Chapter 4 Principles and Preferences

Chapter 4

• Principles and Preferences

Main Topics

• Principles of decision-making

• Consumer preferences

• Substitution between goods

• Utility

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

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 bundle

• Should reflect preferences over various bundles, not just feelings about any one good in isolation

• Decision to consume more of one good is a decision to consume less of another

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.

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

Figure 4.1: Identifying Alternatives and Indifference Curves

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

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

Families of Indifference Curves

• Collection of indifference curves that represent the preferences of an individual

• Do not cross

• Comparing two bundles, the consumer prefers the one on the indifference curve further from the origin

Figure 4.3: A Family of Indifference Curves

Figure 4.4: Indifference Curves Do Not Cross

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

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

Substitution Between Goods

• Economic decisions involve trade-offs

• To 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

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

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

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

Figure 4.9: Marginal Rate of Substitution

• MRSSB=-B/S=-3/2

What Determines Rates of Substitution?

• Differences in tastes

• Preferences for one good over another affect the slope of an indifference curve (weights attached to each good in the utility function)
• Implications for MRS

• Starting 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

Figure 4.10: Indifference Curves and Consumer Tastes

Figure 4.11: MRS along an Indifference Curve

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

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!

Figure 4.12: Perfect Substitutes

Figure 4.13: Perfect Complements

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

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

Figure 4.14: Representing Preferences with a Utility Function

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

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 = XY
• Y = U2 /X
• Then pick some level of utility. Let’s set U = 25

Utility Functions and Indifference Curves

• Thus, Y = 5/X

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

• Describe the indifference curves for the following utility functions:

• U = X + Y
• U = 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

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

Utility Functions and MRS

• Small change in X, X, causes utility to change by MUXX

• Small change in Y, Y, causes utility to change by MUYY

• If we stay on same indifference curve, then –Y/X =MUXMUY

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 + Y
• MUX = 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?