Download The Art and Science of Economics

Indifference Curves and Utility
Maximization
CHAPTER
6 Appendix
© 2003 South-Western/Thomson Learning
1
Indifference Curves and Utility
Maximization
Marginal utility analysis requires some
numerical measure of utility in order to
determine the optimal consumption
combinations
Economists have developed another,
more general, approach to utility and
consumer behavior
This approach does not require that
numbers be attached to specific levels
of utility
2
Indifference Curves and Utility
Maximization
All this new approach requires is that
consumers be able to rank their
preferences for various combinations of
goods
Specifically, the consumer should be able
to say whether
Combination A is preferred to combination B
Combination B is preferred to combination A.
or
Both combinations are equally preferred
3
Consumer Preferences
Indifference curve shows all
combinations of goods that provide the
consumer with the same satisfaction, or
the same utility
Thus, the consumer finds all
combinations on a curve equally
preferred
Since each of the alternative bundles of
goods yields the same level of utility,
the consumer is indifferent about which
combination is actually consumed
4
Indifference Curves
For a person to remain indifferent
among consumption combinations, the
increase in utility from eating more
pizza must just offset the decrease in
utility from watching fewer videos
Thus, along an indifference curve, there
is an inverse relationship between the
quantity of one good consumed and the
quantity of another consumed 
indifference curves slope down
5
Indifference Curves
Indifference curves are also convex to
the origin  they are bowed inward
toward the origin
The curve gets flatter as you move
down it
The marginal rate of substitution, or
MRS, between pizza and videos
indicates the number of videos that the
consumer is willing to give up to get
one more pizza, while maintaining the
same level of total utility
6
Marginal Rate of Substitution
The MRS measures the consumers
willingness to trade videos for pizza 
depends on the amount of each good
the consumer is consuming at the time
Mathematically, the MRS is equal to the
absolute value of the slope of the
indifference curve
For example, in moving from combination a
to combination b, the consumer is willing to
give up 4 videos to get 1 more pizza  slope
between these two points equals –4  MRS
= 4; from b to c, MRS = 1
7
Marginal Rate of Substitution
The law of diminishing marginal rate of
substitution says that as a persons
consumption of pizza increases, the
number of videos that they are willing
to give up to get another pizza declines
This implies that the indifference curve
has a diminishing slope  as we move
down the indifference curve, the
consumption of pizza increases and the
marginal utility of additional pizza
declines
8
Indifference Map
We can use the same approach to
generate a series of indifference curves,
called an indifference map  graphical
representation of a consumer’s tastes
Each curve in the map reflects a
different level of utility
9
Properties of Indifference Curves
A particular indifference curve reflects a
constant level of utility  the consumer
is indifferent among all consumption
combinations along a given curve
If total utility is to remain constant, an
increase in the consumption of one
good must be offset by a decrease in
the consumption of the other good 
indifference curves slope downward
Higher indifference curves represent
higher levels of utility
10
Properties of Indifference Curves
Because of the law of diminishing
marginal rate of substitution,
indifference curves are bowed in toward
the origin
Indifference curves do not intersect
Indifference curves are a graphical
representation of a consumer’s tastes
for the two goods
11
Properties of Indifference Curves
Once we have the consumer’s
indifference may, we turn to the issue of
how much of each good will be
consumed?
To answer this question, we must
consider the relative prices of the two
goods and the consumer’s income
12
Budget Line
Budget line depicts all possible
combinations of movies and pizzas,
given prices and your budget
Suppose movies rent for $4, pizza sells
for $8, and the budget is $40 per week
 if you spend the entire $40 on videos,
consumer can purchase 10 videos, and
if on pizzas person can afford 5 per
week
13
Summary
The indifference curve indicates what
the consumer is willing to buy
The budget line shows what the
consumer is able to buy
When the indifference curve and the
budget line are combined, we find the
quantities of each good the consumer is
both willing and able to buy
14
Consumer Equilibrium
Consumer equilibrium occurs where the
slope of the indifference curve is equal
to the slope of the budget line
Recall that the absolute value of the
slope of the indifference curve is the
marginal rate of substitution, and the
absolute value of the slope of the
budget line equals the price ratio
15
Consumer Equilibrium
Thus,
MRS = Pp / Pv
Further, the marginal rate of
substitution of pizzas for video rentals
can be found from the marginal utilities
of pizza and video  MRS = MUp / MUv
16
Consumer Equilibrium
In fact, the absolute value of the slope
of the indifference curve equals
MUp/MUv and the slope of the budget
line equals pp / pv  the equilibrium
condition for the indifference curve
approach can be written as
MUP  MUV
PP
PV
17
Effects of a Change in Price
What happens to the consumer’s
equilibrium consumption when there is
a change in price?
The answer can be found by using
indifference curve approach to derive
the demand curve
18
Income and Substitution Effects
The law of demand was initially
explained in terms of an income effect
and a substitution effect
With indifference curve analysis we
have the analytical tools to examine
these two effects more precisely
19