CH - 10 sol - Lecture notes 5 PDF

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11 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.

Solution 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

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b.

Quantity of Valley Dew 3 2 1

I1 0

c.

I2

2

4

I3 6 Quantity of cola

Quantity of income

I2 I1 Quantity of leisure

d.

Quantity of skis 3

I3

2

I2

1

I1

0

e.

1

2

3

4 5 6 Quantity of bindings

Quantity of soda

I3 I2 I1 Quantity of water

2.

Use the four properties of indifference curves for ordinary goods illustrated in Figure 11-4 to answer the following questions. a. Can you rank the following two bundles? If so, which property of indifference curves helps you rank them?

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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. Solution

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.” Quantity of breakfasts

A

10

C 7

B 4

I

0

4

7 10 Quantity of dinners

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3.

The four properties of indifference curves for ordinary goods illustrated in Figure 11-4 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

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Solution 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?

Solution 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. Solution

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: CDs and cups of hot chocolate. Both are normal goods for her. Each CD 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 CDs and 5 cups of hot chocolate. At that bundle, her marginal rate of substitution of CDs in place of hot chocolate is 1; that is, she would be willing to forgo only 1 cup of hot chocolate to acquire 1 CD. b. Kory is considering buying 2 CDs and 15 cups of hot chocolate. Kory’s marginal utility of the second CD is 25, and her marginal utility of the fifteenth cup of hot

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Solution 6.

The relative price of CDs in terms of cups of hot chocolate is PCD/Phot chocolate = $10/$2 = 5. That is, to get 1 more CD, 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 CDs She is willing to exchange only 1 cup of hot chocolate for 1 CD. However, the rel ative price of 1 CD is 5 cups of hot chocolate: she would have to give up 5 cups o hot chocolate for 1 CD. Kory values CDs less than they cost her, so she should consume fewer CDs 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 CDs. 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 MUCD/MUhot chocolate = 25/5 = 5. That is, she is willing to exchange 5 cups of hot chocolate for 1 CD. Because the relative price of 1 CD is 5 cups of hot chocolate, Kory values CDs equally as muc 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 on it. 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?

Solution 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 substitu tion 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 o 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 d d h ll h h h b dl

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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. Solution

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 I2 I1

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 six-pack and Pepsi costs $1.00. Draw Sabine’s budget line for Coke and Pepsi on the same diagram. d. What is Sabine’s optimal consumption bundle? Show this on your diagram. e. If the price of Coke and Pepsi is the same, what combination of Coke and Pepsi will Sabine buy?

Solution 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 six-pack 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

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

BL I1 0

10.

I2 2

I3 4 6 Quantity of Coke

For Norma, both nachos and salsa are normal goods. They are also ordinary goods for Norma. The price of nachos rises, but the price of salsa 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 salsa on the vertical axis. b. Can you determine definitively whether she consumes more or less salsa? Explain with a diagram, placing nachos on the horizontal axis and salsa on the vertical axis

10. Solution

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 salsa. 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 salsa

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. I 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

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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 BL2

I1

BL1 Quantity of nachos

11.

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 bundl...