Chapter 5Consumers and Incentives

Questions1. What are the three necessary ingredients that help a consumer decide what to buy?

Answer: The first ingredient is what you like. As a consumer attempts to maximize the benefits from consumption, she would buy what she thinks will give her the most satisfaction according to her tastes and preferences. The second ingredient is prices of goods and services. When a consumer decides what to buy, she must take into account, not only the price of the good she wishes to purchase, but also the prices of all other goods that are available. This allows the consumer to define the relative prices of goods, which determines what she gives up when she purchases something. The third ingredient is how much money you have to spend. Although a consumer may want to buy as many goods and services as she wishes, she can only purchase as much as her limited income allows.

2. The buyer’s problem states that consumers spend money to maximize their benefits, which depend on tastes and preferences, and consider trade-offs to achieve it. Is a consumer’s buying decision based on her budget set or budget constraint?

Answer: Your buying decision is based on your budget constraint; because you can only buy goods based on your level of income to maximize your benefits. The budget set is the set of all possible bundles of goods and services that you can buy with your income, regardless of whether you use your entire income or not.

3. Consider the following figures where the light blue line (lighter line in black and white) is the original budget constraint for a consumer and the darker line is the new one. Examine each case and explain what could have caused the change.

(a)

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(b)

(c)

Answer: In panel (a), the budget constraint pivots inward along the x-axis. This can be explained by an increase in the price of good X.

In panel (b), the budget constraint pivots outward along the y-axis. This can be explained by a decrease in the price of good Y.

In panel (c), the budget constraint shifts outward. This means that the total income that the consumer is willing and able to spend on goods X and Y has increased. This shift could also be the result of an equal percentage decrease in the price of both goods. For example, a 100 percent increase in income would have the same effect on a budget constraint as a 50 percent decline in the price of both goods.

4. Why is a consumer’s satisfaction maximized when the marginal benefit from the last dollar spent on one good is equal to the marginal benefit from the last dollar spent on another good?

Answer: The marginal benefit from each additional dollar spent should be equal across various goods in order to maximize overall well-being. If these marginal units (last units) of satisfaction are not equal, then the consumer can be made better off by shifting consumption toward the good that yields more satisfaction at the margin. Hence, equilibrium occurs at the point where satisfaction from the last dollar spent is equal for all goods.

5. What is meant by consumer surplus? How is it calculated?

Answer: Consumer surplus is the difference between the willingness to pay and the price paid for a good. It is measured as the area between the consumer’s willingness to pay and the market price up to the equilibrium quantity.

6. Consider the following supply and demand diagram:

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Identify which of the three areas labeled A, B, and C represents consumer surplus in this market.

Answer: Consumer surplus is calculated as the area of the triangle above the market price and below the demand curve. In this diagram, the consumer surplus is denoted by area A.

7. What happens to consumer surplus when price decreases? Explain with an example and supplement it with a diagram.

Answer: When the price decreases, consumer surplus increases. The lower the price, the higher the difference between the willingness to pay and the market price. Furthermore, the lower the price, the higher the quantity demanded. However, if the good price drops below the market price, manufacturing the product will be less profitable for the producers, so the market will have a shortage of that product. In this case, the consumer surplus due to the decrease in price might be offset by the fact that consumers cannot purchase the good they want. For example, suppose you want to buy books. The price has just decreased due to lower demand. The consumer surplus for you is higher because your willingness to pay is higher than the price of the good. Students’ diagrams may differ.

8. Can consumer surplus be negative? Explain your answer.

Answer: Consumer surplus is the difference between what a buyer is willing to pay for a good and what the buyer actually pays. In other words, it will become negative if the price of a good is higher than the willingness to pay. However, if that is the case, the buyer will not buy the good and the consumer surplus will be zero, but not negative.

9. Assume that the price of a beverage, Cola, doubles. As a result, the quantity demanded for Cola falls as consumers switch to a less-expensive alternative, Spritzer. What type of elasticity is seen in this situation? What are the other forms of elasticity?

Answer: Price elasticity of demand is seen in this situation. The sensitivity of the demand for Cola with regard to changes in other economic variables, like the price of substitute goods, for instance Spritzer; and the consumer’s income is referred to as demand elasticity. It is an important concept because it takes into account the size of a change along with the direction of change. The other forms include the cross-price elasticity of demand and the income elasticity of demand.

10. Can a price increase lead to lower revenue? Suppose a bookstore sells 15 books a day. The price of one book increases from $10 to $12. At this price, the store sells 10 books a day. Discuss the revenue of the store in this case.

Answer: If the store sells 15 books a day with $10, the yielding revenues are $150 (15 books X $10). After the price increases to 20 percent, the yielding revenues are $120 (10 books X $12). When the price increases with 20 percent, the percentage change in quantity demanded decreases by 40 percent (5/20). This means that the price elasticity of demand is 2 (40 percent/20 percent). When the price elasticity of demand is greater than 1, the percentage change in quantity demanded is greater than the percentage change in price. This means that the price increase leads to lower revenues.

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11. How does the number of available substitutes determine the price elasticity of demand?

Answer: If a good has more substitutes, consumers will be more likely to switch from that good to another when the price of that good rises. In other words, consumers will become more responsive to price changes. Therefore, as the number of available substitutes rises, price elasticity of demand increases.

12. How is cross-price elasticity of demand used to determine whether two goods are substitutes or complements?

Answer: If the cross-price elasticity of demand for two goods is negative then two goods are complements. If the cross-price elasticity of demand for the two goods is positive then wo goods are considered substitutes. Consider coffee and tea, which are surely substitutes: If the price of tea rises, I will switch to coffee and therefor demand for coffee rises. Thus there is a positive relationship between the price of tea and the demand for coffee. In other words, the cross-price elasticity is positive.

13. What does a negative income elasticity of demand mean?

Answer: A negative income elasticity of demand indicates a negative relationship between income and quantity demanded. For a good with a negative income elasticity of demand, when income rises, the quantity demanded falls, and vice versa. This good is called an inferior good.

14. Examine the accuracy of the following statement: “Though Apple iPhones and Samsung mobiles are substitute goods, if the price of an iPhone increases, consumers will still buy them because of brand preference.”

Answer: From the chapter, we learned that two goods are substitutes when both goods have the same characteristics, as one can replace another with the same benefits for the consumer. They are not perfect substitutes, because they are not similar, but when the price of Apple increases, this means that the demand for Samsung will increase. This means that the rise in price of one leads to a right shift in the demand curve for the other.

15. If a good is considered to be a luxury good, does it mean that the law of demand does not hold?

Answer: Luxury goods are those items the demand for which increases more than proportionately with an increase in income and therefore the income elasticity of demand is greater than one. This does not mean that the law of demand does not hold. As price increases, the quantity demanded for that good will still decline regardless of the income elasticity of demand.

16. Examine the accuracy of the following statement: “Given that healthcare services are considered luxury goods based on income elasticity, fewer people can afford to receive assistance to cure their diseases.”

Answer: We learned from the chapter that goods with income elasticity above 1 are luxury goods, so, based on the given examples, healthcare can be considered a luxury good because of its income elasticity of 1.18. However, this is an unsettled issue because healthcare is more a necessity than a luxury good. Income elasticity greater than 1 implies that consumers' preferences drive health expenditure above income growth and could explain the increase in the share of health care in GDP.

A1. What is an indifference curve? Can two indifference curves intersect? Explain your answer.

Answer: All bundles of goods along an indifference curve are equally preferred. Each indifference curve shows a different level of satisfaction. If two indifference curves intersect, this means that at the point of intersection, the same bundle of goods leads to two different levels of satisfaction. Since this is not logically possible, indifference curves cannot intersect. The higher the indifference curve, the higher the level of satisfaction.

A2. Explain the income and substitution effects of an increase in the price of one good on an individual’s consumption choice.

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Answer: Since an increase in the price of one good reduces a consumer’s purchasing power (in other words, the consumer feels less wealthy), she is likely to buy less of both goods. This is called the income effect of a price increase. Also, since the increase in price will make the good more expensive relative to other good, the quantity purchased of that good will fall. This is called the substitution effect of the price increase.

A3. Consider indifference curves for goods X and Y. Suppose we plot the quantity of good Y on the vertical axis and the quantity of good X on the horizontal axis.

a. Why are indifference curves downward sloping?

b. What is the economic interpretation of the slope of an indifference curve?

c. Following what we learned in the Appendix to this chapter, indifference curves would flatten out as someone consumes more of good X and less of good Y. What are we assuming when we draw indifference curves that become flatter?

Answer:

a. Consumers are indifferent among all bundles on the same indifference curve. If indifference curves were upward sloping then a consumer would be indifferent between a bundle that has more of good X and more of good Y than a second bundle that includes less of both goods. This would make no sense, and so indifference curves must be downward sloping.

b. The slope of an indifference curve shows a consumer’s willingness to trade good Y for an additional unit of good X.

c. If indifference curves become flatter then we are assuming that consumers are less willing to give up Y in return for an additional unit of X as they consume more X and less Y.

Problems

1.

2. Elisa earns $2,500 per month and spends her income on flowers and vegetables. Suppose the price of flowers is $80 and the price of vegetables is $120.

a. Draw a diagram for Elisa’s budget constraint, identifying its slope and intercepts.

b. Suppose the price of the flowers falls to $60, Elisa’s income remains $2,500, and the price of vegetables falls to $90. Draw a new diagram that shows Elisa’s new budget constraint, identifying its slope and intercepts.

c. Now suppose the price of flowers rises to $90, the price of vegetables remains at $90, and Elisa’s income rises to $3,000. Draw a new diagram that shows Elisa’s new budget constraint, identifying its slope and intercepts.

d. Compare the budget constraints you drew to answer parts (a), (b) and (c) of this question.

Answer:

a. The original budget constraint is:

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b. After both prices decreases, the new budget constraint is:

c. After the price of flower increases, the new budget constraint is:

d. The budget constraints a and b are the same. The ratio of prices, or the slope, is the same in part a (80/120) and part b (60/90), but is different in part c (90/90).

3. Jean has a budget of $100, which she wants to spend on pens that are priced at $5 per pen and paper that is priced at $10 per bundle of 100 sheets.

a. Draw Jean’s budget constraint. Find its slope and the opportunity cost of buying pens and bundles of paper.

b. If Jean’s budget set is $100, what are the possible combinations of satisfying Jean’s needs and maximizing his benefits by consuming these two goods?

c. What happens to Jean’s budget constraint and budget set if he wants to buy 10 pens and 5 bundles of paper? What about 6 pens and 4 bundles of paper?

Answers:

a. The budget constraint is:

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We compute the opportunity cost of buying pens by dividing the y-intercept (10) by the x-intercept (20), which is equal to 0.5. This means that the opportunity cost of buying 1 pen is equal to 0.5 units of paper. The opportunity cost of buying paper is computed by dividing the x-intercept (20) by the y-intercept (10), which is equal to 2. This means that the opportunity cost of buying 1 unit of paper is equal to 2 pens.

b. A combination of the two goods that lies on the budget constraint will satisfy the equation:

5x + 10y = 100

All the possible combinations are in the table below:

Bundle Quantity of pens Quantity of paperA 0 10B 2 9C 4 8D 6 7E 8 6F 10 5G 12 4H 14 3I 16 2J 18 1K 20 0

c. If Jean wants to buy 10 pens and 5 units of paper, he uses exactly $100. Therefore, this combination will lie on its budget constraint, which equals its budget set. If Jean wants to buy 6 pens and 4 units of paper, he uses $70. Since he does not exhaust his income of $100, this combination will lie below his budget constraint, but will be part of his budget set.

4. Thomas has an income of $500, and he consumes two goods: rods and baits. The price of a rod is $100, and the price of bait is $50.

a. Suppose Thomas receives a prize of 4 rods. Draw Thomas’s budget set.

b. Now suppose Thomas lost $100. Draw Thomas’s new budget set.

Answers:

a. Thomas’s budget set is the area ABC. If Thomas spends all his income on baits, he would buy $500 ÷ $50 =10 baits. If he spends all his income on rods, he would buy $500 ÷ $100 = 5. He

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receives a prize comprising 4 rods, and so he would be able to consume a maximum of 5 + 4 = 9 rods.

b. Thomas’s budget set is the area CDEF.

5. Suppose Gia has $800 to spend on art books and design books. The price of an art book is $40 and the price of a design book is $50.

a. Draw the budget constraint and show its slope.

b. Suppose the price of a design books is $40. Draw the budget constraint and explain the changes.

c. Suppose the price of both books decreases with 25 percent. Draw the budget constraint and explain the changes.

d. Suppose Gia has $1,000. Draw the budget constraint and explain the changes.

e. Can you identify the bundle that Gia is going to consume? Explain.

Answer:

a. Gia will be able to buy 20 art books and 16 design books. The budget constraint is:

b. If the price of the design books drops to $40, then Gia will be able to buy 20 units. The budget line slope is 1, so both kinds of books bring the same satisfaction to Gia for its income.

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c. If the price of the books decreases by 25 percent, then the price of an art book will be reduced to $32 from $40, and to $40 from $50 for a design book. In this case, Gia will buy 25 art books and 20 design books. The budget constraint is:

d. Gia’s income increased to $1,000. Her budget constraint would shift outward, parallel to the original budget constraint. Gia will be able to buy 25 art books and 20 design books. The budget constraint is the same as in part c.

e. We do not have any information about Gia’s preferences, so we cannot determine exactly how many art books or design books she would choose for its budget constraint.

6. Kira will be attending university soon for which she needs new pairs of jeans (j) and shirts (s). Her budget constraint is given by $40j + $20s = $120.

a. What are the bundles of her budget constraint? Draw a table with her possibilities and a diagram.

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b. What is the opportunity cost of jeans in terms of shirts?

c. Suppose that the total benefits for each good is shown in the table below. What is the marginal benefit of the third pair of jeans?

Total Benefit (Jeans)

Total Benefit(Shirts)

1 15 302 35 503 50 60

d. What is the marginal benefit per dollar spent on each of the two goods?

Answers:

a. Kira’s bundles and budget constraint are shown below:

Bundles of the Budget Constraint

Bundle Quantity of jeans

Quantity of shirts

A 0 6B 1 4C 2 2D 3 0

b. The opportunity cost of jeans in terms of shirts is 2. This means that Kira has to give up 2 shirts to buy a pair of jeans.

c. The marginal benefit of the third pair of jeans is 25.

d. The marginal benefit for the dollar spent for the two goods is:

Jeans $40 Shirts $20

Total Benefit

(A)

Marginal

Benefits (B)

Marginal Benefits per Dollar Spent

B/$40

Total Benefit

(A)

Marginal

Benefits (B)

Marginal Benefits per Dollar Spent

B/$201 15 15 0.37 30 30 1.52 25 10 0.25 50 20 13 30 5 0.12 60 10 0.5

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7. The total benefit for burgers and beers is given below. Burgers cost $10 and beers cost $20.

Total Benefit (Burgers) Total Benefit (Beers)

1 15 30

2 30 50

3 45 60

4 60 65

a. What is the marginal benefit of the third beer?

b. What is the “bang for the buck” of a second burger?

c. Using the “bang for the buck” principle, explain why it would never be optimal to purchase two burgers and two beers.

Answer:

a. 60 - 50 = 10 is the marginal benefit of the third beer.

b. 30 - 15 = 15 is the marginal benefit of the second burger. Divide this by price (15/$10 = 1.5) to get the increased benefit for each additional dollar spent on burgers. This is the “bang for the buck” of spending money on a second burger.

c. An extra dollar spent on burgers is worth 1.5, while for beers it is (50-30)/$20 = 1. Since 1.5 > 1, it would be better to spend more on burgers. In fact, if you purchase one fewer beer then you can afford two more burgers. You would thus have 4 burgers and 1 beer and total benefit would increase from 30 + 50 = 80 to 60 + 30 = 90.

8. Consider Sophia and Marcus’ total expenditure on sandwiches:

PriceTotal expenditure (per

month)Sophia Marcus

$5 $90 $50$4 $80 $60

a. Use the midpoint formula to calculate the price elasticity of demand for Sophia when the price of sandwiches increases from $4 to $5.

b. Use the midpoint formula to calculate the price elasticity of demand for Marcus when the price of sandwiches increases from $4 to $5.

c. Based on your answers from parts a and b, explain why Sophia would spend more on sandwiches, while Marcus spends less when the price of sandwiches increases.

Answer:

a. As the price of sandwiches increases from $4 to $5, Sophia’s demanded quantity for sandwiches decreases from $80/$4 = 20 to $90/$5 = 18.

Applying the formula for arc elasticity:

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The price elasticity of demand = (18 – 20)/[(18 + 20)/2] ÷($5 – $4)/[($5 + $4)/2] = −0.47b. As the price of sandwiches increases from $4 to $5, Marcus’s quantity demanded for sandwiches

decreases from $60/$4 = 15 to $50/$5 = 10. The price elasticity of demand = (10 – 15)/[(10 + 15)/2] ÷ ($5 – $4)/[($5 + $4)/2] = −1.8

c. According to the calculation in (a), Sophia’s demand for sandwiches is inelastic (ED < 1). As the price of sandwiches increases, the percentage increase in price is higher than the percentage decrease in quantity demanded. Therefore, Sophia’s total expenditure on sandwiches rises.

According to the calculation in (b), Marcus’s demand for sandwiches is elastic (ED > 1). As the price of sandwiches increases, the percentage decrease in quantity demanded is higher than the percentage increase in price. Therefore, Marcus’s total expenditure on sandwiches falls.

9. Calculate the cross-price elasticities in case of a decrease in the price of cabbages with 20 percent, an increase in the demand for tomatoes with 15 percent and a decrease in the demand for artichokes with 10 percent. Comment on whether tomatoes and artichokes can substitute or complement the cabbage.

Answer: The cross-price elasticity in case of cabbages and tomatoes is 0.75, which is positive and means that the two goods are substitutes. The cross-price elasticity in case of cabbages and artichokes is −0.5, which is negative, and means that the two goods are complements.

10. Three years after graduating from college you get a promotion and a 20% raise. Your consumption habits change accordingly. Use the following information to determine your income elasticity of demand and state whether the good is a normal good, inferior good, or luxury good.

a. You consume 10% fewer frozen hot dogs.

b. You consume 5% more pork chops.

c. You consume 30% more sockeye salmon.

Answer:

a. –10%/20% = -0.5. Since this is negative, frozen hot dogs are an inferior good.

b. 5%/20% = 0.25. Since this is positive, pork chops are a normal good.

c. 30%/20% = 1.5. Since this is not only positive, but also greater than one, sockeye salmon is considered a luxury good.

11. Starbucks and Dunkin’ Donuts are two of the largest eatery chains that specialize in coffee. Despite being founded 20 years after Dunkin’ Donuts, Starbucks has grown aggressively and is now a substantially larger company. Examine the following statements and identify the ones that could explain this outcome.

a. Starbucks generated $16.8 billion in revenue, while Dunkin’ brands reported sales of $828.9 million.

b. Nearly all of Dunkin’ brands’ locations are franchises, while over 51% of Starbucks locations are company operated.

c. Dunkin’ Donuts sells coffee, donuts, and foods, while Starbucks sells a typical coffee house experience.

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d. Both companies attract price-sensitive customers.

e. Starbucks is a destination rather than a simple distribution location.

Answer:

a. The fact that Starbuck’s revenues have been higher than Dunkin’ Donuts explains the success that its products have on the market.

b. Dunkin' Donuts' higher exposure to franchise and rental income leads to a fundamentally different business from Starbucks' largely owner-operator model. The cost of goods sold is much higher for Starbucks than Dunkin’ Donuts, which is not obligated to purchase equipment for franchise locations.

c. Dunkin’ Donuts has a more fast-food approach than Starbucks, which targets customers with higher disposable income and are more willing to pay for higher quality materials.

d. Dunkin’ Donuts is focused on the middle class, and Starbucks is focused on wealthier customers. Only Dunkin’ Donuts attracts price-sensitive customers, as it has more competitive prices and its management intent is to be the lowest cost provider in the market while maintaining quality above an acceptable minimum.

e. Starbucks locations are designed with the comfort of their customers in mind, offering internet services and comfortable decor for those looking for a place to work, read, or relax.

See: http://www.investopedia.com/articles/markets/120215/starbucks-vs-dunkin-donuts-comparing-business-models.asp

12. Examine the following statements and determine how price elasticity of demand changes:

a. Applebee has decided to raise the price of burgers while keeping the price for pizzas and pastas the same.

b. Tom wants to buy a house, but the price just increased by 10 percent.

c. Facebook shares have fallen by 15 percent.

d. The price of electronic goods has risen by 50 percent.

Answer:

a. If the clients are likely to switch to pizza or pasta in case the burgers’ price is too high for them, then the price elasticity of demand increases because of the closeness of substitutes.

b. If Tom really wants to buy the house knowing that the price has risen 10 percent, then the price elasticity of demand increases because of the budget share spent on the good.

c. If investors still want to buy Facebook shares, hoping that they will increase, then the price elasticity of demand decreases because of the closeness of substitutes.

d. If the consumers do want those expensive electronics and buy them no matter how much the price has risen, then the price elasticity of demand increases because of the budget spent on the goods.

13. Suppose demand is given by QD = 6 - P.

a. Graph the demand curve.

b. If the price were $2, what is consumer surplus?

c. If the price goes up to $4, what is the new consumer surplus? This new surplus should be lower; explain why.

Answers:

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a. See below. When price (P) is $0, quantity must be 6. When quantity is 0, price must be $6; these values give you the intercepts of the graph.

b. At a price of $2, the quantity is QD = 6 – 2 = 4, as shown in the graph. The triangle above $2 is the consumer surplus: (1/2)*(base)*(height) = (1/2)*4*($6 - $2) = $8.

c. At a price of $4, the quantity is QD = 6 – 4 = 2, as shown in the graph. The triangle above $4 is the new consumer surplus: (1/2)*(base)*(height) = (1/2)*2*($6 - $4) = $2. Consumer surplus has decreased for two reasons: Some buyers no longer consume; and buyers who remain in the market must pay a higher price and so enjoy lower surplus.

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