Consumer Theory (1)

8/6/2019 Consumer Theory (1)

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Consumer Theory


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What is Consumer Theory?

Study of how people use their limited means tomake purposeful choices.

Assumes that consumers understand theirchoices (possibilities) and the prices(opportunity costs) associated with eachchoice.

Assumes that consumers consider thealternatives and choose the one they like best.


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Consumer Theory - Why?

Two important reasons:

to understand the foundations of market

demand (bake the demand curve fromscratch)

to address several interesting consumertheory issues that are best understood

using this model rather than the aggregatedemand model


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Two Components ofConsumer Demand

Opportunities:

What can the consumer afford?

What are the consumption possibilities? Summarized by the budget constraint

Preferences:

W

hat does the consumer like? How much does a consumer like a good?

Summarized by the utility function


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What is a Budget Constraint?

A budget constraint shows theconsumers purchase opportunities as

every combination of two goods that canbe bought at given prices using a givenamount of income.

The budget constraint measures thecombinations of purchases that a personcan afford to make with a given amountof monetary income.


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Lis Demand forWheat and Rice

Illustration of consumer theory

Lis demand for wheat and rice depends

upon the prices for these goods, herincome, and her preferences.

Suppose we look first at her budget

constraint: Wheat costs $4/lb.

Rice costs $2/lb.

Li has $40 of income.


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Lis Budget Constraint

The mathematical expression forLisbudget constraint is:

I = PWW + PRRR = I/PR- (PW/ PR)W

I like to refer to the |slope| of the budget lineas the ERS=Economic Rate ofSubstitution

In this case it is PW/ PRForLi: PW=$4 PR=$2 I=$40 ERS=2


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Graph ofLis BudgetConstraint

The graph to the rightshows a picture ofLisbudget constraint.

Li's Budget Constraint

0

5

10

15

20

0 5 10 15 20

Wheat

Rice

Each blue diamond is apoint from the table.

The slope is equal to -2,

as shown on the lastslide.


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Budget Line gymnastics

An increase in income only.

An increase in the price of wheat only.

A decrease in the price of rice only. Income doubles as do the prices of wheat and

rice.

Note: Changes in the price of wheat relative tothe price of rice will change the ERS.


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Preferences

Let R= at least as good as

B0 RB1 means: B0 is at least as good as B1

Let IN= indifferent to

B0 RB1 and B1 RB0 impli B0 INB1

Let P= strictly preferred to

B0 RB1 andnot B1 RB0 impli B0 PB1


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Preferences

Basic assumptions about an individualspreferences (R) over bundles (B)

mor i b tt r : If B0 has more in it than B1 then

B0 RB1

transitivity: IfB0 RB1 and B1 RB2 t n B0 RB2

av rage b ndlesareat least asgoodasextreme b ndles: If B0 INB1 and B2 is anaverage of B0 and B1, then B2 RB0 and B1


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Utility and Preferences

Utility is the way economists representpreferences.

Among two bundles, the one with thehigher utility is the preferred bundle.

If two bundles have the same utility, we

say that the consumer is indifferent.


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Indifference Curves Preferences that satisfy the conditions I have

noted above can be represented byindifference curves.

The set of all indifference curves that describean individuals preferences are referred to asan indifference curve map.

An indifference curve connects all of the

bundles that a consumer likes equally.We will assume only two goods when using

indifference curve analysis.


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Indifference Curve Map -Properties

An indifference curve should not slopeup.

Indifference curves can not cross oneanother.

Better bundles are to the northeast.

Indifference curves will not be bowedout.


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Lis Preferences inIndifference Curves

An indifference curve connectsall the bundles that have thesame utility.

Higher indifference curves

indicate more utility (IC2 ispreferred to IC1).

Lower indifference curvesindicate less utility (IC1 ispreferred to IC0).

The indifference curve map isFULL of indifference curves.

L s nd erence ur es

0

5

10

15

20

25

30

0 10 20

hea

ce

I2

I1

I0


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The Marginal Rate ofSubstitution The Marginal Rate of

Substitution(MRS) tells ushow much of one good Liwould willingly trade for anincremental unit of the othergood and remain indifferent.

The MRS=|slope| of theindifference curve at abundle.

Common to assume the MRS

declines as we move downan indifference curve.

L s nd erence ur es

0

5

10

15

20

25

30

0 10 20

hea

ce

I2

I1

I0


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How Much Wheat and Rice

Lis optimal amount of wheat and rice toconsume is the amount that maximizes Lisutility subject to her budget constraint.

In the graph...

Get to the highest indifference curve possible

Stay on the budget constraint (b/c more isbetter)


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How to Find Lis BestCombination

Wheat

Rice

20

10

IC0IC1

IC2

W*

R*

The black bundle is best.

The pink bundle is not thebest. Li has spent all herincome but is not on thehighest indifference curvepossible.

Bundles n/e ofIC0 arebetter and some areaffordable.

At (W*, R*) she is doing the

best she can subject to herbudget constraint.


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How to Find the BestCombination

Utility is maximized when:

the indifference curve is just tangent to the budgetline.

Utility is maximized when: you are on the budget line and

the slope of the indifference curve equals theslope of the budget line

Utility is maximized when:

Income=PRR + PWW

MRS=ERS


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The bang per buck story

Let MUW =Lis marginal utility of wheat

it measures the change in utility as we change wheatconsumption by an incremental unit while holding rice

constant Let MUR =Lis marginal utility of rice

it measures the change in utility as we change riceconsumption by an incremental unit while holding

wheat constantCommon to assume that marginal utilities decline

as we increase consumption - the law ofdiminishing marginal utility


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The bang per buck story

The MRS= MUW/ MURThe ERS= PW / PR

At an optimal bundle: MRS=ERSRewritten we have:

MUW/ MUR = PW / PR

MUW/PW

=

MU

R/PR bang/buck in wheat = bang/buck in rice

Get same optimal bundle either way


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Handling a change in PW

Li wants to achieve thehighest indifference curvethat the budget constraintspermit.

The points A, B, and Crepresents the best that Lican do at prices of $4, $2,and $1 for wheat.

The equation MRS=ERS issatisfied at each of thepoints.

Li's Demand for Wheat

0

5

10

15

20

25

30

0 5 10 15 20

Wheat

Rice

I2

I1

I0

4

2

1

C

B

A


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Lis Demand forWheat

The table shows theamount of wheat

thatL

i demands ateach price.

These are the pointsof tangency from the

previous slide.

Quantity rice oint

6 4

10 2

16 1

Li's emand for Wheat


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Graph ofLis Demand forWheat

When we connect thepoints from the table inthe previous slide weget Lis demand forwheat.

The points A, B, and Ccorrespond to thetangencies of thebudget constraint andthe indifference curves.

L s DemandforWheat

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

Quant ty

Pr

e

C


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Lis Best ChoiceReconsidered

Consider the choice at PW=$2/lb.

The point B is optimal.

The point A is feasible but inferior toall points on the red budget linebetween E and F.

The point C is preferred to B butcannot be purchased with Lis $40income at the given prices; it isabove the red budget line.

The point E is feasible but Li prefersmore wheat and less rice (B).

The point F is feasible but Li prefersless wheat and more rice (B, again).

There is no combination that Liprefers to B that she is able to buy.

L s Best Cho ceof heatand Rice

0

5

10

15

20

25

30

0 5 10 15 20heat

Rice

I2

I1

I0

2

A

E

F

BC


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Handling a change in PW

Li wants to achieve thehighest indifference curvethat the budget constraintspermit.

The points A, B, and Crepresents the best that Lican do at prices of $4, $2,and $1 for wheat.

The equation MRS=ERS issatisfied at each of thepoints.

Li's Demand for Wheat

0

5

10

15

20

25

30

0 5 10 15 20

Wheat

Rice

I2

I1

I0

4

2

1

C

B

A


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Lis Demand forWheat

The table shows theamount of wheat

thatL

i demands ateach price.

These are the pointsof tangency from the

previous slide.

Quantity rice oint

6 4

10 2

16 1

Li's emand for Wheat


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Graph ofLis Demand forWheat

When we connect thepoints from the table inthe previous slide weget Lis demand forwheat.

The points A, B, and Ccorrespond to thetangencies of thebudget constraint andthe indifference curves.

Li's DemandforWheat

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

Quantity

Price

A

B

C


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Li's e and f rWheat

0

5

10

15

20

25

30

0 5 10 15 20

Wheat

ice

I2

I1

I0

4

2

1

C

B

A

i e a Wheat

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ua tit

ice

A

B

C

From IC Map to Lis DemandforWheat


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Income and SubstitutionEffects

Economists decompose the effect of a change in priceon the quantity demanded into an income and asubstitution effect.

Income effect: due to the increase in real incomeassociated with a fall in prices (you can buy more withthe same nominal income) or the loss of real incomeassociated with a rise in prices (you cannot buy as muchas you once did with the same nominal income).

Substitution effect: due to the change in the relativeprice of the good, cheaper goods are substituted formore expensive ones.


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Income and Substitution Effects:Price Decline, X normal

When the price of a good falls, the quantitydemanded rises for two reasons.

The income effect: real income is higher because the

same money income buys more at the lower prices.For normal goods, then, the income effect of a pricefall is positive.

The substitution effect: consumers substitute the nowcheaper good for ones whose price has not fallen,real income held constant. This increase in demandis called the substitution effect of a price decline.


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Lis Income and SubstitutionEffects: Price Fall, Rice normal

Graph shows the income andsubstitution effects of the fall inthe price of wheat from $4/lb. (A)to $1/lb. (C).

The movement from point A to

point D is the substitution effect:Li buys less rice and more wheat,and would do so even if she hadan income of only $20 (as theblack budget line shows).

The movement from point D to

point C is the income effect, theprice decline is like giving Li anadditional $20 of real income.

Li's Income and S bstit tion Effects

0

5

10

15

20

25

30

0 5 10 15 20Wheat

Rice

I2

I0

4

1

1

C

AD


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Lis Substitution Effect

The substitution effect is the amount bywhich Li's wheat consumption increasedholding real income constant.

Substitution effect is the differencebetween Li's consumption of wheat at thenew and old prices holding her real

income constant, that is, staying on thesame indifference curve (compare pointsA and D).


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Lis Income Effect

When the price falls from $4/lb. of wheat to $1/lb. perwheat, Li is able to buy both more wheat and morerice.

The income effect is the difference between whatshe would have bought on the old indifference curveat the lower wheat price (point D) and what sheactually did buy with her nominal income ($40) at thelower price (point C).

Li increases her consumption of wheat and ricebecause of the increase in her real income from theprice decline.


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General effect of a price fall

Income effect - you feel richer

X normal

Substitution EffectX now looks relatively cheaper

PX falls

uantity demanded increases uantity demanded increasesuantity demanded decreases

Total effect is the substitution effect AND the income effectworking at the same time.

X inferior


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From Individual to MarketDemand

Market demand is the sum of allindividual demands in the economy.

In the following example there are twoconsumers of wheat: Li and Juanita.

The market demand, then, is the sum ofthe quantities demand by Li andJuanita.


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Juanitas Demand forWheat

Juanitas income is also$40.

Juanita faces the same

price for rice as Li: $2/lb. Her preferences are

different from Lis.

Her demand for wheat is

derived in the figure atthe left.

Juanita's Demand for Wheat

0

5

10

15

20

25

30

0 5 10 15 20

Wheat

Rice

I2

I1

I0

4

2

1

B


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Graph of Juanitas DemandforWheat

The points A, B andC correspond toJuanitas best

choices given herincome and thethree prices ofwheat illustrated.

This is her demandcurve for wheat.

Juanita' D andfor at

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

uantit

ri

A

B


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Market Demand The market demand (green)

is the sum ofLis (blue) andJuanitas (red) demand forwheat at each price.

At PW=4, Li demands 6 lbs.,

Juanita demands 5 lbs. andthe market demand is 11lbs.

At PW=2, Li and Juanitademand 10 lbs. and themarket demand is 20 lbs.

At PW=1, Li demands 16lbs., Juanita demands 18lbs. and the market demandis 34 lbs.

Mark tfor h at

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1

2

3

4

0 20 40

Quantity of h at

Pri

of

h

atLi' D

ita' D and

Mar t D and


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Application: Effect of a Tax &Transfer Program

Suppose I have thepreferences illustratedat the right.

QuestionA:IfIncome = $16If Price of food = $1If Price of shelter= $1

Food = ?Shelter= ?Indifference curve = ?

references

0

12

3

4

5

67

91011

121314

1516

0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16

Food

Shelter

I4

I5

I6

I1

I2

I3


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Answer A

PointA:IfIncome = $16If Price of food = $1I

f Price of shelter=

$1

Food =Shelter=Indifference curve =I4

Initial oint

0

12

3

4

5

6

7

91011

12

13

14

15

16

0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A


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Effect of a Tax and TransferProgram: Addition of Tax QuestionB:IfIncome = $16If Price of food = $1If Price of shelter= $1

and Tax on shelter=100%

Tax-inclusive price ofshelter= ?Food = ?Shelter= ?Indifference curve = ?

Initial oint

012

3

4

5

67

91011

121314

1516

0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A


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Answer B Point BIfIncome = $16If Price of food = $1If Price of shelter= $1

and Tax on shelter=100%

Tax-inclusive price ofshelter=2Food =Shelter=3.5Indifference curve =I2

Tax Only

0

12

3

4

5

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7

91011

12

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15

16

0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A

B


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Effect of a Tax and TransferProgram: Tax & Transfer

Question :

IfIncome = $16If Price of food = $1If Price of shelter= $1and Tax on shelter=100% andTransfer payment = $8

Food = ?Shelter= ?Indifference curve = ?

Tax Only

012

3

4

5

678

91011

121314

1516

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A

B


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Answer C

Point CIfIncome = $16If Price of food = $1If Price of shelter= $1and Tax on shelter=100% andTransfer payment = $8

Food =10Shelter=Indifference curve =I4

Tax and Transfer

0

12

3

4

5

6

7

91011

12

13

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15

16

0 1 2 3 4 5 6 7 9 10 11 12 13 14 15 16

Food

Shelter

I1

I2

I3

I4

I5

I6A

B

C

T d T f S


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Tax and TransferSystemsGive Pure Substitution Effects

Notice in the example that the consumer ends up on the sameindifference curve after the tax and transfer program as in theinitial choice (I4).

In public finance (the study of tax and transfer systems) this

result usually occurs when the tax and transfer system iscombined with a balanced budget.

In our example, tax receipts are $ per person (= units ofshelter x $1 tax), while the transfer is $8 per person. This is asclose to balanced as we can get and still be able to graph the

consumers choice legibly. Knowledge of the substitution effect of the price change induced

by the shelter tax is sufficient to predict the effect of thecomplete tax and transfer system.


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Food Stamps vs. $$$$$

Suppose the following for the Parker family:

u(F, $aog) where $aog=$all other goods

I=$200

PF = $2/unit

Paog = $1

Consider three alternative governmentpolicies

no support

$200 in food stamps

$200 in cash


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Food

$aog

BL0

IC0

IC1

Notes: the budget line under the

food stamp program isthe thick black segment

and the purple segment The budget line with

cash is the red andpurple segments

the Parkers areindifferent between foodstamps and cash

100

200

200


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Food

$aog

BL0

IC0

ICFS

IC$$

Notes: the budget line under the

food stamp program isthe thick black segment

and the purple segment The budget line with

cash is the red andpurple segments

if this is the case then theParkers prefer cash tofood stamps

Consumer Theory (1)

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