Chapter 20 - Consumer Choice.doc

308 Miller•Economics Today, Nineteenth Edition Chapter 20 Consumer Choice299 Answers to Questions for Critical Analysis Why a Consumer Optimum Can Include “Unlimited” Consumption in a Pay-by-the-Minute Café (p. 442) What fact ultimately constrains consumption of any item said to be available in “unlimited” amounts at a fixed price? (Hint: Recall the law of diminishing marginal utility) Because of the law of diminishing marginal utility, the marginal utility derived from the consumption of any item would ultimately become zero. Consumers try to avoid consuming any item with a negative marginal utility, even if the item is available at a price of zero. Monitoring the Provision of Legal Services to Ensure Attainment of a Consumer Optimum (p. 444) To ensure attainment of a consumer optimum, why might a client seek to ensure that the hourly legal-service fee continues to apply to constant-quality hours of legal services? Consumer optimum requires that a client would ensure that the last dollar spent on each quality-hour of legal services yields the same amount of marginal utility as the last dollar spent on other items. Do “Big-Box” Discount Retailers Contribute to Higher Obesity Rates among Consumers? (pp. 446–447) What happened to the marginal utility derived from food consumption as people responded to lower food prices by purchasing more food? People responded to lower food prices by purchasing more food, and more food consumption in turn reduced their marginal utility from consumption of food items. You Are There Confronting the Challenge of Comparing Levels of Disutility from Pain (p. 449) 1. Why might two people diagnosed with exactly the same type of pain-inducing physical problem opt to place different levels of daily stress on their bodies? The level of disutility or body stress from a given type of pain may be different across different people. 2. What does Michel’s experience imply about the idea of computing levels of utility derived from consumption and contrasting these utilities across individuals? Explain. Comparing different levels of utility derived from consumption and contrasting these utilities across individuals are effective ways to gauge people’s pain because this method provides more reliable predictions about the levels of pain actually experienced by the people. Issues and Applications Two Different Utility Issues Associated with a “Pacemaker for the Stomach” (pp. 449–450) 1. Explain why it must be true, even for someone trying to lose weight, that the last bite of food consumed must have positive marginal utility at a consumer optimum? People will stop food consumption only if an additional bite of food generates zero or negative marginal utility. Hence, even for those trying to lose weight, the last bite of food consumed must have positive marginal utility at a consumer optimum. 2. What is true of the marginal utility per dollar spent on a stomach pacemaker compare with the marginal utility per dollar of food consumed during that interval? The marginal utility per dollar spent on a stomach pacemaker must equal to the marginal utility per dollar of food consumed. Research Project 1. Learn about one example of a stomach pacemaker device in the Web Links in MyEconLab. 2. Read the Food and Drug Administration’s description of how a stomach pacemaker works in the Web Links in MyEconLab. Appendix F—More Advanced Consumer Choice Theory On Being Different: A difference curve is a curve composed of a set of consumption alternatives, each of which yields the same total amount of satisfaction. (See Figure F-1.) Properties of Indifference Curves: Downward Slope: The indifference curve has a negative slope. (See Figure F-2.) Curvature: The indifference curve is curved. (See Figure F-1.) Imagining a Straight-Line Indifference Curve (See Figure F-2.) Convexity of the Indifference Curve (See Figure F-1.) B. The Marginal Rate of Substitution: The change in the quantity of one good that just offsets a one-unit change in the consumption of another good, such that total satisfaction remains constant. (See Table F-1.) C. The Indifference Map: A set of indifference curves. (See Figure F-4.) The Budget Constraint and the Consumer Optimum: The budget constraint includes all of the possible combinations of goods that can be purchased (at fixed prices) with a specific budget. Slope of the Budget Constraint: The budget constraint is a line that slopes downward from left to right. (See Figure F-5.) Consumer Optimum Revisited: Consumer optimum is the tangency point at which the marginal rate of substitution is just equal to feasible rate of exchange between two goods. (See Figure F-6.) Deriving the Demand Curve: The demand curve can be derived by changing the price of one good, so that the budget line rotates. (See Figure F-7.) Answers to Problems 20-1. The campus pizzeria sells a single pizza for $12. If you order a second pizza, however, the pizzeria charges a price of only $5 for the additional pizza. Explain how an understanding of marginal utility helps to explain the pizzeria’s pricing strategy. The campus pizzeria indicates by its pricing policy that it recognizes the principle of diminishing marginal utility. As shown in Figure 20-1 (substituting slices of pizza for apps), a customer’s marginal utility for the second pizza is typically lower than for the first. Thus, the customer is likely to value the second pizza less and, therefore, only be willing to pay less for it. 20-2. As an individual consumes more units of an item, the person eventually experiences diminishing marginal utility. This means that to increase marginal utility, the person must consume less of an item. Explain the logic of this behavior using the example in Problem 201. To raise marginal utility, an individual would consume fewer pizzas. As long as marginal utility is positive, however, the individual’s total utility is rising with the second pizza even though marginal utility is falling. 20-3. Where possible, complete the missing cells in the table below. Number of Cheeseburgers Total Utility of Cheeseburgers Marginal Utility of Cheeseburgers Bags of French Fries Total Utility of French Fries Marginal Utility of French Fries 0 0 — 0 0 — 1 20 — 1 — 10 2 36 — 2 — 8 3 — 12 3 — 2 4 — 8 4 21 — 5 — 4 5 21 — The total utility of the third, fourth, and fifth cheeseburgers is 48, 56, and 60, respectively. The marginal utility of the first and second cheeseburgers is 20 and 16, respectively. The total utility of the first, second, and third bags of French fries is 10, 18, and 20, respectively. The marginal utility of the fourth and fifth bags of French fries is 1 and 0, respectively. 20-4. From the data in Problem 20-3, if the price of a cheeseburger is $2, the price of a bag of French fries is $1, and you have $6 to spend (and you spend all of it), what is the utility-maximizing combination of cheeseburgers and French fries? The utility-maximizing combination of cheeseburgers and bags of French fries that equates marginal utility per dollar spent and exhausts the total $6 budget is two cheeseburgers and two bags of French fries. The individual purchases 2 cheeseburgers at $2 each, spends $4 on cheeseburgers, and has a marginal utility per dollar spent equal to the ratio of 16 units of utility to $2, or 8 units of utility per dollar. The individual buys 2 bags of French fries at $1 per bag, spends $2 on cheeseburgers, and has a marginal utility per dollar spent equal to the ratio of 8 units of utility to $1, or 8 units of utility per dollar. Thus, the individual equalizes marginal utility per dollar spent at 8 units of utility per dollar and spends the available $6. 20-5. Return to Problem 20-4. Suppose that the price of cheeseburgers falls to $1. Determine the new utility-maximizing combination of cheeseburgers and French fries. The new utility-maximizing combination of bags of French fries and cheeseburgers that equates marginal utility per dollar spent and exhausts the total $6 budget is four cheeseburgers and two bags of French fries. The individual purchases 4 cheeseburgers at $1 each, spends $4 on cheeseburgers, and has a marginal utility per dollar spent equal to the ratio of 8 units of utility to $1, or 8 units of utility per dollar. The individual buys 2 bags of French fries at $1 per bag, spends $2 on cheeseburgers, and has a marginal utility per dollar spent equal to the ratio of 8 units of utility to $1, or 8 units of utility per dollar. Thus, the individual equalizes marginal utility per dollar spent at 8 units of utility per dollar and spends the available $6. 20-6. Suppose that you observe that total utility rises as more of an item is consumed. What can you say for certain about marginal utility? Can you say for sure that it is rising or falling or that it is positive or negative? When total utility is rising, the only thing we can say about marginal utility for certain is that it is positive. 20-7. You determine that your daily consumption of soft drinks is 3 and your daily consumption of tacos is 4 when the prices per unit are 50 cents and $1, respectively. Explain what happens to your consumption bundle, and, after your consumption choices adjust, to the marginal utility of soft drinks and the marginal utility of tacos, when the price of soft drinks rises to 75 cents. Other things being equal, when the price of soft drinks rises, the substitution effect comes into play, and the individual tends to consume less of the more expensive item, soft drinks, and more of the item with the unchanged price, tacos. Hence, the marginal utility of soft drinks rises, and the marginal utility of tacos falls. 20-8. At a consumer optimum, for all goods purchased, marginal utility per dollar spent is equalized. A high school student is deciding between attending Western State University and Eastern State University. The student cannot attend both universities simultaneously. Both are fine universities, but the reputation of Western is slightly higher, as is the tuition. Use the rule of consumer optimum to explain how the student will go about deciding which university to attend. The student should compare the marginal utility per tuition dollar spent at the two Texas universities. Assuming that a “unit” of college is a degree, a Texas high school student should divide the additional satisfaction derived from a degree at each university by the total tuition it would take to earn a degree at each institution. The university with the higher marginal utility per tuition dollar is the one the student should attend. 20-9. Consider the movements that take place from one point to the next (A to B to C and so on) along the total utility curve at the next column as the individual successively increases consumption by one more unit, and answer the questions that follow. a. Which one-unit increase in consumption from one point to the next along the total utility curve generates the highest marginal utility? b. Which one-unit increase in consumption from one point to the next along the total utility curve generates zero marginal utility? c. Which one-unit increase in consumption from one point to the next along the total utility curve generates negative marginal utility? a. Of all the possible one-unit increases in consumption displayed, the movement from point A to point B generates the highest marginal utility. Total utility rises by 5 units between these points, so the marginal utility of the first unit consumed is 5 units. b. Between points E and F, a one-unit increase in the quantity consumed leaves total utility unchanged at 11 units, so marginal utility is equal to zero. c. Between points F and G, a one-unit increase in the quantity consumed causes total utility to decline from 11 units to 10 units, so marginal utility is negative and equal to ?1 unit. 20-10. Draw a marginal utility curve corresponding to the total utility curve depicted in Problem 20-9. 20-11. Refer to the table below. If the subscription price for a sports app is $2 per week, the subscription price of a game app is $1 per week, and a student has $9 per week to spend, what quantities will she purchase at a consumer optimum? Quantity of Sports Apps per week Marginal Utility (utils) Quantity of Game Apps per Week Marginal Utility (utils) 1 1,200 1 1,700 2 1,000 2 1,400 3 800 3 1,100 4 600 4 800 5 400 5 500 6 100 6 200 For this consumer, at these prices the marginal utility per dollar spent on 2 sports apps is 500 units of utility per dollar, and the marginal utility per dollar spent on 5 game apps is also 500 units of utility per dollar. In addition, the entire budget of $9 is spent at this combination, which is the consumer optimum. 20-12. Refer to the following table for a different consumer, and assume that each year this consumer buys only annual subscriptions to economics statistics apps and subscriptions to office productivity apps. The price of a subscription to each type of economics statistics app is $2 per year, and the price of a subscription to each office productivity app is $60 per year. If the consumer’s available income is $128 per year, what quantity of each item will the individual purchase each week at a consumer optimum? Quantity of Subscriptions to Economics Statistics Apps per Year Total Utility (utils) Quantity of Subscriptions to Office Productivity Apps per Week Total Utility (utils) 1 40 1 400 2 60 2 700 3 76 3 850 4 86 4 950 5 91 5 1,000 6 93 6 1,025 The table below displays the marginal utilities and the values of marginal utility per dollar spent at a price of $2 per economic statistics app and a price of $60 per office productivity app. The marginal utility per dollar spent is equalized at a value of 5, which yields a consumer optimum of 4 economic statistics apps and 2 office productivity apps per week, for which the consumer’s entire available income of $128 is spent. Note that the marginal utility per dollar spent is also equalized at 2.50 if 5 economic statistics apps and 3 office productivity apps are consumed, but the individual has insufficient income for this weekly consumption combination. Quantity of Hot Dogs per Week Total Utility Marginal Utility Marginal Utility per Dollar Spent Quantity of Baseball Games per Week Total Utility Marginal Utility Marginal Utility per Dollar Spent 1 40 — — 1 400 — — 2 60 20 10 2 700 300 5 3 76 16 8 3 850 150 2.5 4 86 10 5 4 950 100 1.7 5 91 5 2.5 5 1000 50 0.8 6 93 2 1 6 1025 25 0.4 20-13. In Problem 20-12, if the consumer’s income rises to $190 per week, what new quantities characterize the new consumer optimum? The marginal utility per dollar spent is equalized at 2.50 if 5 economic statistics apps and 3 office productivity apps are consumed, and this consumption combination just exhausts the now-available $190 in weekly income. 20-14. At a consumer optimum involving goods A and B, the marginal utility of good A is twice the marginal utility of good B. The price of good B is $3.50. What is the price of good A? The price of good A is twice the price of good B, or 2 $3.50 per unit = $7.00 per unit. 20-15. At a consumer optimum involving goods X and Y, the marginal utility of good X equals 3 utils. The price of good Y is three times the price of good X. What is the marginal utility of good Y? The marginal utility of good Y is three times the marginal utility of good X, or 3 × 3 utils = 9 utils. 20-16. At a consumer optimum involving goods A and B, the marginal utility of good A is 2 utils, and the marginal utility of good B is 8 utils. How much greater or smaller is the price of good B compared with the price of good A? Because the marginal utility of good B is four times greater than the marginal utility of good A, at a consumer optimum the price of good B must be four times greater than the price of good A. 20-17. At a consumer optimum involving goods X and Y, the price of good X is $3 per unit, and the price of good Y is $9 per unit. How much greater or smaller is the marginal utility of good Y than the marginal utility of good X? Because the price of good Y is three times greater than the price of good X, the marginal utility of good Y must be three times greater than the price of good X. 20-18. The marginal utility that an individual would experience if she were to consume the first unit of a digital app is 15 utils, and the marginal utility that she would experience if she were to consume a second unit is 18 utils. If one app is the amount that the individual decides to consume, what is the person’s total utility? Consuming no digital apps would yield 0 units of total utility, so the fact that marginal utility derived from the 1st unit is 15 utils implies that the total utility of consuming 1 unit is 15 utils. 20-19. Take a look at Figure 20-1. Suppose that the individual currently consumes 5 digital apps. What happens to the person’s total utility if he were to reduce his consumption to 4 units? Why does this fact imply that the marginal utility curve cuts through the horizontal axis of panel (c) between the fourth and fifth app consumed? As shown in the table in panel (a) and the graph in panel (b), reducing consumption from 4 apps to 5 leaves total utility unchanged at 20 utils. Hence, marginal utility between these two apps equals 0, which is the amount of marginal utility at the origin, which corresponds to the horizontal axis of the graph in panel (c). Thus, the marginal utility curve crosses this axis between units 4 and 5. 20-20. Consider Figure 20-1. If this individual were to contemplate consuming a seventh digital app and experience a total utility of 15 utils as a consequence, what would be the resulting marginal utility? Would the points on the total utility and marginal utility graphs in panels (a) and (b) lie higher and lower to the right of the current endpoints of those graphs? The marginal utility would be 15 utils – 18 utils = -3 utils, so the person would experience even more marginal disutility than for the 6th digital app consumed. The 15 utils in total utility for 7 apps would be lower than the 18 utils for 6 apps and the marginal utility of -3 for the 7th app would be lower than the -2 for the 6th app, so both new points would lie lower to the right on both graphs in panels (a) and (b). 20-21. Take a look at Table 20-1. Suppose that the price of each digital app falls to $3.30. At the same time, the price of each portable power bank increases to $5.37. Income remains unchanged at $26. Rework the marginal-utility-per-dollars-spent columns and round each amount to the nearest one-tenth. What are the quantities of digital apps and portable power banks now purchased by this consumer? As shown in the revised table that after redoing the columns, the marginal utility per dollars spent is now equalized at 6.7 units of utility per dollar spent. The quantity of digital apps purchased is 3, and the quantity of portable power banks bought is 3. Total and Marginal Utility from Consuming Digital Apps and Portable Power Banks on an Income of $26 (1) (2) (3) (4) (5) (6) (7) (8) Digital Apps per Period Total Utility of Digital Apps per Period (utils) Marginal Utility (utils) MUd Marginal Utility per Dollars Spent (MUd?/Pd) (price = $5.97) Portable Power Banks per Period Total Utility of Portable Power Banks per Period (utils) Marginal Utility (utils) MUp Marginal Utility per Dollar Spent (MUp?/Pp) (price = $2.70) 0 0 – – 0 0 – – 1 50.0 50.0 8.4 1 25 25 9.3 2 95.0 45.0 5.0 2 47 22 8.1 3 135.0 40.0 6.7 3 65 18 6.7 4 171.5 36.5 7.8 4 80 15 5.6 5 200.0 28.5 8.6 5 89 9 3.3 20-22. At the optimal quantities of digital apps and portable power banks determined in your answer to Problem 20-21, after rounding to the nearest 10 cents, is the $26 income all spent at the new consumer optimum? Spending on digital apps is now 3 apps times $5.97 per app, or $17.91, which rounded to the nearest ten cents is $17.90. Spending on portable power banks equals 3 portable power banks times $2.70, which equals $8.10. Total spending is $17.90 + $2.70 = $26, so all income is spent. 20-23. Consider figure 20-2, and suppose that the initial point is A. Explain why a decrease in the price of each digital app from $5 to $4 results in a change in the marginal utilities of digital apps in a direction that is consistent with re-attainment of a new consumer optimum at point B. At A, the marginal utility per dollar spent on apps was equalized with the marginal utility per dollar spent on any other item. When the price of apps falls, the marginal utility per dollar spent on apps rises. The rise in the quantity of app demanded causes the marginal utility of apps to drop, which pushes the marginal utility per dollar spent on apps back up toward consistency with a consumer optimum at B. Appendix F F-1. Consider the indifference curve illustrated in Figure F-1. Explain, in economic terms, why the curve is convex to the origin. The indifference curve is convex to the origin because of a diminishing marginal rate of substitution. As an individual consumes more and more of an item, the less the individual is willing to forgo of the other item. The diminishing marginal rate of substitution is due to diminishing marginal utility. F-2. Your classmate tells you that he is indifferent between three soft drinks and two hamburgers or two soft drinks and three hamburgers. a. Draw a rough diagram of an indifference curve containing your classmate’s consumption choices. b. Suppose that your classmate states that he is also indifferent between two soft drinks and three hamburgers or one soft drink and four hamburgers, but that he prefers three soft drinks and two hamburgers to one soft drink and four hamburgers. Use your diagram from part (a) to reason out whether he can have these preferences. a. The indifference curve appears in the figure. b. Your classmate cannot possibly have this set of preferences, because as stated the indifference curves intersect. F-3. The table below represents Sue’s preferences for bottled water and soft drinks, the combination of which yields the same level of utility. Combination of Bottled Water and Soft Drinks Bottled Water per Month Soft Drinks per Month A 5 11 B 10 7 C 15 4 D 20 2 E 25 1 Calculate Sue’s marginal rate of substitution of soft drinks for bottled water at each rate of consumption of water (or soft drinks). Relate the marginal rate of substitution to marginal utility. Sue’s marginal rate of substitution is calculated below: Combination of Bottled Water and Soft Drinks Bottled Water per Month Soft Drinks per Month MRS A 5 11 B 10 7 5:4 C 15 4 5:3 D 20 2 5:2 E 25 1 5:1 The diminishing marginal rate of substitution of soft drinks for water shows Sue’s diminishing marginal utility of bottled water. She is willing to forgo fewer and fewer soft drinks to get an additional five bottles of water. F-4. Using the information provided in Problem F-3, illustrate Sue’s indifference curve, with water on the horizontal axis and soft drinks on the vertical axis. Plotting points A through E yields Sue’s convex indifference curve, along which she obtains equal utility from the alternative combinations of bottled water and soft drinks F-5. Sue’s monthly budget for bottled water and soft drinks is $23. The price of bottled water is $1 per bottle, and the price of soft drinks is $2 per bottle. Calculate the slope of Sue’s budget constraint. Given this information and the information provided in Problem F-3, find the combination of goods that satisfies Sue’s utility maximization problem in light of her budget constraint. Given that water is measured along the horizontal axis and soft drinks are measured along the vertical axis, the slope of Sue’s budget constraint is the price of water divided by the price of soft drinks, or PW/PS = $1 per bottle of water/$2 per unit of soft drinks. The only combination of bottled water and soft drinks that is on Sue’s indifference curve and budget constraint is combination C, at which total expenditures on water and soft drinks equal (15 × $1) + (4 × $2) = $15 + $8 = $23. F-6. Using the indifference curve diagram you constructed in Problem F-4, add in Sue’s budget constraint using the information in Problem F-5. Illustrate the utility-maximizing combination of bottled water and soft drinks. As shown in the figure, the utility-maximizing combination C is the point at the indifference curve is just tangent to the budget constraint. At this point, Sue has allocated her consumption of bottled water and soft drinks consistent with attaining the maximum feasible utility given her available budget F-7. Suppose that at a higher satisfaction level than in Problem F-3, Sue’s constant-utility preferences are as shown in the table below. Calculate the slope of Sue’s new budget constraint using the information provided in Problem F-5. Supposing now that the price of a soft drink falls to $1, find the combination of goods that satisfies Sue’s utility maximization problem in light of her budget constraint. Combination of Bottled Water and Soft Drinks Bottled Water per Month Soft Drinks per Month A 5 22 B 10 14 C 15 8 D 20 4 E 25 2 With the quantity of bottled water measured along the horizontal axis and the quantity of soft drinks measured along the vertical axis, the slope of Sue’s budget constraint is the price of water divided by the price of soft drinks. This ratio equals ½. The only combination of bottled water and soft drinks that is on Sue’s indifference curve and budget constraint is combination C, where expenditures on water and soft drinks total $23. F-8. Illustrate Sue’s new budget constraint and indifference curve in a diagram from the data in Problem F-3. Illustrate also the utility-maximizing combination of goods. As shown in the figure, when the price of soft drinks drops to $1, the slope of the budget constraint changes to $1 per bottle of water/$1 per unit of soft drink = 1. Hence, the budget constraint rotates outward, and Sue can reach a new point of consumer optimum at the point where the higher indifference curve is tangent to the new budget constraint F-9. Given your answers to Problems F-5 and F-7, are Sue’s preferences for soft drinks consistent with the law of demand? Yes, Sue’s revealed preferences indicate that her demand for soft drinks obeys the law of demand. When the price of soft drinks declines from $2 to $1, her quantity demanded rises from 4 to 8. F-10. Using your answer to Problem F-8, draw Sue’s demand curve for soft drinks. In the figure, the two price combinations from Problem F-9 have been drawn, and these two points lie along the demand curve. Selected References Ferguson, C.W., “Substitution Effect in Value Theory: A Pedagogical Note,” Southern Economic Journal, Vol. XXVI, 1960, pp. 310–314. 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