The Consumer Theory
How Consumers Make Choices under
Income Constraints
Some Questions
• What is behind a consumer’s demand
curve?
• How do consumers choose from among
various consumer “goods”?
• What determines the value of a consumer
good?
Utility
• The value a consumer places on a unit of a good or
service depends on the pleasure or satisfaction he or she
expects to derive form having or consuming it at the
point of making a consumption (consumer) choice.
• In economics the satisfaction or pleasure consumers
derive from the consumption of consumer goods is called
“utility”.
• Consumers, however, cannot have every thing they wish
to have. Consumers’ choices are constrained by their
incomes.
• Within the limits of their incomes, consumers make their
consumption choices by evaluating and comparing
consumer goods with regard to their “utilities.”
Our basic assumptions about a
“rational” consumer:
• Consumers are utility maximizers
• Consumers prefer more of a good (thing) to less of it.
• Facing choices X and Y, a consumer would either prefer
X to Y or Y to X, or would be indifferent between them.
• Transitivity: If a consumer prefers X to Y and Y to Z, we
conclude he/she prefers X to Z
• Diminishing marginal utility: As more and more of good
is consumed by a consumer, ceteris paribus, beyond a
certain point the utility of each additional unit starts to
fall.
How to Measure Utility
Measuring utility in “utils” (Cardinal):
• Jack derives 10 utils from having one slice of pizza but only 5 utils from
having a burger.
• In many introductory microeconomics textbooks this approach to
measuring utility is still considered effective for teaching purposes.
Measuring utility by comparison (Ordinal):
• Jill prefers a burger to a slice of pizza and a slice of pizza to a hotdog.
Often consumers are able to be more precise in expressing their preferences.
For example, we could say:
• Jill is willing to trade a burger for four hotdogs but she will give up only
two hotdogs for a slice of pizza.
• We can infer that to Jill, a burger has twice as much utility as a slice of
pizza, and a slice of pizza has twice as much utility as a hotdog.
Utility and Money
• Because we use money (rather than hotdogs!) in just about
all of our trade transactions, we might as well use it as our
comparative measure of utility.
(Note: This way of measuring utility is not much different
from measuring utility in utils)
• Jill could say: I am willing to pay $4 for a burger, $2 for a
slice of pizza and $1 for a hotdog.
Note: Even though Jill obviously values a burger more (four
times as much) than a hot dog, she may still choose to buy a
hotdog, even if she has enough money to buy a burger, or a
slice of pizza, for that matter. (We will see why and how
shortly.)
Total Utility versus Marginal Utility
• Marginal utility is the utility a consumer
derives from the last unit of a consumer good
she or he consumes (during a given
consumption period), ceteris paribus.
• Total utility is the total utility a consumer
derives from the consumption of all of the
units of a good or a combination of goods
over a given consumption period, ceteris
paribus.
Total utility = Sum of marginal utilities
The Law of Diminishing Marginal
Utility
• Over a given consumption period, the more of a good a
consumer has, or has consumed, the less marginal
utility an additional unit contributes to his or her overall
satisfaction (total utility).
• Alternatively, we could say: over a given consumption
period, as more and more of a good is consumed by a
consumer, beyond a certain point, the marginal utility of
additional units begins to fall.
Total and Marginal Utility for Ice
Cream
Q
0
1
2
3
4
5
6
7
8
9
10
($) TU
0
40
85
120
140
150
157
160
160
155
145
($) MU
40
45
35
20
10
7
3
0
-5
-10
145
Total Utility
200
150
100
50
0
1
2
3
4
5
6
7
8
9
7
8
9
10 11
($) M U
50
40
30
20
10
0
1
-10
-20
2
3
4
5
6
1
11
Q
0
1
2
3
4
5
6
7
8
9
10
($) TU
0
40
85
120
140
150
157
160
160
155
145
($) MU
40
45
35
20
10
7
3
0
-5
-10
145
How much ice cream does Jill buy in a month?
Some facts of life:
• Limited income
• Opportunity cost of making a choice:
Buying ice cream leaves Jill less money to
buy other things: each dollar spent on ice
cream could be spent on hamburger.
• In fact, consumers compare the (expected)
utility derived from one additional dollar
spent on one good to the utility derived from
one additional dollar spent on another good.
More facts
• The prices of hamburger and ice cream are marketgiven; the consumer cannot change the price of a good.
• Jill, like any other rational consumer, wishes to
maximize her utility.
• The opportunity cost of one dollar spent on ice cream is
the forgone utility of one dollar that could be on
hamburger.
• If the utility of one additional dollar of ice cream is
greater than the utility of the last dollar spent on
hamburger, Jill can increase her total utility by spending
one dollar less on hamburger and one dollar more one
ice cream.
Hamburger or Hotdog
• If based on their perceived marginal utilities
Jill values a hamburger four times as much
as a hotdog, but the market price of a burger
is eight times the price of a hotdog, she will
buy a hotdog. That is because one dollar’s
worth of hotdogs would give her more
utility that one dollar’s worth of burgers.
That is:
MUD/PD > MUH/PH
Utility Maximizing Rules
• A rational consumer would buy an additional unit
of a good as long as the perceived dollar value of
the utility of one additional unit of that good (say,
its marginal dollar utility) is greater than its
market price.
• The Two-Good Rule
MUI
MUH
--------- = ---------$PI
$PH
Utility Maximization under An
Income constraint
• Consumers’ spending on consumer goods is constrained
by their incomes:
Income = Px Qx + Py Qy + Pw Ow + ….+Pz Qz
• While the consumer tries to equalize MUx/Px , MUy/
Py, MUw/Pw,………. and MUz/Pz , to maximize her
utility her total spending cannot exceed her income.
For example, with an and income of $86 Jill is trying to
decide how much ice cream and how much hamburger
she should buy.
Jill’s income = 5x10 + 6 x 6 = 86
Optimal Purchase Mix: Ice Cream and Hamburger
Q
1
2
3
4
5
6
7
8
MUI
40
45
35
20
10
7
3
0
PI
10
10
10
10
10
10
10
10
MUI/PI MUH PH MUH/PH
4
45 6
7.5
4.5
30 6
5
3.5
20 6
3.3
2
15 6
2.5
1
10 6
1.7
0.7
6
6
1
0.3
3
6
0.5
0
0
6
0
The Budget Line
Income = QI.PI + QH.PH = (5 x 10)+(6 x 6) = 86
Ice Cream
86/10
Slope = PH/PI = 6/10
= 8.6/14.33 = 0.6
8.6
5
86/6
Hamburger
o
6
14.33
An Optimal Change
Recall that to maximize utility a consumer
would set:
(MUx/Px) = (MUy/Py)
If Px increases this equality would be
disturbed: (MUx/Px) < (MUy/Py)
To return to equality the consumer must adjust
his/her consumption. (Have in mind that the
consumer cannot change prices, and he/she has
an income constraint.)
What are the consumer’s options?
(MUx/Px) < (MUy/Py)
In order to make the two sides of the above
inequality equal again, given that Px and Py
could not be changed, we would have to
increase MUx and decrease MUy. Recalling
the law of diminishing marginal utility, we
can increase MUx by reducing X and
decrease MUy by increasing Y.
Price and the Shape of the Demand
Curve
The two effects of a price change:
– Income effect:
Normal good (-)
Inferior goods (+)
– Substitution effect
Buying less X and substituting it with Y until the optimizing
condition is restored (-)
As Px increases, Qx decreases
Consumer Surplus
• The difference between what a consumer is
willing to pay for an addition unit of a good
and the market price that he/she actually
pays is referred to as “consumer surplus”.
• The area between the demand curve and the
price (line) measures the total consumer
surplus.
Consumer Surplus
P
Price
D
0
Qx
P
Consumer Surplus
Price
P’
D
0
D’
Qx
An Alternative Approach to the
Consumer Theory
• Indifference curves
An indifference curve is a line drawn in a twodimensional space showing different combinations of
two goods from which the consumer draws the same
amount of utility and therefore he/she is “indifferent”
about.
• Budget lines
A budget line is a line drawn in a two-dimensional
space representing a certain level of income with which
the consumer can purchase various combinations of
two goods at given prices.
Properties of Indifference curves
• Indifference curves for two “goods” are generally
negatively sloped
• The slope of an indifference curve reflects the degree of
substitutability of two goods for one another
• Indifference curves are generally convex, reflecting the
principle of diminishing returns
• Indifference curves never cross
• Indifference curves that are farther from the origin
represent higher levels of utility
• Indifference curves for a “good” and a “bad” are
positively sloped
Indifference Curves
Y
Slope = Change in Y/Change in X
= MUx/MUy
U4
U3
U2
U1
O
X
Budget Line
Y
Income = Px .Qx + Py. Qy
I/Py
Slope = Px/Py
X
O
I/Px
Indifference Curves
Y
MRS = MUx/MUy= Px/Py
a
b
c
U4
U3
U2
d
e
O
U1
X
A change in the price of X: Income and substitution effects
Y
a
b
Y1
Yo
c
C’
U5
c”
U4
U3
d
e
O
Xo
X1
U2
U1
X
A change in the price of X: Income and substitution effects
Y
a
b
Y1
Yo
C’
c
U5
U4
c”
U3
d
e
O
Xo
X1
U2
U1
X