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CHAPTER 5 CONSUMER CHOICE ANSWERS TO ONLINE REVIEW QUESTIONS 1. The prices of the two goods and the consumer’s income are always assumed constant along a budget line. 2. A change in income will shift the budget line in a parallel fashion—increases in income shift the budget line outward and away from the origin, decreases shift it inward and nearer the origin. Changes in income alone do not affect the budget line’s slope. A change in one or both prices will rotate the budget line and change its slope. For example, a decrease in the price of the good measured on the horizontal axis will cause a rotation of the budget line around its vertical axis intercept; the rotation will result in a horizontal intercept farther to the right. 3. [Using the Marginal Utility Approach] Total and marginal are often confused. However, marginal always refers to the change in the total that results from one more of something, e.g., one more unit of consumption or production. Marginal utility, for example, represents the change in total utility from the consumption of one more unit of a good. 4. [Using the Marginal Utility Approach] The law of diminishing marginal utility states that marginal utility declines as more of a good is consumed. It is a reasonable assumption for most goods: The more of a good one consumes, the less additional satisfaction is derived from each additional unit. There are, indeed, exceptions to the law. One example might be found among collectors. As the collection becomes more complete, the marginal utility of additional paintings might actually increase. Marginal utility would be negative for any good that a consumer dislikes. An additional unit consumed in this case would decrease utility. One example is garbage. 5. “Logically consistent” preferences are transitive. For example, if A is preferred to B, and B to C, then A should be preferred to C. In addition, economists assume that a consumer can make choices, i.e., she can look at two alternatives and compare them to see whether one is preferred to another, or whether she is completely indifferent between them. When a consumer can make comparisons, and when all comparisons are logically consistent, the consumer’s preferences are said to be rational. Finally, two assumptions in addition to rationality are (1) that marginal utility is positive (“more is better”) and (2) that marginal utility diminishes as more of a good is consumed. 6. The statement makes an error. Rationality does not mean that individuals make choices that are “sensible” to others. Preferences are called rational if (1) they satisfy the logical consistency requirement detailed in question 5, and if (2) the consumer can compare any two combinations of goods and state either that he/she is indifferent between them or that he/she prefers one of them. 7. [Marginal Utility Analysis answer] A consumer maximizes utility subject to a budget constraint when she or he consumes that combination of goods at which marginal utility per dollar is the same for all goods consumed. Hence, for any two goods X and Y, MU X MU Y = . PX PY [Indifference Curve Analysis answer] A consumer maximizes utility subject to a budget constraint when she or he consumes that combination of goods at which the marginal rate of substitution between those goods equals the slope of the budget line at that combination. Hence, for any two goods X and Y, MRSY,X = Px/Py 8. A change in the price of one good relative to another gives rise to the substitution effect—the tendency of consumers to substitute more of the good made relatively cheaper by the price decline for the good that is now relatively more expensive. Hence, the substitution effect always works to increase the quantity demanded of a good whose price has decreased. In this sense, the substitution effect is always consistent with the law of demand. The income effect is the change in quantity demanded that arises because of the change in purchasing power caused by a price change. For example, if the price of a good declines, a given income will “go farther”—as if the consumer has more income. Any given price change sets in motion both income and substitution effects. If a good is normal, these effects reinforce each other to increase quantity demanded, in the case of a price decrease, or decrease quantity demanded when price increases. When a good is inferior, the income and substitution effects work in opposite directions. The question then becomes, Which effect is stronger? If the substitution effect dominates, the law of demand will still hold; but if the income effect is stronger, a price increase will actually cause quantity demanded to increase, in violation of the law of demand. 9. False. As explained in the answer to Question 8, as long as the substitution effect is stronger than the income effect, the demand curve for an inferior good will still be downward sloping. Only when the good is inferior and the income effect dominates will the demand curve have a positive slope. 10. The market demand curve for a particular good is found as the horizontal sum of the demand curves of all consumers in the market for the good. Each individual demand is found by varying the price of the good and observing how the optimal quantity of a good changes as the consumer’s budget line rotates outward or inward. PROBLEM SET Novels 1. a. Original budget line 15 Budget line after PCD ↑ to $10 12 20 CDs b. 2. [Using the Marginal Utility Approach] No, he is not maximizing utility. For each dollar spent on novels, Parvez gets 5 units of utility; for each dollar’s worth of CDs, only 4. He should spend less of his budget on CDs and more on novels. As he does so, the marginal utility of CDs will rise and the marginal utility of novels will fall, until the ratio of marginal utility to price is the same for both goods. 3. [Using the Marginal Utility Approach] Anita’s utility is maximized where MU pizza MU Pepsi = , Ppizza PPepsi or, given the prices in the problem, she should consume slices and cans such that MU pizza = 2MU Pepsi . This will be satisfied at 8 cans of Pepsi (the eighth can gives her additional utility of 10) and 5 slices of pizza (the marginal utility of the fifth slice is 20). 4. a. Recall that the market demand curve is simply the horizontal sum (summed over quantities at each price) of the individual demand curves. In this case, then, the market demand schedule is: Price $5.00 $4.00 $3.00 D $2.00 $1.00 3 5 7 Price $5.00 $4.50 $4.00 $3.50 9 Quantity Qty. Demanded 3 5 7 9 b. The three consumers have different demand schedules because they have different preferences for the cereal. 5. a. 75,000 bottles. This is 1000 × (100 – 25($1)) = 1000 × 75. b. 50,000 bottles. This is 1000 × (100 – 25($2)) = 1000 × 50. c. QD = 100,000 – 25,000P 6. An increase in income always decreases demand for an inferior good. Hence, the demand curve would behave as below, with new (post-income increase) demand shown by D2. Price S1 P1 P2 D1 D2 Q2 Q1 Quantity 7. a. Since the price of inputs is a determinant of the supply curve, an increase in paper prices will shift the firm’s supply curve to the left, increasing the equilibrium price for its books to P2 as shown below: Price S2 S1 P2 P1 D1 Q2 Q1 Quantity b. By the substitution effect, the increased price for Pulp Fiction’s books will cause consumers to substitute other goods (perhaps the publications of other publishers) for Pulp’s books, decreasing quantity demanded. Assuming Pulp’s novels are normal goods for most consumers, the income effect acts to reinforce the substitution effect, decreasing quantity demanded. (If Pulp’s novels are inferior goods, then the income effect will work against the substitution effect—tending to increase quantity demanded while the substitution effect decreases quantity demanded.) 8. False. The price increase generates both income and substitution effects. With an inferior good, both effects work against each other. While it is possible for the income effect to dominate (a case that would, indeed, violate the law of demand), this would be extremely rare. More commonly, the substitution effect dominates, so the good would obey the law of demand. 9. a. Violates the assumption of rational preferences, since the condition that Joseph will be able to state that he prefers one choice over the other, or that he is indifferent between the two, is not fulfilled. b. Does not violate the assumption of rational preferences. Brenda can state her preference for mustard. c. Violates the assumption of rational preferences, since the condition that Brewster’s preferences are logically consistent is not fulfilled. 10. [Using the Indifference Curve Approach] a. b. c. 11. [Using the Marginal Utility Approach] Income = $300| Concerts at $30 each Movies at $10 each (1) (2) (3) (4) (5) (6) Marginal Marginal Number of Marginal Marginal Number of Utility from Utility per Movies Utility Utility per Concerts per Last Dollar Spent per Month from Last Dollar Month Concert on Last Movie Spent on Concert Last Movie 3 600 20 21 4 0.4 4 450 15 18 6 0.6 5 360 12 15 10 1 6 300 10 12 20 2 7 180 6 9 30 3 8 150 5 6 35 3.5 9 120 4 3 40 4 Max’s utility maximizing combination is 9 concerts and 3 movies. This corresponds to point H’ in Figure 5. 12. [Using the Marginal Utility Approach] Income = $300 per month| Concerts at $30 each Movies at $10 each (1) (2) (3) (4) (5) (6) Number of Marginal Marginal Number of Marginal Marginal Concerts per Utility from Utility per Movies Utility Utility per Month Last Dollar Spent per Month from Last Dollar Concert on Last Movie Spent on Concert Last Movie 1 450 15 27 150 15 2 390 13 24 175 17.5 3 300 10 21 200 20 4 225 7.5 18 225 22.5 5 180 6 15 250 25 6 150 5 12 275 27.5 7 90 3 9 300 30 8 75 2.5 6 325 32.5 9 60 2 3 350 35 Max’s utility maximizing combination is 1 concert and 27 movies. This corresponds to point H” in Figure 5. 13. [Using the Indifference Curve Approach] a. The original equilibrium is at point A. b. The new budget line is BL2. The new tangency must occur at a point with MORE THAN 25 pounds of potatoes, for instance, at point B. If potatoes are inferior, then Cameron will consume more potatoes and fewer steaks than at his original position. 14. [Using the Indifference Curve Approach] a. The original equilibrium is at point A. b. The new budget line is BL2. The new tangency must occur at a point where Rafaella is consuming MORE THAN 4 pounds of chicken, and LESS than 10 eggs, for instance, at point B. 15. [Using the Indifference Curve Approach] a. The original equilibrium is at point A. b. A new tangency will occur at a point where she consumes more clothes and less food, such as point B. c. A new tangency will occur at a point where she consumes fewer clothes and more food, such as point C. 16. Income = $150 per month Concerts at $5 each Movies at $10 each Number of Marginal Marginal Number of Marginal Marginal concerts per utility from utility per movies per utility from utility per month last concert dollar spent month last movie dollar spent on last on last concert movie 3 600 120 4 450 90 5 360 72 6 300 60 7 180 36 8 150 30 12 100 10 9 100 20 11 120 12 10 67.5 13.50 10 135 13.50 From this table, the marginal utility per dollar spent on last concert is equal to the marginal utility per dollar spend on the last movie when Max consumes 10 concerts and 10 movies per month. This does, indeed, demonstrate that point K on Figure 6 is optimal. MORE CHALLENGING QUESTIONS 17. a. Current consumption is at A, where 2,500 units of food and 5,000 units of shelter are consumed. The Smiths spend $5000 = $2 x 2500 on food and $5000 = $1 x 5000 on shelter. Food (in units) 7,500 B'' 5,000 A 2,500 B' 5,000 10,000 7,500 Shelter (in sq ft/ year) b. When the price of housing rises to $2 per square foot, the new budget line is given by the line marked B′ in the figure above. The Smiths cannot continue to consume at point A. c. The income supplement shifts the budget constraint rightward to the line marked B′′. The original consumption levels, represented by point A, is again affordable. d. No, the family will not necessarily return to point A. The utility-maximizing consumption choice will be somewhere on the new budget line, B′′. But all the points on this budget line below A could have been reached with the original prices and income, and were not chosen before, so they must be less preferred than point A. They will not be chosen now. All the points above point A are newly available. Any of these points might be preferred to point A, and could be chosen. (If you use the indifference curve approach, you can actually show that point A will never be chosen after the cash grant. To do so, draw an indifference curve tangent to point A, reflecting the best initial choice before the price change and the cash grant. Then, after the price change and the cash grant, the best choice is the point of tangency between some new indifference curve and budget line B”. This new tangency cannot occur at point A, as you can see by trying to draw it.) 18. Nothing would happen to consumer choices in this situation. If prices alone were increasing, then the budget line would shift towards the origin. However, in this example, wages are increasing by enough to keep the combination of goods and services the consumer can afford unchanged. 19. [Using the Indifference Curve Approach] a. b. c. 20. [Using the Indifference Curve Approach]