1. Chapter Four
Consumer Choice

2. Consumer Choice In this chapter, we examine four main topics.
Preferences
Utility
Budget constraint
Constrained consumer choice
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3. Preferences
To explain consumer behavior, economists assume that consumers have a set of tastes or preferences that they use to guide them in choosing between goods. These tastes differ substantially among individuals.
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4. Properties of Consumer Preferences
Economists make three critical assumptions about the properties of consumers’ preferences. For brevity, these properties are referred to as completeness, transitivity, and more is better.
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5. Completeness
The completeness property holds that, when facing a choice between any two bundles of goods, a consumer can rank them so that one and only one of the following relationships is true: The consumer prefers the first bundle to the second, prefers the second to the first, or is indifferent between them.
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6. Transitivity
The transitivity (or what some people refer to as rationality) property is that a consumer’s preferences over bundles is consistent in the sense that, if the consumer weakly prefers Bundle to Bundle (like at least as much as ) and weakly prefers Bundle to Bundle , the consumer also weakly prefers Bundle to Bundle .
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7. More is Better
The more-is-better property holds that, all else the same, more of a commodity is better than less of it (always wanting more is known as nonsatiation).
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8. Properties of Consumer Preferences
good
a commodity for which more is preferred to less, at least at some levels of consumption
bad
something for which less is preferred to more, such as pollution
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9. Preference Maps
One of the simplest ways to summarize information about a consumer’s preferences is to create a graphical interpretation—a map—of them.
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10. Preference Maps indifference curve
the set of all bundles of goods that a consumer views as being equally desirable
indifference map (or preference map)
a complete set of indifference curves that summarize a consumer’s tastes or preferences
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11. Indifference Curves
All indifference curve maps must have four important properties:
Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin.
There is an indifference curve through every possible bundle.
Indifference curve cannot cross.
Indifference curves slope downward.
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12. Figure 4.1 Bundles of Pizzas and Burritos Lisa Might Consume25 25 f 20 20 f e 15 15 e a a d d 10 b 10 b I 1 5 B 15 25 30 15 25 30 Z
, Pizzas per semester Z
, Pizzas per semester
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13. Figure 4.1 Bundles of Pizzas and Burritos Lisa Might Consume (cont’d)25 f 20 2 e I 15 d 10 I 1 I 15 25 30 Z
, Pizzas per semester
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14. Figure 4.2 Impossible Indifference Curves
(a) Crossing
(b) Upward Sloping b a e b I I 1 a I Z
, Pizzas per semester Z
, Pizzas per semester
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15. Figure 4.2 Impossible Indifference Curves (cont’d)
(c) Thick b a I Z
, Pizzas per semester
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16. Willingness to Substitute Between Goods
Marginal Rate of Substitution (MRS)
the maximum amount of one good a consumer will sacrifice to obtain one more unit of another good
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17. Willingness to Substitute Between Goods
The marginal rate of substitution of burritos for pizza is
where is the number of pizzas Lisa will give up to get more burritos or vice versa and pizza (Z) is on the horizontal axis. The marginal rate of substitution is the slope of the indifference curve.
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18. Curvature of Indifference Curves
An indifference curve doesn’t have to be convex, but casual observation suggests that most people’s indifference curves are convex. When people have a lot of one good, they are willing to give up a relatively large amount of it to get a good of which they have relatively little. However, after that first trade, they are willing to give up less of the first good to get the same amount more of the second good.
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19. Curvature of Indifference Curves
This willingness to trade fewer burritos for one more pizza as we move down and to the right along the indifference curve reflects a diminishing marginal rate of substitution: The marginal rate of substitution approaches zero as we move down and to the right along an indifference curve.
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20. Figure 4.3 Marginal Rate of Substitution
(a) Indifference Curve Convex to the Origin
(b) Indifference Curve Concave to the Origin a 8 a 7 – 3 – 2 b b 5 5 1 1 – 2 c – 3 3 1 d c – 1 2 2 1 1 I I 3 4 5 6 3 4 5 6 Z
, Pizzas per semester Z
, Pizzas per semester
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21. Curvature of Indifference Curves
Perfect Substitutes
goods that a consumer is completely indifferent as to which to consume
Perfect Complements
goods that a consumer is interested in consuming only in fixed proportions
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22. Figure 4.4 Perfect Substitutes, Perfect Complements, Imperfect Substitutes
(a) Perfect Substitutes
(b) Perfect Complements 4 e c 3 3 I 3 d b 2 2 I 2 a 1 1 I 1 I 1 I 2 I 3 I 4 1 2 3 4 1 2 3
Pepsi, Cans per week
Pie, Slices per week
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23. Figure 4.4 Perfect Substitutes, Perfect Complements, Imperfect Substitutes (cont’d)
(c) Imperfect Substitutes I Z
, Pizzas per semester
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24. Application (Page 83) Indifference Curves Between Food and Clothing4 I 3 I 2 I 1
Clothing per year
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25. Utility Utility Utility Function
a set of numerical values that reflect the relative rankings of various bundles of goods
Utility Function
the relationship between utility values and every possible bundle of goods
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26. Ordinal Preferences
If we know only consumers’ relative rankings of bundles, our measure of pleasure is ordinal rather than cardinal. An ordinal measure is one that tells us the relative ranking of two things but not how much more one rank is than another.
Because utility is an ordinal measure, we should not put any weight on the absolute differences between the utility associated with one bundle and another. We care only about the relative utility or ranking of the two bundles.
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27. Utility and Marginal Utility
the extra utility that a consumer gets from consuming the last unit of a good
Thus marginal utility is the slope of the utility function
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28. Figure 4.5 Utility and Marginal Utility
(a) Utility
350
Utility function, U
(10, Z )
250 D U = 20
230 D Z = 1 1 2 3 4 5 6 7 8 9 10 Z
, Pizzas per semester
(b) Marginal Utility
130 20 MU Z 1 2 3 4 5 6 7 8 9 10
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, Pizzas per semester

29. Utility and Marginal Rates of Substitution
The marginal rate of substitution (MRS) is the slope of the indifference curve. The marginal rate of substitution can also be expressed in terms of marginal utilities.
The marginal rate of substitution can be written as
(4.1)
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30. Budget Constraint
Consumers maximize their well-being subject to constraints. The most important constraint most of us face in deciding what to consume is our personal budget constraint.
For simplicity, we assume that each consumer has a fixed amount of money to spend now, so we can use the terms budget and income interchangeably.
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31. Budget Constraint
If Lisa spends all her budget, Y, on pizza and burritos, then
(4.2)
where is the amount she spends on burritos and is the amount she spends on pizzas.
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32. Budget Constraint Budget Line (or Budget Constraint) Opportunity Set
the bundles of goods that can be bought if the entire budget is spent on those goods at given prices
Opportunity Set
all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint
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33. Slope of the Budget Constraint
Marginal Rate of Transformation (MRT)
the trade-off the market imposes on the consumer in terms of the amount of one good the consumer must give up to obtain more of the other good
The marginal rate of transformation is the rate at which Lisa can trade burritos for pizza in the marketplace:
(4.5)
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34. Table 4.1 Allocations of a $50 Budget Between Burritos and Pizza
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35. Figure 4.6 Budget Constraint25 = Y / p B b 20 L 1 ( p
= $1, Y
= $50) Z c 10
Opportunity set d 10 30 50 = Y / p Z Z
, Pizzas per semester
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36. Effect of A Change in Price on Consumption
If the price of pizza doubles but the price of burritos is unchanged, the budget constraint swings in toward the origin in panel a of Figure 4.7.
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37. Figure 4.7 Changes in the Budget Constraint
(a) Price of Pizza Doubles
(b) Income Doubles 25 50 L 3 ( Y =
$100) L 1 ( p Z
= $1) 25
Loss
Gain L 2 ( p
= $2) L 1 ( Y =
$50) Z 25 50 50
100 Z
, Pizzas per semester Z
, Pizzas per semester
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38. Effect of a Change in Income on Consumption
If the consumer’s income increases, the consumer can buy more of all goods. The budget constraint shifts outward—away from the origin—and is parallel to the origin constraint in panel b of Figure 4.7.
A change in income affects only the position and not the slope of the budget line. The slope is determined solely by the relative prices of pizza and burritos.
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39. Page 91 Solved Problem 4.2 Quota Budget line A B 10 1210 12
Water, Thousand gallons per month
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40. The Consumer’s Optimal Bundle
The optimal bundle must be on the budget constraint. Bundles that lie on indifference curves above the constraint, such as those on I3, are not in the opportunity set.
For any bundle inside the constraint (such as d on I1), there is another bundle on the constraint with more of at least one of the two goods, and hence she prefers that bundle. Therefore, the optimal bundle must lie on the budget constraint.
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41. The Consumer’s Optimal Bundle
Bundles that lie on indifference curves that cross the budget constraint (such as I1, which crosses the constraint at and ) are less desirable than certain other bundles on the constraint.
Thus the optimal bundle must lie on the budget constraint and be on an indifference curve that does not cross it. Such a bundle is the consumer’s optimum.
The optimal bundle must lie on an indifference curve that touches the budget constraint but does not cross it.
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42. Figure 4.8 Consumer Maximization
(a) Interior Solution
Budget line g 25 c f 20 B e 10 I 3 d a I A 2 I 1 10 30 50 Z
, Pizzas per semester
(b) Corner Solution e 25 I 3 I 2
Budget line I 1 50
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, Pizzas per semester

43. Interior Solution Rearranging terms, this condition is equivalent to
For the indifference curve I2 to touch the budget constraint but not cross it, it must be tangent to the budget constraint: The budget constraint and the indifference curve have the same slope at the point where they touch.
Rearranging terms, this condition is equivalent to
(4.6)
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44. Page 95 Solved Problem 4.3 Corner Solution1 N l L B L N e B 1
SUVs per decade
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45. Figure 4.9 Optimal Bundles on Convex Sections of Indifference Curves
(a) Strictly Concave Indifference Curves
(b) Concave and Convex Indifference Curves e
Budget
Budget
line
line d d e I 2 I 1 I 2 I 3 I 1 Z
, Pizzas per semester Z
, Pizzas per semester
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46. Buying Where More is Better
If both goods are consumed in positive quantities and their prices are positive, more of either good must be preferred to less.
In summary, we do not observe consumer optima at bundles where indifference curves are concave or consumers are satiated. Thus we can safely assume that indifference curves are convex and that consumers prefer more to less in the ranges of goods that we actually observe.
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47. Page 98 Solved Problem 4.4 L L f a I I American meals per year F A 2 1
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48. Food Stamps Cash preferred to food stamps
Poor people who receive cash have more choices than those who receive a comparable amount of food stamps.
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49. Figure 4.10 Food Stamps Versus Cash
Budget line with cash Y +
100 f C e Y I 3 d I 2 I 1 B
Budget line with
food stamps A
Original
budget line
100 Y Y +
100
Food per month
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