Theory of Consumer Behavior

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

9-403

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

0

General function operator

4

The Utility FunctionGiven 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 25B 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 25B 3.0 7.0 21

C 2.0 12.5 25

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 MU1 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)

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Marginal Utility

Total Utility =f(QH, QP)QH = quantity of

hamburgersQP = quantity of pizza

∆QH∆U

UMUQ

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

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

Bundles N, P preferred to bundles M, Q and R

Indifferent betweenbundles N and P

Increasingutility

The further from the origin thegreater the utility (satisfaction)

15

Assume you consume hamburgers and tacos

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

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”)

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T

H

ΔQMRSΔQ

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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

ΔQMRSΔQ

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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 MUMRSΔQ MU

22

The MRS of moving from point M and Q on I2 equals:= (5 − 7) ÷ (2 − 1)= − 2.0 ÷ 1.0= − 2.0

23

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

An MRS = − 2 means the consumer is willing to give up 2 tacos in exchange for 1 additional hamburger

25

Which bundle would you prefer more…bundle M or bundle Q?

26

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

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What about the choice between bundle M and P?

28

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 ConstraintThe 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

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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?

32

$B

The Budget ConstraintHow 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


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


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


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


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 $5.00C 5 2 $5.00A 0 4 $5.00

Page 46

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

AG

43

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

AG

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)

QT

QH0

5

10

15

20

2 4 6 8

B

AG

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The Budget Constraint

QT

QH0

5

10

15

20

2 4 6 8

B

AG

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

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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

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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

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Theory of Consumer Behavior

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