Chapter 2: Consumer Preferences
Consumer Preferences
Commodity Bundle
Preference
Relation
Marginal Rate
of Substitution
Preference
Ordering
Utility
Function
Indifference
Curves
Monotonic
Transformation
Convexity
Stricitly
Convex
Stricitly
Concave
Household
Preferences
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?
© Michael E. Wetzstein, 2012
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 = U1/2?
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
© Michael E. Wetzstein, 2012
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
© Michael E. Wetzstein, 2012
The utility function represents the level of
satisfaction an agent receives from
consuming a commodity bundle
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 xj
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 xj
d. Is equal to the derivative of the utility function with respect to xj.
5. Suppose Pearl’s utility function is
If Pearl is currently consuming 5 units of x1
and 2 units of x2, her marginal utility of x1 is
a. 40
b. 100
c.
d.
6. Suppose Tim’s utility function is
utility level of 8 is
a. (1, 1)
b. (2, 2)
c. (0, 8)
d. (1, 2).
© Michael E. Wetzstein, 2012
One possible commodity bundle that yields a
7. Given
a. 1
b. 1½
c. 2
d. 2½.
if x1 = 2 and x2 = 3, then MRS(x2 for x1) is equal to
8. Considering the following graph, which of the following statements is false?
.
..
x2
B
A
0
U’ > Uo
C
U’
Uo
x1
a. Commodity bundles B and C yield the same level of utility
b. Uo represents a lower level of utility than U′
c. Commodity bundle A has more of x1 than bundle B, and bundle B has more of x2, so it is
impossible to rank them
d. Commodity bundle B provides a higher level of utility than bundle A.
9. Suppose x1 and x2 are two commodities that Karen purchases. The Nonsatiation Axiom
implies
a. MU1 = MU2 = 0
b. MRS(x2 for x1) increases as more x1 is consumed
c. MRS(x2 for x1) decreases as more x1 is consumed
d. Both MU1 and MU2 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.
© Michael E. Wetzstein, 2012
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 x1 and x2 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?
x2
Uo
U’
Uo < U’
0
a.
b.
c.
d.
x1
Commodity x2 is a bad commodity
Commodity x2 is a neutral commodity
Commodity x1 is a bad commodity
Commodity x1 is a neutral commodity.
© Michael E. Wetzstein, 2012
Short Answer
1. List and describe the four consumer preference axioms.
2. Illustrate graphically a utility function for commodity x1. 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(x2 for x2) declines as x1 increases?
8. Suppose x1 and x2 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)?
© Michael E. Wetzstein, 2012
Problems
1. For the following utility functions, derive the marginal utility of x1:
a.
b.
c.
2. Consider the utility function
increases?
What happens to the marginal utility of x1 as x1
3. Consider the utility function U = 2x1x2. Find three commodity bundles that yield a utility
level of 48.
4. Consider the utility function
x1). Is it diminishing?
Calculate the marginal rate of substitution (x2 for
5. Consider the utility function U = 2x1 + 4x2. Calculate MRS(x2 for x1). 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
axioms?
© Michael E. Wetzstein, 2012
Does this utility function satisfy the preference