Task 4 For each of the following situations, determine whether the consumption bundle that Lotte is thinking about is optimal or not. If it's not optimal, how could Lotte increase its level of utility? (So determine which good she should spend more on and which less.) A. Lotte can spend 200 euros on sneakers and sweaters. A pair of sneakers costs 50 euros and a sweater costs 20 euros. She is wondering whether she 2 Fig. 10 2 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 Boundaries Use a E ur o (in U til en) Notebooks Boundary utility of a given for MP3s Euro Marginal utility of a Euro spent on notebooks 10 8 6 4 2 0MP3s The rational consumer 93 should buy 10 pairs of shoes and 5 sweaters. She tells her friend that the added benefit she gets from the second pair of sneakers is just as great as the added benefit she gets from the fifth sweater. b. Lotte can spend 5 euros on pens and pencils. A ballpoint pen costs 0.50 euros and a pencil 0.10 euros. She wonders whether to buy 6 ballpoint pens and 20 pencils. The last ballpoint pen would add five times more total utility than the last pencil. c. Lotte can spend 50 euros on soccer and hockey games each season. Each ticket for a football game costs 10 euros and each ticket for a hockey game costs 5 euros. She is considering buying 3 tickets for soccer games and 2 tickets for hockey games. The marginal utility that accrues to her from the third ticket for soccer games is twice as high as the marginal utility of the second ticket for hockey games. Solution a. The consumption bundle, consisting of 2 pairs of shoes and 5 sweaters, is not ideal. It is on Lotte's budget line, but the marginal utility of one euro for a pair of sneakers and the marginal utility of one euro for a sweater are not the same. The marginal utility of one euro for a pair of sneakers is 2.5 times smaller than the marginal utility of one euro for a sweater. Lotte should therefore spend more on sweaters (then the marginal utility of a euro spent on sweaters falls) and less on shoes (then the marginal utility of a euro spent on shoes increases). b. The bundle of 6 ballpoint pens and 20 pencils is on the budget line and is also ideal. The marginal utility of a euro spent on pens is just as high as the marginal utility of a euro spent on pencils. c. It is true that the marginal utility of one euro that is spent on football tickets is just as high as the marginal utility of one euro that is spent on hockey tickets. But the bundle of consumption is not optimal, as Lotte does not spend her entire budget. She should invest the remaining 10 euros in either 2 hockey tickets or another football ticket, depending on which option increases the level of use. Task 5 Anna is an actress and while making a new film she meets a friend. She tells him that she would much rather like movies than go to the gym. More precisely, she says that she would have to go to the gym twice to make up for the loss she would incur if she had to forego watching a movie in the cinema. Her boyfriend then tells her that she doesn't watch enough movies. Is he right? The Rational Consumer 94 10 Solution Anna's friend is right. The marginal utility of a visit to the sports studio is at the optimum point the same as the marginal utility of a visit to the cinema. But that is not the case with Anna: The marginal utility of a visit to the sports studio is only half as high as that of a visit to the cinema. She should go to the cinema more often (then the marginal utility of going to the cinema decreases, while the marginal utility of a visit to the sports studio increases). Exercise 6 Sven is a poor student who lives almost exclusively on cheap breakfast cereals for the whole day. As the price of cereal goes up, he decides to buy less other foods and eat more cereals to fill up. Breakfast cereals are therefore a Giffen good for Sven. Describe in words the substitution and income effects resulting from the rise in breakfast cereal prices. In which direction does each of the effects work? Why? What is the implication for the slope of Sven's demand curve for breakfast cereals? Solution A Giffen good is an inferior good in which the income effect dominates the substitution effect. The substitution effect arises here from the rise in the price of breakfast cereals. This price increase leads to a decrease in the demand for the relatively more expensive breakfast cereals and to an increase in the demand for other, relatively cheaper goods (food). The rise in prices also has an income effect. When breakfast cereals become more expensive, the purchasing power of Sven's income falls. This decline in income leads to an increase in demand for inferior goods. Since the income effect outweighs the substitution effect in the case of Giffen goods, an increase in the price of breakfast cereals leads to an increase in the quantity demanded. This means that the law of demand does not apply and the demand curve is sloping upwards. Exercise 7 Describe the substitution effect and (if relevant) the income effect for each of the following situations. In which direction do these effects work? Why? a. Eduard spends a large part of his income on the education of his children. Because tuition fees are rising, one of his children has to drop out. b. Hans spends a large part of his monthly income on the interest on a loan he took out to build his house. The floating rate on his loan goes down, which reduces his interest payments. Hans decides to buy a bigger house. The rational consumer 95 10 c. Paula believes porridge is an inferior good. But when the price of porridge rises, she decides to buy less. Solution a. The substitution effect leads to a decrease in the demand for training because training has become relatively more expensive. The income effect is based on the fact that a considerable part of the income is spent on training, which in turn reduces purchasing power. Training is a normal good. Therefore, the income effect leads to a decrease in the demand for training. The income effect intensifies the substitution effect. b. The substitution effect leads to an increase in the demand for houses, as the house has become relatively cheaper due to a lower interest rate. The income effect is based on the fact that a significant part of the income is spent on the loan and the falling interest rate increases purchasing power. The house is obviously a normal commodity, since a drop in price ultimately leads to an increase in demand. Therefore, the income effect amplifies the substitution effect. c. The substitution effect leads to a decrease in the demand for porridge, as porridge has become relatively more expensive. If porridge is an inferior good, then the income effect counteracts the substitution effect. The income effect is based on the fact that porridge, which has become relatively more expensive, lowers the purchasing power of income. The drop in purchasing power is only noticeable if a significant part of the income is spent on porridge. That's not the case. The substitution effect thus dominates the income effect and leads to a decline in the demand for porridge. Task 8 Eating in a restaurant and using the apartment (measured by the number of rooms) are the only two goods that Nadine can buy. She has an income of 1,000 euros. With her bundle of consumption, she spends half of her income on restaurant meals and half on apartment use. Then their income increases by 50 percent. At the same time, however, the price for restaurant meals is also increasing by 100 percent. Only the price for apartment use remains unchanged. After these changes, can Nadine still afford the same bundle of consumption? Solution If the price for restaurant meals increases by 100 percent, then Nadine will now have to spend twice as much as before. If her income were unchanged, Nadine would be forced to spend all of her income on restaurant meals in order to maintain the level of consumption of restaurant meals. However, their income has also increased. The 50 percent increase in income corresponds exactly to their spending on housing use (which remains unchanged). The rational consumer 96 10 This means that Nadine can afford the same bundle of consumption despite the increased price for restaurant meals. Exercise 9 Maria's marginal utility from a visit to the hairdresser is 100 utiles per visit. Your marginal utility from a new pair of sneakers is 300 util. The price of a visit to the hairdresser is 50 euros. She spends her entire income and buys the optimal bundle of consumption for her. What is the price of a pair of sneakers? Solution The marginal utility of one euro that is spent on visiting the hairdresser is 2 utiles. According to the rule for optimal consumption, the marginal utility per euro for visiting the hairdresser must be the same as the marginal utility per euro for sneakers if Maria maximizes her utility. The price for a pair of sneakers is 150 euros. Exercise 10 Stefan found out that he spends more money on orange juice when the price of orange juice increases. Can we conclude from this that orange juice is a Giffen good for Stefan? Solution Orange juice is not necessarily a Giffen good for Stefan. In the case of a Giffen good, the quantity demanded increases when the price of the good increases. However, Stefan has only found that if the price of orange juice increases, he will spend more money on orange juice. But that doesn't mean that he also bought more orange juice. For example, if the price for a bottle of orange juice rises from 1 euro to 2 euros and Stefan buys only 7 bottles of orange juice instead of 10 bottles, his expenses for orange juice have increased from 10 euros to 14 euros, although the amount bought has decreased. An increase in expenditure for a particular good as a result of a price increase does not necessarily mean that this good is a Giffen good.

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