Theory ofConsumerBehavior
Chapter 3
Discussion TopicsThe 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 FunctionA model of consumer behaviorUtility: 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
Page 39-403
The Utility FunctionA more general representation of a utility
function without specifying a specific functional form:
Total Utility =f(Qhamburgers, Qpizza)
Interpretation: The amount of utility (i.e.
satisfaction) is determined by the number of hamburgers and pizza consumed
Page 40
General function operator
4
The Utility Function
Given our use of the above functional notationThis approach assumes that one’s
utility is cardinally measurable Similar to a ruler used to measure
distanceYou can tell if one bundle of goods
gives you twice as much satisfaction (i.e., utils is a satisfaction measure)
Page 405
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
Page 406
Ranking Total Utility
BundleQuantity of
HamburgersQuantity of
PizzaTotal
Utility
A 2.5 10.0 25
B 3.0 7.0 21
C 2.0 12.5 25
7
Ranking Total Utility
BundleQuantity of
HamburgersQuantity of
PizzaTotal
Utility
A 2.5 10.0 25
B 3.0 7.0 21
C 2.0 12.5 25
Prefer A and C over BIndifferent (equal satisfaction) from
consuming bundle A and C
Prefer A and C over BIndifferent (equal satisfaction) from
consuming bundle A and C8
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 goodMUi = Utility ÷ Qi
Ceteris paribus concept
MU will ↓ 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 ↑Page 40-419
• ∆ means “change in”• i identifies a good
(i.e. the ith good)
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
Page 40-41
= (47-39) ÷ (4-3)
10
Marginal Utility
Total Utility =f(QH, QP)QH = quantity of
hamburgersQP = quantity of pizza
∆QH∆U
UMU
Q
Marginal utility goesto zero at the peak ofthe total utility curve(i.e., maximum utility)
Marginal utility goesto zero at the peak ofthe total utility curve(i.e., maximum utility)
Page 42
Note: MU is the slopeof the utility function,ΔU÷ΔQH
Total Utility
Marginal Utility
11
Total Utility = f(QH, |QP)
Note: The other good, i.e. pizza, remains unchanged
Note: The other good, i.e. pizza, remains unchanged
Example of ceteris paribus
Indifference CurvesCardinal 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”
Page 41-4312
Indifference CurvesCardinal 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
Page 41-4313
Indifference CurvesModern consumption theory is based upon the
notion of isoutility curvesiso in Greek means equalIsoutility 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 41-4314
Page 43
Bundles N, P preferred to bundles M, Q and R
Indifferent betweenbundles N and P
Increasingutility
Increasingutility
The further from the origin thegreater the utility (satisfaction)
15
Assume you consume hamburgers and tacos
Page 43
Note that the rankings don’tchange if measured utility as 10 and 35
The two indifferencecurves here can be thought of as providing 200 and 700 utils of utility.
16
Page 43
Theoretically there are an infinite (large) number of isoutility or indifference curves
17
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
Page 43
Change in quantityof tacos (i.e., “rise”)
Change in quantityof hamburgers (i.e., “run”)
18
Page 43
T
H
ΔQMRS
ΔQ
19
Slope of the Indifference Curve
The MRS reflects (i) The number of tacos a
consumer is willing to give up for an additional 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
T
H
ΔQMRS
ΔQ
20
Slope of the Indifference Curve
Lets assume we have two goods and an associated set of indifference curvesWe 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
→ ∆QTMUT = –∆QHMUH
→ MRS = ∆QT÷∆QH = –MUH ÷MUT
Page 43
Change in Utility
21
Due to being onthe sameindifference curve
Slope of the Indifference Curve
Page 43
T H
H T
ΔQ MUMRS
ΔQ MU
22
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 1 additional hamburger
25
Page 43
Which bundle would you prefer more…bundle M or bundle Q?
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
27
Page 43
What about the choice between bundle M and P?
28
Page 43
You would prefer bundle P 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?
29
The Budget Constraint We can represent the weekly budget for fast food
(BUDFF) as: (PH x QH) + (PT x QT) BUDFF
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
Page 45
$ spent on ham. $ spent on tacos
30
The Budget Constraint
The graph depicting this fixed amount of expenditure referred to as the budget constraint
Page 45
QH0 A
B
CQT1
QH1
Values on the boundary (BCA) can be represented as:BUDFF = (PH1 x QH1) + (PT1 x QT1)
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
D
QH2
QT2
QT
31
The Budget ConstraintPoints on the boundary of the budget
constraint represent all commodity combinations whose total expenditure equals the available budget Important Assumption: Prices do not change
with the amount purchased
Page 45QH
QT
How can we transform the graph of the budget setshown on the left to a mathematical representation?
How can we transform the graph of the budget setshown on the left to a mathematical representation?
32
$B
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 1/Good 2 space?
Page 4533 Good 1
Good 2
$B budget line
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
Page 4534
QP
QTSlope at point A = ΔQT÷ ΔQH as you move away from point A•A
The Budget ConstraintHow 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)
→ –PH x ΔQH = PT x ΔQT
→ (–PH ÷ PT) = (ΔQT÷ ΔQH)
Page 45
Slope of budget constraint < 0, Why? QH
QT
Slope = ΔQT÷ ΔQH
35
The Budget ConstraintHow 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 $0ΔBUDff = (PH x ΔQH) + (PT x ΔQT) → 0 = (PH x ΔQH) + (PT x ΔQT)
→ –PH x ΔQH = PT x ΔQT
→ –(PH ÷ PT) = (ΔQT÷ ΔQH)
Page 45
Slope of budget constraint < 0 QH
QT
Slope = ΔQT÷ ΔQH
36
The Budget ConstraintHow 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)
Page 45
This equation shows the combinations of tacos and hamburgers that equal budget BUDFF given fixed prices
37
The Budget ConstraintGiven the above we can represent the budget
constraint in quantity (QT, QH) space via:
Page 45
QT
QH
QT = (BUDFF ÷ PT ) – ((PH ÷ PT) x QH)
(BUDFF ÷ PT)
0 A
B
0BCA are combinationsof burgers and tacos that can be purchased with $BUDFF
C
Line BCA are all combo’s of burgers and tacos where total expenditures= $BUDFF
QT1
QH1
Slope of BCA = – PH ÷ PT
How many hamburgersare represented by A?
38
Example of a Budget Constraint
Point on Budget
Line
Tacos(PT =
$0.50)
Hamburgers(PH =$1.25)
Total Expenditure
(BUDFF)
B 10 0 $5.00
C 5 2 $5.00
A 0 4 $5.00
Page 46
Combinations representing points on budget line BCA shown below
Combinations representing points on budget line BCA shown below
39
The Budget Constraint Given a budget of $5, PH = $1.25, PT = $0.50:
You can afford either 10 tacos, or 4 hamburgers or a combination of both as defined by the budget constraint
Page 45
QT
QH0
5
10
15
20
2 4 6 8
B
C
A
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 = 0At A, QT = 0
40
The Budget ConstraintDoubling 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 = 5 – 1.25 x QH
QH = 4 – 0.8 x QT
Note that the budget line pivots around point A given that the hamburger price does not change!
Page 45
QT
QH0
5
10
15
20
2 4 6 8
B
A
F
41
The Budget ConstraintLets cut the original price of tacos in
half to $0.25:You can afford either 20 tacos, or 4
hamburgers or a combination of both as shown by new budget constraint, EA:
QT = 20 – 5 x QH
QH = 4 – 0.2 x QT
Page 45
QT
QH0
5
10
15
20
2 4 6 8
B
A
F
E
42
The Budget ConstraintChanges in the price of burgers:
Similar to what we showed with respect to taco priceIf 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
Page 45
QT
QH0
5
10
15
20
2 4 6 8
B
A
G43
The Budget ConstraintWhat is the impact of a change in your
budget (i.e., income), ceteris paribus?Under this scenario both prices do not
change →the budget constraint slope does not change
→A parallel shifit of budget constraint depending on whether income ↑ or ↓
Page 45
QT
QH0
5
10
15
20
2 4 6 8
B
A
G
Budget ↑
Budget ↓
44
The Budget ConstraintWith prices fixed, why does a budget
change result in a parralell budget constraint shift?Due to the equation that defines the
budget constraint: Q2 = (BUD ÷ P2 ) – ((P1÷ P2) x Q1)
Page 45
QT
QH0
5
10
15
20
2 4 6 8
B
A
G45
The Budget Constraint
Page 46
QT
QH0
5
10
15
20
2 4 6 8
B
A
G
BUD reduced by 50%:Original budget line (BA) shifts in
parallel manner (same slope) to FGSame if both prices doubledReal income ↓
BUD doubled:BA shifts in parallel manner (same
slope) out to EDSame if both prices cut by 50%Real income ↑F
G
E
D
46
In SummaryConsumers rank preferences based upon utility
or the satisfaction derived from consumptionA budget constraint limits the amount we can
buy in a particular period• Given a fixed budget, the amount of commodities
that could be purchased are determined by their prices
47
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 made
48