A Consumer Theory

8/2/2019 A Consumer Theory

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Consumer Theory


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What is Consumer Theory?x Study of how people use their limited means to

make purposeful choices.x

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

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


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Consumer Theory - Why?x Two important reasons:

to understand the foundations of marketdemand (bake the demand curve fromscratch)

to address several interesting consumer theory issues that are best understood

using this model rather than the aggregatedemand model


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Two Components of Consumer Demand

x Opportunities: What can the consumer afford?

What are the consumption possibilities? Summarized by the budget constraintx Preferences:

What 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?x A budget constraint shows the

consumers purchase opportunities asevery combination of two goods that canbe bought at given prices using a givenamount of income.

x 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 for Wheat and Ricex Illustration of consumer theoryx Lis demand for wheat and rice depends

upon the prices for these goods, her income, and her preferences.x 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 Constraintx The mathematical expression for Lis

budget constraint is:I = P

W W + P

R R

R = I/P R - (P W / P R )W x I like to refer to the |slope| of the budget line

as the ERS= Economic Rate of Substitutionx In this case it is P W / P R x For Li: P W =$4 P R =$2 I=$40 ERS=2


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Graph of Lis BudgetConstraintx The graph to the right

shows a picture of Lisbudget constraint.

Li's Budget Constraint

0

5

10

15

20

0 5 10 15 20

Wheat

R i c e

x Each blue diamond is apoint from the table.

x The slope is equal to -2,

as shown on the lastslide.


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Budget Line gymnastics

x An increase in income only.x An increase in the price of wheat only.x

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

rice.

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


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Preferencesx Let R = at least as good as

B0 R B1 means: B 0 is at least as good as B 1

x Let IN = indifferent to B0 R B1 and B1 R B0 implies B0 IN B1

x Let P = strictly preferred to B0 R B1 and not B1 R B0 implies B0 P B1


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Preferencesx Basic assumptions about an individuals

preferences ( R ) over bundles (B) more is better : If B0 has more in it than B 1 then B 0

R B1

transitivity: If B0 R B1 and B1 R B2 then B0 R B2

average bundles are at least as good asextreme bundles: If B0 IN B1 and B 2 is anaverage of B 0 and B 1, then B 2 R B0 and B 1


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Utility and Preferencesx Utility is the way economists represent

preferences.x

Among two bundles, the one with thehigher utility is the preferred bundle.x If two bundles have the same utility, we

say that the consumer is indifferent.


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Indifference Curvesx Preferences that satisfy the conditions I have

noted above can be represented byindifference curves.

x

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

x An indifference curve connects all of thebundles that a consumer likes equally.

x We will assume only two goods when usingindifference curve analysis.


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Indifference Curve Map -Properties

x An indifference curve should not slopeup.

x

Indifference curves can not cross oneanother.x Better bundles are to the northeast.x

Indifference curves will not be bowedout.


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Lis Preferences inIndifference Curves

x An indifference curve connectsall the bundles that have thesame utility.

x Higher indifference curves

indicate more utility (IC 2 ispreferred to IC 1).x Lower indifference curves

indicate less utility (IC 1 ispreferred to IC 0).

x The indifference curve map isFULL of indifference curves.

Li's Indifference Curves

0

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10

1520

25

30

0 10 20

Wheat

R i c e

I2I1I0


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The Marginal Rate of Substitution

x The Marginal Rate of Substitution(MRS) tells ushow much of one good Liwould willingly trade for anincremental unit of the other good and remain indifferent.

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

x Common to assume the MRSdeclines as we move downan indifference curve.

Li's Indifference Curves

0

5

10

1520

25

30

0 10 20

Wheat

R i c e

I2I1I0


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How Much Wheat and Ricex Lis optimal amount of wheat and rice to

consume is the amount that maximizes Lisutility subject to her budget constraint.

x In the graph... Get to the highest indifference curve possible

Stay on the budget constraint (b/c more is better)


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How to Find Lis BestCombination

Wheat

Rice

20

10

IC0IC1

IC2

W*

R*

x The black bundle is best.x The pink bundle is not the

best. Li has spent all her income but is not on thehighest indifference curve

possible.x Bundles n/e of IC 0 are

better and some areaffordable.

x At (W*, R*) she is doing thebest she can subject to her budget constraint.


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How to Find the BestCombination

x Utility is maximized when: the indifference curve is just tangent to the budget

line.

x Utility is maximized when: you are on the budget line and the slope of the indifference curve equals the slope

of the budget linex Utility is maximized when:

Income=P RR + P WW MRS=ERS


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The bang per buck storyx Let MUW = Lis marginal utility of wheat

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

x Let MUR = Lis marginal utility of rice it measures the change in utility as we change rice

consumption by an incremental unit while holding wheat

constantx Common to assume that marginal utilities decline

as we increase consumption - the law of diminishing marginal utility


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The bang per buck storyx The MRS = MU W / MURx The ERS = P W / P Rx

At an optimal bundle: MRS=ERSx Rewritten we have:

MUW / MUR = P W / P R

MUW/P W = MUR/P R bang/buck in wheat = bang/buck in rice

x Get same optimal bundle either way


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Handling a change in P Wx Li wants to achieve the

highest indifference curvethat the budget constraintspermit.

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

x

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

R i c e

I2

I1

I0

4

2

1

CB

A


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Lis Demand for Wheat

x The table shows theamount of wheatthat Li demands ateach price.

x These are the pointsof tangency from theprevious slide.

Quantity Price Point6 4 A

10 2 B16 1 C


f f


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Graph of Lis Demand for Wheat

x When we connect thepoints from the table inthe previous slide we getLis demand for wheat.

x The points A, B, and Ccorrespond to thetangencies of the budgetconstraint and theindifference curves.


0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

Quantity

P r i c e

A

B

C

h


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Lis Best ChoiceReconsidered

x Consider the choice at P W=$2/lb.x The point B is optimal.x The point A is feasible but inferior to

all points on the red budget linebetween E and F.

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

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

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

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

Li's Best Choice of Wheat and Rice

0

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10

15

20

25

30

0 5 10 15 20Wheat

R i c e

I2I1I02

A

E

F

BC


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Handling a change in P Wx Li wants to achieve the

highest indifference curvethat the budget constraintspermit.

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

x

The equation MRS=ERS issatisfied at each of thepoints.


0

5

10

15

20

25

30

0 5 10 15 20

Wheat

R i c e

I2

I1

I0

4

2

1

CB

A


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Lis Demand for Wheat

x The table shows theamount of wheatthat Li demands ateach price.

x These are the pointsof tangency from theprevious slide.

Quantity Price Point6 4 A

10 2 B16 1 C


G h f Li D d f


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Graph of Lis Demand for Wheat

x When we connect thepoints from the table inthe previous slide we getLis demand for wheat.

x The points A, B, and Ccorrespond to thetangencies of the budgetconstraint and theindifference curves.


0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20

Quantity

P r i c e

A

B

C

F IC M Li D d


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0

5

10

15

20

25

30

0 5 10 15 20

Wheat

R i c e

I2

I1

I0

4

2

1

CB

A

Li 's Dem an d fo r W

0

1

2

3

4

0 1 2 3 4 5 6 7 8 9 1 0 11 1 2 13 1 4 1 5 1 6 17 1 8 1 9 20

Quan t i t

P r

i c e

A

B

C

From IC Map to Lis Demandfor Wheat

I d S b i i


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Income and SubstitutionEffects

x Economists decompose the effect of a change in price onthe quantity demanded into an income and a substitution effect.

x Income effect : due to the increase in real incomeassociated with a fall in prices (you can buy more with thesame 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).

x Substitution effect : due to the change in the relative priceof the good, cheaper goods are substituted for moreexpensive ones.


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Income and Substitution Effects:Price Decline, X normal

x When the price of a good falls, the quantity demandedrises for two reasons.

x The income effect : real income is higher because thesame money income buys more at the lower prices.For normal goods, then, the income effect of a pricefall is positive.

x The substitution effect : consumers substitute the nowcheaper good for ones whose price has not fallen, realincome held constant. This increase in demand iscalled the substitution effect of a price decline.


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Lis Income and SubstitutionEffects: Price Fall, Rice normal

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

x 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).

x The movement from point D topoint C is the income effect, theprice decline is like giving Li anadditional $20 of real income.

Li's Income and Substitution Effects

0

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10

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20

25

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0 5 10 15 20Wheat

R i c e

I2

I0

4

1

1

C

AD


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Lis Substitution Effectx The substitution effect is the amount by

which Li's wheat consumption increasedholding real income constant.

x Substitution effect is the differencebetween Li's consumption of wheat at thenew and old prices holding her realincome constant, that is, staying on thesame indifference curve (compare points

A and D).


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Lis Income Effectx When the price falls from $4/lb. of wheat to $1/lb. per

wheat, Li is able to buy both more wheat and morerice.

x The income effect is the difference between what shewould have bought on the old indifference curve at thelower wheat price (point D) and what she actually didbuy with her nominal income ($40) at the lower price(point C).

x 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

P X falls

Quantity demanded increases Quantity demanded increasesQuantity demanded decreases

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

X inferior

F I di id l t M k t


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From Individual to MarketDemand

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

x

In the following example there are twoconsumers of wheat: Li and Juanita.x The market demand, then, is the sum of

the quantities demand by Li andJuanita.


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Juanitas Demand for Wheatx Juanitas income is also

$40.x Juanita faces the same

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

different from Lis.x Her demand for wheat is

derived in the figure atthe left.

Juanita's Demand for Wheat

0

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25

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0 5 10 15 20

Wheat

R i c e

I2

I1

I0

4

2

1

B

G h f J it D d


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Graph of Juanitas Demandfor Wheat

x The points A, B andC correspond toJuanitas best

choices given her income and thethree prices of wheat illustrated.

x This is her demandcurve for wheat.

Juanita's Demand for Wheat

0

1

2

3

4

0 2 4 6 8 10 12 14 16 18 20Quantity

P r i c e

A

B

C


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Market Demandx The market demand (green)

is the sum of Lis (blue) andJuanitas (red) demand for wheat at each price.

x At P W=4, Li demands 6 lbs.,

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

x At P W=2, Li and Juanitademand 10 lbs. and themarket demand is 20 lbs.

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

Market for Wheat

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1

2

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0 20 40Quantity of Wheat

P r i c e o

f W h e a t

Li's Demand

Juanita's Demand

Market Demand


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Application: Effect of a Tax & Transfer Program

x Suppose I have thepreferences illustratedat the right.

x Question A:If Income = $16If Price of food = $1If Price of shelter = $1

Food = ?Shelter = ?Indifference curve = ?

Preferences

01

234

5

678

910

11

12

1314

1516

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

Food

S h e

l t e r

I4

I5

I6

I1

I2

I3


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Answer Ax Point A:

If Income = $16If Price of food = $1If Price of shelter = $1 Food = 7Shelter = 9Indifference curve = I4

Initial Point

01

234

5

678

910

11

12

1314

1516

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

Food

S h e

l t e r

I1

I2

I3

I4

I5

I6 A

Effect of a Tax and Transfer


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Effect of a Tax and Transfer Program: Addition of Tax

x Question B :If Income = $16If Price of food = $1If Price of shelter = $1

and Tax on shelter =100%

Tax-inclusive price of shelter = ?Food = ?Shelter = ?Indifference curve = ?

Initial Point

01

234

5

678

910

11

12

1314

1516

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

Food

S h e

l t e r

I1

I2

I3

I4

I5

I6 A


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Answer Bx Point B

If Income = $16If Price of food = $1If Price of shelter = $1

and Tax on shelter =100%

Tax-inclusive price of shelter = 2Food = 9Shelter = 3.5Indifference curve = I2

Tax Only

01

234

5

678

910

11

12

1314

1516

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

Food

S h e

l t e r

I1

I2

I3

I4

I5

I6 A

B

Effect of a Tax and Transfer


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Effect of a Tax and Transfer Program: Tax & Transfer

x Question C:If Income = $16If Price of food = $1If Price of shelter = $1and Tax on shelter =100% andTransfer payment = $8

Food = ?Shelter = ?Indifference curve = ?

Tax Only

01

234

5

678

910

11

12

1314

1516

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

Food

S h e

l t e r

I1

I2

I3

I4

I5

I6 A

B


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Answer Cx Point C

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

Food = 10Shelter = 7Indifference curve = I4

Tax and Transfer

01

234

5

678

910

11

12

1314

1516

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

Food

S h e

l t e r

I1

I2

I3

I4

I5

I6 A

B

C

Tax and Transfer Systems


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Tax and Transfer SystemsGive Pure Substitution Effects

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

x 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.x In our example, tax receipts are $7 per person (= 7 units of

shelter 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.x Knowledge of the substitution effect of the price changeinduced by the shelter tax is sufficient to predict the effect of thecomplete tax and transfer system.


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Food Stamps vs. $$$$$x Suppose the following for the Parker family:

u(F, $aog) where $aog=$all other goods I=$200

P F = $2/unit P aog = $1

x Consider three alternative government

policies no support $200 in food stamps $200 in cash


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Food Stamps vs. $$$$$

Food

$aog

BL0

IC0

IC1

x Notes: the budget line under the

food stamp program isthe thick black segmentand the purple segment

The budget line withcash is the red andpurple segments

the Parkers areindifferent between foodstamps and cash

100

200

200


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Food Stamps vs. $$$$$

Food

$aog

BL0

IC0

ICFS

IC$$

x Notes: the budget line under the

food stamp program isthe thick black segmentand the purple segment

The budget line withcash is the red andpurple segments

if this is the case thenthe Parkers prefer cashto food stamps

Documents

A Consumer Theory