Chapter 2: Consumer Preferences

Transcription

1 Chapter 2: Consumer Preferences Consumer Preferences Commodity Bundle Preference Relation Preference Ordering Indifference Curves Utility Function Monotonic Transformation Marginal Rate of Substitution Convexity Household Preferences Stricitly Convex Stricitly Concave Perfect Substitutes Perfect Complements Bad Commodities Neutral Preferences Satiated Preferences Outline and Conceptual Inquiries Household Preferences and Grocery Carts How many grocery carts are there anyway? The World of only Two Commodities How are two commodities really k commodities? Preference Relation: Arranging Grocery Carts Preference Ordering: Ranking Grocery Carts When waiting in line at a supermarket, can you rank the various grocery carts? Utility Functions Dissected Application: Economic Man as a Moral Individual Do Utility Functions have Personalities? Indifference Curves: Apathy Can you read a utility-relief map? How much are you willing to substitute partying for studying? Are averages preferred to extremes? Are extremes preferred to averages? How Indifference Curves Represent Household Preferences Imperfect Substitutes: Apples and Oranges Perfect Substitutes: Brown and White Eggs When are earrings perfect substitutes? Application: Only a Bad Reproduction is a Good Reproduction Perfect Complements: Shoes and Shoe Laces When are earrings perfect complements? Application: Big Business versus Big Government - Are they Perfect Complements? Bad Commodities: Cigarettes Neutral Preferences: Inert Ingredients Do zombies have neutral preferences?

2 Satiated Preferences: Heaven Are there economists in Shangri-La? Appendix to Chapter 2 How to Measure Utility Is there a hedonimeter? Application: Is a Hedonimeter Feasible? What is a Positive Monotonic Transformation of a Utility Function? When does U = U 1/2? Summary 1. The problem facing a household is deciding how much of each available commodity it should consume to maximize satisfaction. 2. A household must compare tastes and preferences for alternative commodity bundles to determine which bundle yields the highest satisfaction it can afford. Such a comparison is determined by the preference relation is preferred to or indifferent to. 3. The preference relation provides a method for ordering the set of consumption bundles from the most to the least preferred. The two axioms, Completeness and Transitivity, allow this ordering of bundles. 4. The preference ordering of bundles may be represented by a utility function, which assigns a numerical value to each commodity bundle. Because utility functions are ordinal, it is not possible to determine the magnitude of a change in satisfaction between two commodity bundles. 5. Assuming nonsatiation (more of a commodity is preferred to less), all marginal utilities are positive. Marginal utility is the additional utility derived from consuming an additional unit of a commodity while holding the consumption of all other commodities constant. 6. Indifference curves are based on three axioms: Completeness, Transitivity, and Nonsatiation. An indifference curve is a locus of points (commodity bundles) yielding the same level of utility. 7. The negative of the slope of an indifference curve is the marginal rate of substitution (MRS). MRS measures the rate at which one commodity can be substituted for another that is, how much a household is willing to pay to substitute one commodity for another. 8. Strictly convex indifference curves imply the Diminishing Marginal Rate of Substitution Axiom. This axiom states that the willingness to give up some of a commodity decreases as the amount of the commodity declines. Households will then choose a diversified commodity bundle over a bundle concentrated in one particular commodity. In other works, households prefer averages to extremes. 9. Preferences where two commodities are perfect substitutes result in a constant MRS. The

3 willingness to give up one commodity for another does not depend on the amount of the commodities consumed. In contrast, for preferences where commodities must be consumed in the same fixed proportion (perfect complements) a household is unwilling to substitute one commodity another. 10. A bad commodity is one that decreases satisfaction when it is consumed. For a household to be willing to consume additional amounts of this bad commodity, it would have to be compensated with additional units of some desirable commodity. 11. A commodity is neutral if a household does not derive any utility from it. The commodity does not have any effect on the household s level of satisfaction, so it does not enter into a household s utility function. 12. A household is satiated when further increases in the commodities it is consuming do not result in any enhancement of satisfaction. 13. (Appendix) A household s preferences for substituting one commodity, represented by a utility function measured on an ordinal scale, will not change if the utility function is transformed by any positive monotonic transformation. Key Concepts bad commodity cardinal utility commodity commodity bundle commodity space composite commodity commodity convex set demand free markets good commodity household imperfect substitutes income indifference indifference curve indifference sets indifference space Law of Demand marginal rate of substitution (MRS) marginal utilities (MU) numeraire commodity ordinal utility perfect complements perfect substitutes rationality utility utility function Key Equations This preference relation indicates that commodity bundle is preferred to or indifferent to bundle The utility function represents the level of satisfaction an agent receives from consuming a commodity bundle

4 TEST YOURSELF Multiple Choice 1. A household s objective is to a. Maximize income for a given level of utility b. Minimize income for a given level of utility c. Maximize social welfare for given level of resources d. Maximize utility for a given level of income. 2. A household s most preferred commodity bundle depends on a. Its limited income b. Its tastes and preferences c. Given commodity prices d. All of the above. 3. Which of the following axioms is not required for utility maximization? a. Diminishing marginal rate of substitution b. Completeness c. Nonsatiation d. Transitivity. 4. The marginal utility of x j a. Is characterized by the Law of Diminishing Marginal Utility b. At first rises and then eventually declines c. Is equal to the negative of the derivative of the utility function with respect to x j d. Is equal to the derivative of the utility function with respect to x j. 5. Suppose Pearl s utility function is If Pearl is currently consuming 5 units of x 1 and 2 units of x 2, her marginal utility of x 1 is a. 40 b. 100 c. d. 6. Suppose Tim s utility function is One possible commodity bundle that yields a utility level of 8 is a. (1, 1) b. (2, 2) c. (0, 8) d. (1, 2).

5 7. Given if x 1 = 2 and x 2 = 3, then MRS(x 2 for x 1 ) is equal to a. 1 b. 1½ c. 2 d. 2½. 8. Considering the following graph, which of the following statements is false? x 2 0. B U > U o.. C A U x 1 U o a. Commodity bundles B and C yield the same level of utility b. U o represents a lower level of utility than U c. Commodity bundle A has more of x 1 than bundle B, and bundle B has more of x 2, so it is impossible to rank them d. Commodity bundle B provides a higher level of utility than bundle A. 9. Suppose x 1 and x 2 are two commodities that Karen purchases. The Nonsatiation Axiom implies a. MU 1 = MU 2 = 0 b. MRS(x 2 for x 1 ) increases as more x 1 is consumed c. MRS(x 2 for x 1 ) decreases as more x 1 is consumed d. Both MU 1 and MU 2 are positive. 10. Two commodities that are perfect substitutes have indifference curves, which are a. Linear b. Strictly convex c. Right angles d. Upward-sloping. 11. If a consumer has indifference curves that are right angles, then a. MRS is constant b. The consumer does not derive any satisfaction from either good c. The two goods are perfect substitutes d. The two goods are perfect complements.

6 12. Which preference axioms are violated in the case of perfect complements? a. Transitivity and Strict Convexity b. Nonsatiation and Transitivity c. Nonsatiation and Strict Convexity d. All of the above. 13. In which of the following utility functions are x 1 and x 2 perfect substitutes? a. b. c. d. 14. Indifference curves are generally strictly convex due to a. Individuals preferring a variety of commodities b. Marginal utilities are always positive c. Most commodities are desirable d. The marginal rate of substitution is always positive. 15. Considering the following graph, which of the following statements is true? x 2 U o U U o < U 0 x 1 a. Commodity x 2 is a bad commodity b. Commodity x 2 is a neutral commodity c. Commodity x 1 is a bad commodity d. Commodity x 1 is a neutral commodity.

7 Short Answer 1. List and describe the four consumer preference axioms. 2. Illustrate graphically a utility function for commodity x 1. Why does the utility function have the shape that you illustrated? 3. Define marginal utility. How is it calculated? 4. What is an indifference curve? Why are indifference curves generally downward-sloping and convex? 5. Graphically illustrate why two indifference curves cannot intersect. 6. Define marginal rate of substitution. What does it measure? 7. Generally, why do we assume that MRS(x 2 for x 2 ) declines as x 1 increases? 8. Suppose x 1 and x 2 are perfect complements. Illustrate graphically a consumer s indifference curves between these two goods. Explain why the indifference curves have this shape. 9. Erick is following a low-carbohydrate diet and chooses to eat his hamburgers without a bun. In fact, he believes that the consumption of a bun will make him worse off. Illustrate Erick s indifference curves for buns and hamburgers. 10. Gale enjoys pretzels but gets no pleasure or displeasure from beer. Illustrate her indifference curves for these two commodities. What is the marginal utility of beer? What is Gale s MRS(beer for pretzels)?

8 Problems 1. For the following utility functions, derive the marginal utility of x 1 : a. b. c. 2. Consider the utility function What happens to the marginal utility of x 1 as x 1 increases? 3. Consider the utility function U = 2x 1 x 2. Find three commodity bundles that yield a utility level of Consider the utility function Calculate the marginal rate of substitution (x 2 for x 1 ). Is it diminishing? 5. Consider the utility function U = 2x 1 + 4x 2. Calculate MRS(x 2 for x 1 ). What shape will the indifference curves for this utility function have? 6. Consider the utility function Find three commodity bundles that yield a utility level of 1. What shape will the indifference curves for this utility function have? 7. Consider the utility function Does this utility function satisfy the preference axioms?