Chapter 4

Principles and Preferences

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Main Topics

Principles of decision-making

Consumer preferences

Substitution between goods

Utility

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Building Blocks of Consumer Theory

Preferences tell us about a consumer’s likes and dislikes

A consumer is indifferent between two alternatives if she likes (or dislikes) them equally

The Ranking Principle: A consumer can rank, in order of preference, all potentially available alternatives

The Choice Principle: Among available alternatives, the consumer chooses the one that he ranks the highest

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The Consumer’s Problem

Consumer’s economic problems is to allocate limited funds to competing needs and desires over some time period

Chooses a consumption bundleShould reflect preferences over various bundles,

not just feelings about any one good in isolationDecision to consume more of one good is a

decision to consume less of another

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Principles of Consumer Decision-Making

The More-is-better Principle: When one consumption bundle contains more of every good than a second bundle, a consumer prefers the first bundle to the second

Transitivity: if a > b and b > c, then a > c.

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Indifference Curves

Use when goods are (or assumed to be) available in any fraction of a unit

Represent alternatives graphically or mathematically rather than in a table

Starting with any alternative, an indifference curve shows all the other alternatives a consumer likes equally well

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Figure 4.1: Identifying Alternatives and Indifference Curves

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Properties of Indifference Curves

Thin

Do not slope upward

Separates bundles that are better from bundles that are worse than those that are on the indifference curve

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Figure 4.2: Indifference Curves Ruled Out by the More-is-better Principle

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Families of Indifference Curves

Collection of indifference curves that represent the preferences of an individual

Do not crossComparing two bundles, the consumer

prefers the one on the indifference curve further from the origin

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Figure 4.3: A Family of Indifference Curves

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Figure 4.4: Indifference Curves Do Not Cross

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Formulas for Indifference Curves

More complete and precise to describe preferences mathematically

For example, can write a formula for a consumer’s indifference curves

Formula describes an entire family of indifference curves

Each indifference curve represents a particular level of well-being

Higher levels of well-being are on indifference curves further from the origin

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Figure 4.6: Plotting Indifference Curves

Formula for indifference curves is B = U/S (Starting from U=B*S)

U is well-being, or “utility”

To find a particular curve, plug in a value for U, then plot the relationship between B and S

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Substitution Between Goods

Economic decisions involve trade-offsTo determine whether a consumer has

made the best choice, we need to know the rate at which she is willing to make trade-offs between different goods

Indifference curves provide that information

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Rates of Substitution

Consider moving along an indifference curve, from one bundle to another

This is the same as subtracting units of one good and compensating the consumer for the loss by adding units of another good

Slope of the indifference curve shows how much of the second good is needed to make up for the decrease in the first good

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Figure 4.8: Rates of Substitution

Look at move from bundle A to C

Consumer gains 1 soup; gains 2 bread

Willing to substitute for soup with bread at 2 ounces per pint

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Marginal Rate of Substitution

The marginal rate of substitution for X with Y, MRSXY, is the rate at which a consumer must adjust Y to maintain the same level of well-being when X changes by a tiny amount, from a given starting point

Tells us how much Y a consumer needs to compensate for losing a little bit of X

Tells us how much Y to take away to compensate for gaining a little bit of X

XYMRSXY

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Figure 4.9: Marginal Rate of Substitution

MRSSB=-B/S=-3/2

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What Determines Rates of Substitution?

Differences in tastesPreferences for one good over another affect the

slope of an indifference curve (weights attached to each good in the utility function)

Implications for MRSStarting point on the indifference curve

People like variety so most indifference curves get flatter as we move from top left to bottom right

Link between slope and MRS implies that MRS declines; the amount of Y required to compensate for a given change in X decreases

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Figure 4.10: Indifference Curves and Consumer Tastes

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Figure 4.11: MRS along an Indifference Curve

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Formulas for MRS

MRS formula tells us the rate at which a consumer will exchange one good for another, given the amounts consumed

Every indifference curve formula has an MRS formula that describes the same preferences

Indifference curves: B=U/S; MRSSB=B/S

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Perfect Substitutes and Complements

Some special cases of preferences represent opposites ends of the substitutability spectrum

Two products are perfect substitutes if their functions are identical; a consumer is willing to swap one for the other at a fixed rate

Two products are perfect complements if they are valuable only when used together in fixed proportions

Note that the goods do not have to be exchanged one-for-one!

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Figure 4.12: Perfect Substitutes

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Figure 4.13: Perfect Complements

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Sample Problem 1 (4.3):

Gary has two children, Kevin and Dora. Each one consumes “yummies” and nothing else. Gary loves both children equally. For example, he is equally happy when Kevin has two yummies and Dora has three, or when Kevin has three yummies and Dora has two. But he is happier when their consumption is more equal. Draw Gary’s indifference curves. What would they look like if he loved one child more than the other?

Utility

Summarizes everything that is known about a consumer’s preferences

Utility is a numeric value indicating the consumer’s relative well-being

Recall that the consumer’s goal is to benefit from the goods and services she uses

Can describe the value a consumer gets from consumption bundles mathematically through a utility function

BSSBSU 52, 4-28

Utility Functions and Indifference Curves

Utility functions must assign the same value to all bundles on the same indifference curve

Must also give higher utility values to indifference curves further from the origin

Can start with information about preferences and derive a utility function

Or can begin with a utility function and construct indifference curves

Can also think of indifference curves as “contour lines” for different levels of utility

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Figure 4.14: Representing Preferences with a Utility Function

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Deriving Indifference Curves from a Utility Function

For each bundle, the utility correspond to the height of the utility “hill”

The indifference curve through A consists of all bundles for which the height of the curve is the same

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Sample Problem 2:

For example assume preferences are described by the following utility function:U = X1/2Y1/2

To plot an indifference curve for this utility function, first isolate Y: U2 = XYY = U2 /X

Then pick some level of utility. Let’s set U = 25

Utility Functions and Indifference Curves

Thus, Y = 5/XWhen X = 1, Y = 25When X = 2, Y = 12.5When X = 3, Y = 8.33When X = 4, Y = 6.25When X = 5, Y = 5And so on…

Describe the indifference curves for the following utility functions:U = X + YU = min(X,Y)

Ordinal vs. Cardinal Utility

Information about preferences can be ordinal or cardinal

Ordinal information allows us to determine only whether one alternative is better than another

Cardinal information reveals the intensity of preferences, “How much worse or better?”

Utility functions are intended to summarize ordinal information

Scale of utility functions is arbitrary; changing scale does not change the underlying preferences

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Marginal Utility

To make a link between MRS and utility, need a new concept

Marginal utility is the change in a consumer’s utility resulting from the addition of a very small amount of some good, divided by the amount added

XUMU X

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Utility Functions and MRS

Small change in X, X, causes utility to change by MUXX

Small change in Y, Y, causes utility to change by MUYY

If we stay on same indifference curve, then –Y/X =MUXMUY

Y

XXY MU

MUMRS

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Marginal Rate of Substitution

Let’s find the MRS for each of the following utility functions:U = X1/2Y1/2;

MUX=(1/2)X-1/2Y1/2 and MUY =(1/2) X1/2Y-1/2

U = X1/3Y2/3

MUX=(1/3)X-2/3Y2/3 and MUY =(2/3) X1/3Y-1/3

U = X + YMUX = Y and MUY = X

Sample Problem 3 (4.14):

Latanya likes to talk on the telephone. We can represent her preferences with the utility function U(B,J) = 18B + 20J, where B and J are minutes of conversation per month with Bill and Jackie, respectively. If Latanya plans to use the phone for one hour to talk with only one person, with whom would she rather speak? Why? What is the formula for her indifference curves?