microecnomics& consumer behavior

7/29/2019 Microecnomics& consumer behavior

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Lecture 3: Consumer

Behavior and Welfare

Professor: David Cheong

MicroeconomicsSAIS Johns Hopkins

Bologna Center

(PreTerm 2010)


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Lecture Outline

Case Study: Food Stamps

Individual Demand

Case Study: A Two-Part Tariff

Income and Substitution Effects

Case Study: Labor Supply

Measuring the Welfare of Consumers

Case Study: The US Sugar Import Quota


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Using the consumer-choice framework:

The Budget Line

IIs household money income

PF and PA are prices of food and all other goods

S is amount of food stamps. Each stamp is redeemable for 1

unit of food. Stamps cannot be exchanged for cash. Preferences

Typical downward-sloping indifference curves.

What does the model predict regarding:1. The change in food consumption given foods stamps?

2. Whether

a household prefers foods stamps or an equivalent cashtransfer?


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Food (units)

O

All OtherGoods(units) R

FCASH

CCASH

A1

What happens to the budget line

given food stamps, S?What is the consumers new optimal

choice?

What happens to thebudget line given a cash-equivalent transfer of S*PF?

Optimal choice?

F1

A2

Consider a differentconsumer who has moreof a preference for othergoods than food. How dothe effects of food stamps

differ from the cash-equivalent transfer?

F2

FKIND

FKIND


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Individual Demand or The Effects ofPrice Changes on Quantity

Each price leads todifferent amounts of

food purchased5

U3

D

4

U2

B

12 20

Assume: I =$20 PC = $2 PF =$2, $1, $0.50

Food (unitsper month)

Clothing

6 A

U1

4

10


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Individual Demand or The Effects ofPrice Changes on Quantity

Each price leads todifferent amounts of

food purchased5

U3

D

4

U2

B

12 20

Assume: I =$20 PC = $2 PF =$2, $1, $0.50


Clothing

6 A

U1

4

10


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Effect of a Price Change

By changing pricesand showing what theconsumer will

purchase, we cancreate a demandschedule and demandcurve for the individual

From the previousexample:

Demand Schedule

P Q

$2.00 4

$1.00 12

$0.50 20


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Effect of a Price Change

Demand Curve

Individual Demand relatesthe quantity of a good thata consumer will buy to the

price of that good.


Priceof Food

H

E

G

$2.00

4 12 20

$1.00

$.50


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The Cobb-Douglas Utility Function

A widely-used mathematical representation of

consumer preferences.

Fulfils the 3 assumptions of rationality.

On a graph, this utility function comes out as

indifference curves that are convex to the origin In general, the Cobb-Douglas utility function is:

U(X,Y) = CXaYb , where a, b, and Care positive

constants. Ifa + b= 1, then one special property of this

function is that the consumer will always spendthe same share of her budget on a good

regardless of income level or prices.


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n xamp e o aCobb-Douglas Utility Function

Suppose that a consumers utility function is

U(X,Y) = X0.6Y0.4 MUX = (U/ X) = 0.6X

-0.4Y0.4

MUY = (U/ Y) = 0.4Y-0.6X0.6

Therefore, the MRS = 0.6X

-0.4

Y

0.4

/ 0.4Y

-0.6

X

0.6

= 3Y/2XAt the optimal choice, MRS = Px/Py 3Y/2X = Px/Py

The optimal choice must also be on the budget

line, i.e. PxX+PyY = I or Y=(I PxX)/Py

Substitute for Y in the eq. above to get:

PxX = 3I/5 = 0.6I

Note the share of income spent on X is constant.


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n xamp e o aCobb-Douglas Utility Function

Rearranging the previous equation, the optimal

choice of X is: X = 0.6I/Px Suppose the consumers income is $1000, then the

consumers demand for good X is X = 600/Px Note the consumers demand for good X does not

involve the price of Y.

0

100

200

300

400

500

600

0 50 100 150

Price

Quantity


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Estimating aCobb-Douglas Utility Function Given

Observed Expenditure Shares

Suppose we observe that a consumer spends40% of his income on mobile communication andthe rest on other goods.

Assuming that the consumers preferences canbe represented by a Cobb-Douglas utility functionwith parameters that sum to 1, what is the

consumers utility function?


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There are many goods (e.g. phone plans, health clubs, barswith cover charges) for which a consumer must pay a fixedaccess(or entry) charge and a unit charge for each unit bought.

Consider phone plans. Suppose: (i) plan A has no accesscharge but a unit charge of $0.05 while plan B has a certainfixed access charge (F) and a unit charge of $0.01.

If a firm had information about a consumers demand, the firmcould extract the maximum fixed access charge. How would itdo so?

Suppose (i) Other goods cost $1 per unit, (ii) The consumer

has $1000 as income, and (iii) The consumers utility function isU(M,G) = M0.4G0.6

Solving for the optimal choice under plan A,

M = 0.4*1000/0.05 = 8,000 and G = 0.6*1000/1 = 600

This bundle yields a total utility of 8,0000.46000.6 = 673

Case Study: A Two-Part Tariff

C ti th M i Fi d F i


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Computing the Maximum Fixed Fee in aTwo-Part Tariff

The maximum access fee that can be imposed for

plan B is when the consumer is indifferent betweenplan A and plan B (i.e., total utility must be the same).If the consumer prefers plan B to A, then the accessfee can be increased. If the consumer prefers plan Ato B, then the access fee is too much.

As computed, utility under plan A is 673 Solving for the optimal choice under plan B, M = 0.4*(1000-F)/0.01 = 40,000-40F and G = 0.6*(1000-

F)/1= 600 0.6F

Plugging these into the consumers utility function andsetting it equal to 673 yieldsM0.4G0.6 = (40,000-40F)0.4(600 0.6F )0.6 = 673 This is a scary equation in F. So, well use Excel to

help us solve for F.

C ti th M i Fi d F i


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Fixed Fee Utility786$ 689

787$ 686

788$ 682

789$ 679

790$ 676

791$ 673

792$ 670

793$ 666

794$ 663

795$ 660

796$ 657797$ 653

798$ 650

799$ 647

800$ 644

Computing the Maximum Fixed Fee in aTwo-Part Tariff

Excel Formula

((40000-40*F)^0.4)*((600 -0.6*F)^0.6)


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A change in the price of a good has twoeffects:

Substitution Effect

Income Effect


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Substitution Effect

The substitution effect is the change in anitems consumption associated with a changein the price of the item, with the level of utilityheld constant

When the price of an item declines, thesubstitution effect always leads to an increase

in the quantity demanded of the good


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Income Effect

The income effect is the change in an itemsconsumption brought about by the increase inpurchasing power, with the price of the itemheld constant

When a persons real income increases, thequantity demanded for the product may

increase or decrease


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Income and SubstitutionEffects: Normal Good

Food (units

per month)O

Clothing(units per

month) R

F1

S

C1 A

U1

The income effect, EF2,(from Dto B) keeps relativeprices constant butincreases purchasing power.

Income Effect

C2

F2

T

U2

B

When the price of food falls,consumption increases by F1F2as the consumer moves from Ato B.

ETotal Effect

SubstitutionEffect

D

The substitution effect, F1E,(from point A to D), changes therelative prices but keeps utility constant.


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Food (units

per month)

O

R

Clothing(units per

month)

F1 SF2 T

A

U1

E

SubstitutionEffect

D

Total Effect

Since food is aninferior good, theincome effect is

negative. However,the substitution effect

is larger than theincome effect.

B

Income Effect

U2

Income and SubstitutionEffects: Inferior Good


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A Special Case: The Giffen Good

The income effect may theoretically be largeenough to cause the demand curve for a good

to slope upward

This rarely occurs and is of little practicalinterest


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The Lump Sum Principle

Lump-sum principle holds that taxes imposed onincome will have smaller welfare costs than taxesimposed on commodities.

Suppose an individual initially hasI0dollars to spend andchooses to consume F0 and C0 , yielding U0 utility.

Tax on Food raises its price, resulting in a pivoted budget lineI1

and consumption reduced to F1, C1 and utility level U1.An income tax that generates same total tax revenue is

represented by budget constraintI2 that must goes though F1,C1. With an income tax, the consumers optimal choice is F2, C2.


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Lump-Sum Principle

Food (unitsper month)O

Clothing(units per

month)

Income Effect

F0

U0

A

Total Effect

SubstitutionEffect

R

F1

C1 B

U1

C0C

U2

C2

F2

Assume: Food andClothing are Normal

GoodsB


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The Lump Sum Principle

Intuitive explanation of lump-sum principle: single-commodity tax affects consumers in two ways:

Reduces purchasing power,

Directs consumption away from good being taxed.

The lump-sum tax only has first of these two effects.

Therefore, the consumer is better off with the lump-sum tax rather than the commodity tax.


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For most households, the most important source of income is from

work. The work decision is a choice of how to allocate timebetween labor and leisure (and/or household production).

We can use the consumption choice framework to analyze thisdecision:

The consumer chooses a stylized bundle that containsconsumptions goods (C) and leisure hours (N).

To simplify, the price of a unit of C is $1. Let the hourly wage be wper hour.

Recall that the budget equation makes total expenditure equal

total income. The consumers total expenditure on consumption issimply C. Total income depends on the number of hours worked.Suppose that the consumer has 16*7=112 hours in a week toallocate between laborand leisure. So, the consumers totalincome is (112-N)w.

The budget line equation: C = w(112-N) or 1C + wN = w*112


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From previous slide, the budget-line equation: C = w(112-N)or 1C + wN = w*112

The second equation shows us:The price of an hour of leisure is the opportunity cost, which is the

hourly wage, w.

The total cost of the consumers chosen bundle of consumption andleisure must equal the value of his/her time endowment (which is theproduct of the wage rate and the total hours to be allocated betweenlabor and leisure).

The consumers preferences over consumption goods and

leisure can be represented by downward-sloping indifferencecurves that are convex to the origin (i.e., the typicalindifference curves that we have used so far). We assume thatleisure and consumption goods are normal goods.


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Leisure (hoursin a week)O

ConsumptionGoods(units) R

N1

C3

C1

T=112

The slope of the budget line = -W/1.Suppose that the wage rate rises,

what happens to the budget line?

What happens to theoptimal choice of leisurehours? Work hours?

N2

C2

Suppose that the wage

rate rises again, whathappens to the budgetline? What happens to theoptimal choice of leisurehours? Work hours?

N3


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T=112

The Decision Not to Workis a Corner Solution

Note the shape of theindifference curves. Whatdoes this imply about theconsumers marginal rate

of substitution between

consumption goods andleisure?

At a corner solution like theone in the diagram, theMRS is not equal to the

price ratio. What is therelationship between thetwo? How do we interpretthis relationship?

ase u y: o am es w


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ase u y: o am es wDependent Children (AFDC)



NR1

CR1

10

T=112

These programs provide cash to families withdependent children and an absent or incapacitated

parent. They have been used in the US, Europe, andother countries.

In the US version, the aidrecipient would get a grant,say $10, but the grantwould be reduced by $1 for

each $1 earned by working.How do we draw theconsumers budget under

this program?

NG

CGWhat are the work

incentives of thisprogram?

102


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Price Changes andConsumer Welfare

We have seen that price changes take theconsumer from one indifference curve toanother

Can we say something quantitative aboutthe effect of a given price change on theconsumers welfare?


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Consumer Welfare

Can we measure in monetary terms the effect of aprice change on the consumers utility (well-being)?

Economists use three concepts:Compensating variation: what change in income would

restore the consumers utility to what it was before theprice change

Equivalent variation: what change in the consumers

income would have an equal effect on the consumersutility as the price change

Change in consumer surplus


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Quantifying A Change in Welfare:The Problem

x

A

Suppose the consumer'soptimal choice is now A

let the Price of good X

fall...after a price fall, theconsumer is better off at B,but by how much?

U'

B

y

U0

How do we

quantify this gap?


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The Compensating Variation (CV)

x

B

A

U0

The Price of good x falls

The original utility level isthe reference point

Original

prices

New

price

CV is reduction in incometo make consumer just aswell off as before price fall

y

CV

C


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The Equivalent Variation (EV)

x

B

A

U1

The Price of good x falls

The new utility level is nowthe reference point

Original

prices

New

price

EV is increase in income that

raises utility to as much as theprice fall would have.

y

EV

E


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Consumer Surplus

It can be shown that, given a change in price,the monetary measure of a change inconsumer surplus is between themeasures of compensating and equivalent

variations.As such, consumer surplus is an approximate

measure of changes in consumer welfare butuseful because it is easily applied.

To apply it, all we need to have is the demandfunction whereas with CV and EV we wouldneed individual consumer preferences.


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Price ($/unit)

15

An IndividualsDemand

Quantity(units)

Consumer Surplus

11

9

1510 20

7

On each unit of the good, there is a surplus that is thedifference between the maximum amount a consumer iswilling to pay for that unit and the amount actually paid(i.e. market price).

Consumer Surplus is thus calculated as the area underthe demand curve and above the market price. What is

consumer surplus if the market price is $9? $7?

The concept also applies in the same wayto market demand


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Case Study:The US Sugar Import Quota

1. Consider a supply and demand model of the US market for raw sugar.Draw one supply curve involving only domestic supply and anothersupply curve that combines both domestic supply and imports of 1.2million metric tons under the quota. To simplify, ignore above-quotaimports and non-quota imports from Mexico.

2. The articles states that the US price of raw sugar is about 35 cents perpound. 1 metric ton corresponds to 2204.6 lbs. So, the US price of rawsugar is about $772 per metric ton. Indicate this price in your diagramin (1).

3. 85% of the US raw sugar market is supplied by domestic producerswith the other 15% imported. Suppose that the 15% corresponds to the1.2 million metric tons of imported sugar (i.e., ignore above-quota andnon-quota imports). This implies that the total quantity traded of rawsugar in the US is 8 million metric tons with US producers supplying 6.8million metric tons. Indicate the total quantity traded, the quantitysupplied by only US producers, and the quantity imported in yourdiagram in (1).


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4. The global price of sugar is at about 20 cents per pound, whichcorresponds to $441 per metric ton. If US raw sugar consumersfaced the global price instead of the domestic price, show thequantity demanded of raw sugar on your diagram. Does thisexceed the current quantity traded?

5. The article states that, Imperial Sugar Co., the nation's secondlargest buyer of sugar behind Domino Foods Inc., wants thegovernment to almost double the quota to 2.2 million tons.Suppose that US demand for raw sugar has an insignificanteffect on the global price. What effect will an increase in theimport quota have on the domestic price of raw sugar in the US?

6. What effect will an increase in the sugar import quota have on

domestic sugar production?


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7. Suppose that the new quota requested by Imperial Sugar Co.results in a quantity supplied (combining domestic supply andimports) that equals quantity demanded at the global price. Whymust this market equilibrium quantity be less than 9.2 million

tons?

8. Suppose that the market equilibrium quantity is 9 million tons.Indicate this in your diagram in (1) and compute the increase inconsumer surplus.

9. Given the assumptions in (4) and (6) above, will relaxing thesugar import quota to allow more than 2.2 million tons of importshave an effect on the US market for raw sugar?

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