### Chapter 3 Powerpoint

```Theory of
Consumer
Behavior
Chapter 3
Discussion Topics
The concept of consumer utility
(satisfaction)
Evaluation of alternative
consumption bundles using
indifference curves
What is the role of your budget
constraint in determining what you
purchase?
2
The Utility Function
 A model of consumer behavior
 Utility: Level of satisfaction obtained
from consuming a particular bundle of
goods and/or services
 Utility function: an algebraic expression
that allows one to rank consumption
bundles with respect to satisfaction level
• A simple (unrealistic) example:
Total utility = Qhamburgers x Qpizza
3
Page 39-40
The Utility Function
A more general representation of a utility
function without specifying a specific
functional form:
Total Utility =f(Qhamburgers, Qpizza)
General function operator
Interpretation: The amount of utility (i.e.
satisfaction) is determined by the number of
hamburgers and pizza consumed
4
Page 40
The Utility Function
 Given our use of the above functional
notation
This approach assumes that one’s
utility is cardinally measurable
 Similar to a ruler used to measure
distance
You can tell if one bundle of goods
gives you twice as much satisfaction
(i.e., utils is a satisfaction measure)
5
Page 40
The Utility Function
 Ordinal vs. Cardinal ranking of purchase choices
 Cardinally measurable: Can quantify how
much utility is impacted by consumption
choices
 Commodity bundle X provides 3 times the
utility than obtained from bundle Y
 Ordinally measurable: You can only provide a
relative ranking of choices
 Commodity bundle X provides more utility
than bundle Y
 Don’t know how much more
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Page 40
Ranking Total Utility
Bundle
A
7
Quantity of Quantity of
Hamburgers
Pizza
Total
Utility
2.5
10.0
25
B
3.0
7.0
21
C
2.0
12.5
25
Ranking Total Utility
Bundle
A
Quantity of Quantity of
Hamburgers
Pizza
2.5
10.0
25
B
3.0
7.0
21
C
2.0
12.5
25
Prefer A and C over B
Indifferent (equal satisfaction) from
consuming bundle A and C
8
Total
Utility
Marginal Utility
 Marginal utility (MU):
The change in your
utility (ΔUtility) as a result of a change in the
level of consumption (ΔQ) of a particular good
MUi = Utility ÷ Qi
Ceteris paribus concept • ∆ means “change in”
 MU will
• i identifies a good
(i.e. the ith good)
↓ as consumption ↑
 Marginal benefit of last unit consumed ↓ as
you ↑ consumption of a particular good
 The opposite holds true
 Total utility (satisfaction) could still be ↑
9
Page 40-41
Marginal Utility
Total Utility =f(QH, QP)
QH = quantity of
hamburgers
QP = quantity of pizza
10
QH/week
Total Utility
MU
1
20
----
2
30
10
3
39
9
4
47
8
5
54
7
6
60
6
7
65
5
8
69
4
9
72
3
10
74
2
11
74
0
12
70
-4
∆QH
∆U
= (47-39) ÷ (4-3)
MU 
U
Q
Page 40-41
Total Utility
Marginal Utility
Note: MU is the slope
of the utility function,
ΔU÷ΔQH
Marginal utility goes
to zero at the peak of
the total utility curve
(i.e., maximum utility)
Note: The other good, i.e.
pizza, remains unchanged
Total Utility = f(QH, |QP)
11
Example of ceteris paribus
Page 42
Indifference Curves
Cardinal measurement
 Quantitative characterization of a
particular entity
 “I had 2 beers last night”
Ordinal measurement
 Ranking of a particular entity versus
another
 “I had more beers than you last night”
12
Page 41-43
Indifference Curves
Cardinal measurement of utility is both
unreasonable and unnecessary
 i.e., what is the correct functional form
of the relationship between utility and
goods consumed?
Economists typically use an ordinal
measurement of utility
 All we need to know is that one
consumption bundle is preferred over
another
13
Page 41-43
Indifference Curves
Modern consumption theory is based upon the
14
notion of isoutility curves
iso in Greek means equal
Isoutility curves are a collection of bundles of
goods and services where the consumer’s utility
is the same
 Consumer is referred to as being indifferent
between these alternative combinations of
goods and services
 For two goods connect these different
isoutility bundles
 Collection referred to as an isoutility or
indifference curve
Page 41-43
The further from the origin the
greater the utility (satisfaction)
 Bundles N, P preferred
to bundles M, Q and R
 Indifferent between
bundles N and P
Increasing
utility
Assume you consume
hamburgers and tacos
15
Page 43
The two indifference
curves here can be
thought of as providing
200 and 700 utils of
utility.
Note that the rankings don’t
change if measured utility as
10 and 35
16
Page 43
Theoretically there are
an infinite (large)
number of isoutility or
indifference curves
17
Page 43
Slope of the Indifference Curve
 Like any other curve one can evaluate the slope

of each indifference curve
 Indifference curve slope is given a special
name:
Marginal Rate of Substitution (MRS)
Given the above graph the MRS of substitution
of hamburgers for tacos as you move along an
indifference curve is calculated as:
MRS = QT ÷ QH
Change in quantity
of tacos (i.e., “rise”)
18
Change in quantity
of hamburgers (i.e., “run”)
Page 43
MRS 
19
ΔQ T
ΔQ H
Page 43
Slope of the Indifference Curve
MRS 
ΔQ T
ΔQ H
 The MRS reflects

20
(i) The number of tacos a
consumer is willing to give
hamburger
(ii) While keeping the overall
utility level the same
The MRS measures the
curvature of indifference curve
as you move along that curve
Page 43
Slope of the Indifference Curve
 Lets assume we have two goods and an
associated set of indifference curves
 We can relate the MRS to the MU’s associated
with consumption of these two goods
 Along an indifference curve we know that
 ∆U = ∆QTMUT + ∆QHMUH = 0
Change in
Utility  → ∆Q MU = –∆Q MU
T
T
H
H
Due to being on
the same
indifference curve
 → MRS = ∆QT÷∆QH = –MUH ÷MUT
21
Page 43
Slope of the Indifference Curve
MRS 
22
ΔQ T
ΔQ H

MUH
MUT
Page 43
The MRS of moving from
point M and Q on I2 equals:
= (5 − 7) ÷ (2 − 1)
= − 2.0 ÷ 1.0= − 2.0
23
Page 43
 The MRS changes as one
moves from on point to another
 MRSM→Q ≠ MRSQ→R
 What do you think happens
to the MRS when going
from M to Q?
24
Page 43
An MRS = − 2 means the
consumer is willing to give
up 2 tacos in exchange for
25
Page 43
Which bundle would you
prefer more…bundle M or
bundle Q?
26
Page 43
 The answer is that you would
be indifferent as they give the
same utility
 The ultimate choice will
depend on the prices of these
two products
Page 43
27
between bundle M and P?
28
Page 43
 You would prefer bundle P

29
over bundle M because it
generates more utility
 Shown by being on a
higher indifference curve
Can you afford to buy 5
tacos and 5 hamburgers?
Page 43
The Budget Constraint
 We can represent the weekly budget for fast food
(BUDFF) as: (PH x QH) + (PT x QT)  BUDFF
\$ spent on ham.
\$ spent on tacos
 PH and PT represent current price of burgers and tacos,
respectively
 QH and QT represent quantities of burgers and tacos you
plan to consume during the week
The budget constraint is what limits the amount
that can be spent on these items
30
Page 45
The Budget Constraint
 The graph depicting this fixed amount of
QT
expenditure referred to as the budget
constraint
Values on the boundary (BCA) can
be represented as:
BUDFF = (PH1 x QH1) + (PT1 x QT1)
B
QT1
31
C
QT2
D
0
QH1 QH2
In the interior, (i.e., point D) , amt.
spent can be represented as:
BUDFF > (PH1 x QH1) + (PT1 x QT1)
→ Not all of the budget is spent
A
QH
Page 45
The Budget Constraint
 Points on the boundary of the budget
constraint represent all commodity
combinations whose total expenditure
equals the available budget
QT
 Important Assumption: Prices do not change
with the amount purchased
How can we transform the graph of the budget set
shown on the left to a mathematical representation?
\$B
32
QH
Page 45
The Budget Constraint
How can we determine the equation of the
budget line (i.e., the boundary)?
 Given the assumption of fixed prices, to
determine the location of a budget in good
space all we need is the
• Slope and
• Intercept on either the vertical or horizontal axis
 Why do we only need the slope to identify
where the \$B budget curve is located in Good
Good 2
1/Good 2 space?
\$B budget line
33
Good 1
Page 45
The Budget Constraint
How can we determine the equation of the
budget line (i.e., the boundary)?
 Remember from your calculus that the slope
of a straight line is the ratio of the change in
arguments of that straight line as you move
along it
QT
•A
Slope at point A =
ΔQT÷ ΔQH as you
move away from
point A
QP
34
Page 45
The Budget Constraint
How can we determine the equation of the
budget line (i.e., the boundary)?
 Budget line represents the collection of
pairs where total expenditures is \$B
 → movement along a budget line the
change in amount spent is \$0 (i.e., Δ\$B = 0)
ΔBUDff = (PH x ΔQH) + (PT x ΔQT) = 0
→ 0 = (PH x ΔQH) + (PT x ΔQT)
Q
Slope = ΔQT÷ ΔQH
→ –PH x ΔQH = PT x ΔQT
→ (–PH ÷ PT) = (ΔQT÷ ΔQH)
T
Slope of budget constraint < 0, Why?
35
QH
Page 45
The Budget Constraint
How can we determine the equation of the
budget line (i.e., the boundary)?
 What is the budget constraint’s slope?
 Movement along a budget line means
the change in amount spent is \$0
ΔBUDff = (PH x ΔQH) + (PT x ΔQT)
→ 0 = (PH x ΔQH) + (PT x ΔQT) Q
Slope = ΔQT÷ ΔQH
→ –PH x ΔQH = PT x ΔQT
→ –(PH ÷ PT) = (ΔQT÷ ΔQH)
T
Slope of budget constraint < 0
36
QH
Page 45
The Budget Constraint
How can we determine the equation of the
budget line (i.e., the boundary)?
 The equation for the budget line can be
obtained via the following:
BUDFF = (PH x QH) + (PT x QT)
→ (PT x QT) = BUDff – (PH x QH)
→ QT = (BUDFF ÷ PT ) – ((PH x QH) ÷ PT )
→ QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH)
This equation shows the combinations of
tacos and hamburgers that equal budget
BUDFF given fixed prices
37
Page 45
The Budget Constraint
Given the above we can represent the budget
constraint in quantity (QT, QH) space via:
QT
0BCA are combinations
of burgers and tacos
that can be purchased
B
with \$BUDFF
QT1
(BUDFF ÷ PT)
How many hamburgers
are represented by A?
Slope of BCA = – PH ÷ PT
C
QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH)
Line BCA are all combo’s
of burgers and tacos
where total expenditures
= \$BUDFF
0
38
QH1
A
QH
Page 45
Example of a Budget Constraint
Point on
Budget
Line
B
C
Tacos
(PT =
\$0.50)
10
5
A
0
Hamburgers
Total
(PH =
Expenditure
\$1.25)
(BUDFF)
0
\$5.00
2
\$5.00
4
\$5.00
Combinations representing
points on budget line BCA
shown below
39
Page 46
The Budget Constraint
 Given a budget of \$5, PH = \$1.25,
QT
20
PT = \$0.50:
You can afford either 10 tacos, or 4
hamburgers or a combination of both as
defined by the budget constraint
15
10 B
C
5
QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH)
= (\$5 ÷ \$0.50) – ((\$1.25 ÷ \$0.50) x QH)
→QT = 10 – 2.5 x QH
→QH = 4 – 0.4 x QT
At B, QH = 0
At A, QT = 0
A
0
40
2
4
6
8
QH
Page 45
The Budget Constraint
 Doubling the price of tacos to \$1.00:
You can now afford either 5 tacos or 4
burgers or a combination of both as
shown by new budget constraint, FA:
QT
20
QT = 5 – 1.25 x QH
QH = 4 – 0.8 x QT
15
Note that the budget line pivots around
point A given that the hamburger price
does not change!
B
10
F
5
A
0
41
2
4
6
8
QH
Page 45
The Budget Constraint
 Lets cut the original price of tacos in
half to \$0.25:
QT
You can afford either 20 tacos, or 4
hamburgers or a combination of both as
shown by new budget constraint, EA:
E
20
15
QT = 20 – 5 x QH
QH = 4 – 0.2 x QT
B
10
F
5
A
0
42
2
4
6
8
QH
Page 45
The Budget Constraint
 Changes in the price of burgers:
Similar to what we showed with respect to
taco price
If you ↑ PH (i.e., double it), the budget
constraint shifts inward with 10 tacos
still being able to be purchased (BG
If you ↓ PH, (i.e., cut in half) the budget
constraint shifts outward with 10 tacos
still being able to be purchased
QT
20
15
B
10
5
A
0
43
G
2
4
6
8
QH
Page 45
The Budget Constraint
 What is the impact of a change in your
budget (i.e., income), ceteris paribus?
QT
Under this scenario both prices do not
change
20
 →the budget constraint slope does not change
→A parallel shifit of budget constraint
depending on whether income ↑ or ↓
15
B
10
Budget ↑
Budget ↓
5
A
0
44
G
2
4
6
8
QH
Page 45
The Budget Constraint
 With prices fixed, why does a budget
change result in a parralell budget
constraint shift?
QT
20
Due to the equation that defines the
budget constraint:
15
Q2 = (BUD ÷ P2 ) – ((P1÷ P2) x Q1)
B
10
5
A
0
45
G
2
4
6
8
QH
Page 45
The Budget Constraint
 BUD reduced by 50%:
Original budget line (BA) shifts in
parallel manner (same slope) to FG
Same if both prices doubled
Real income ↓
 BUD doubled:
BA shifts in parallel manner (same
slope) out to ED
Same if both prices cut by 50%
Real income ↑
QT
E
20
15
B
10
F
5
A
G
0
46
G
2
4
D
6
8
QH
Page 46
In Summary
Consumers rank preferences based upon utility
or the satisfaction derived from consumption
A budget constraint limits the amount we can
•
47
Given a fixed budget, the amount of commodities
that could be purchased are determined by their
prices
Chapter 4 unites the concepts of
indifference curves with the budget
constraint to determine consumer
equilibrium which we represent by
the amount of purchases of the
available commodities actually
48
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