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A brief about demand function!
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Chapter 4
Principles and Preferences
McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Main Topics
Principles of decision-makingConsumer preferencesSubstitution between goodsUtilityRecommended Reading: Applications
4.1, 4.2; Example 4.3
4-2
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
4-3
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 isolation
Decision to consume more of one good is a decision to consume less of another
4-4
Principles of Consumer Decision-Making
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 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
4-5
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
4-6
Figure 4.1: Identifying Alternatives and Indifference Curves
4-7
Properties of Indifference Curves
ThinDo not slope upwardSeparates bundles that are better from
bundles that are worse than those that are on the indifference curve
4-8
Figure 4.2: Indifference Curves Ruled Out by the More-is-better Principle
4-9
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
4-10
Figure 4.3: A Family of Indifference Curves
4-11
Figure 4.4: Indifference Curves Do Not Cross
4-12
Formulas for Indifference Curves
More complete and precise to describe preferences mathematically
For example, we 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
4-13
Figure 4.6: Plotting Indifference Curves
Formula for indifference curves is B = U/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
4-14
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
4-15
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
4-16
Figure 4.8: Rates of Substitution
Look at movement from bundle A to C
Consumer loses 1 soup; gains 2 bread
Willing to substitute for soup with bread at 2 ounces per pint
4-17
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
4-18
Figure 4.9: Marginal Rate of Substitution
MRSSB=-B/S=3/2
4-19
What Determines Rates of Substitution?
Differences in tastesPreferences for one good over another affect the
slope of an indifference curveImplications for MRS
Starting point on the indifference curvePeople like variety so most indifference curves get
flatter as we move from top left to bottom rightLink between slope and MRS implies that MRS
declines; the amount of Y required to compensate for a given change in X decreases
4-20
Figure 4.10: Indifference Curves and Consumer Tastes
4-21
Figure 4.11: MRS along an Indifference Curve
4-22
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
4-23
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!
4-24
Figure 4.12: Perfect Substitutes
4-25
Figure 4.13: Perfect Complements
4-26
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, 4-27
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
4-28
Figure 4.14: Representing Preferences with a Utility Function
4-29
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
4-30
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
4-31
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
4-32
Marginal Utility
Using Calculus, marginal utility of X in the change in U when X changes by a very small amount.
X
UMU X
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
4-34