6 Consumer Welfare

8/4/2019 6 Consumer Welfare

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Lecture 6: Consumer Welfare


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Outline1. Consumer Welfare2. Consumer Surplus

3. Expenditure Function and Consumer

Welfare4. Effects of Government Policies on

Consumer Welfare


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Consumer Welfare Welfare of consumers is affected by price changes

Shocks may come from new inventions that reduce firm costs,natural disasters, or government-imposed taxes, subsidies, orquotas.

How do we measure welfare of consumers? Why do we want to measure welfare of consumers?

To evaluate impact of price changes,

To evaluate government programs,

To evaluate impact of firms actions Firm may be interested in knowing impact of its decisions on wlefare

If an action was unlawful, we need measure of welfare loss to computecompensation


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Consumer Welfare How do we measure welfare of consumers?

You might think utility is a natural measure of consumerwelfare. Utility is problematic because:

we rarely know a consumers utility function

utility doesnt allow for easy comparisons across consumers

A better measure of consumer welfare is in terms ofdollars. Consumer surplus,

Compensating variation,

Equivalent variation.


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Consumer Surplus

Consumer surplus(CS) is the monetarydifference between

the maximum amountthat a consumer iswilling to pay for thequantity purchasedand what the goodactually costs.

Step function


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Consumer Surplus

Consumer surplus(CS) is the areaunder the inverse

demand curve andabove the marketprice up to thequantity purchasedby the consumer.

Smooth inversedemand function


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Consumer Surplus

Formally, consumersurplus from quantityq* at price p=p(q*) is

where q(p) is the demand function,

p(.) is the inverse demandfunction, and

p1=q(p1) is the price.

( ) ( ) ( )

==1

1

0

111

p

q

dppqqpdqqpqCSCS


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Consumer Surplus

In general, consumer surplus is not the same asutility gain from buying goods.

Exception: quasi-linear preferences

q good that we purchase, m money.

Then, inverse demand is equal to themarginal utility , and

( ) ( ) mqumqU +=,

( ) ( )quqp '=

( ) ( ) ( ) ( ) ( )[ ] *0**'***

0

*

0

pququpqdqqupqdqqpqCS

qq

===


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Effect of a Price Change onConsumer Surplus

If the price of agood rises (e.g.0.50 to 1),

purchasers of thatgood loseconsumer surplus(falls by A + B)


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Expenditure Function andConsumer Welfare

Other measure of consumer welfare: How much moneydoes consumer need to offset the change in utility? CS is based on uncompensated demand and utility is not

constant along an uncompensated demand curve.

More precise CS measure utilizes compensated demand andthe expenditure function, which both do hold utility constant.

Recall that the minimal expenditure necessary toachieve a specific utility level and given a set of prices is:

Welfare change associated with price increase to p1*:


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Which level of utility should be used in thiscalculation?

Two options: We can use the orginal utility level,

We can use the utility level after price change

( ) ( )( )212211

,,, ppqppqUUold =

( ) ( )( )212211

,*,,* ppqppqUUnew =


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Which level of utility should be used in thiscalculation?

Two options: Compensating variationis the amount of money we

would have to give a consumer after a price increaseto keep the consumer on their original indifference

curve. Equivalent variationis the amount of money we

would have to take away from a consumer to harmthe consumer as much as the price increase did.


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Compensating Variation andEquivalent Variation

Indifferencecurves can beused todetermine

compensatingvariation (CV)andequivalent

variation(EV).


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Compensating Variation andEquivalent Variation

Formally,

Recall that Thus,

Similarly

( ) ( )UppqUpppE dcompensate

,,,,21121

1

=

( ) ( ) ( ) ( ) =

==

*1

1

*1

1

,,,,,,,,212

1

212

*

1

p

p

old

dcompensate

p

p

oldoldold dpUppqdpUppp

EUppEUppECV

( )=*1

1

,,21

p

p

new

dcompensatedpUppqEV


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Three Measures: CS, CV, andEV

Relationship betweenthese measures fornormal goods:

|CV| > |CS| > |EV|

For small changes inprice, all threemeasures are verysimilar for most goods.


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Equivalent and Compensatingvariation

Changes in economic environment: Price changes,

New government programs, regulations

Innovation,

Changes in the market structure: entrance of competitors,

mergers

Compensating variationis the amount ofmoney we would have to give a consumer afterthe change to keep the consumer on their

original indifference curve.

Equivalent variationis the amount of moneywe would have to take away from a consumer

before the change to harm the consumer as


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Effects of Government Policieson Consumer Welfare

Government programs can alter consumersbudget constraints and thereby affectconsumer welfare.

Examples Quota: reduces the number of units that a

consumer buys

Subsidy: causes a rotation or parallel shift ofthe budget constraint

Welfare programs: may produce kinks inbudget constraint


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Effects of Government Policies Quotaslimit how much

of a good consumerscan purchase.

Quota of 12 units

generates kink inbudget line andremoves shadedtriangle region fromindividuals choice set.

EV of this quota is theincome reduction (L2 toL3) that would moveher onto the lowerindifference curve, I2.


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Effects of Government Policies Welfare programs

provide either in-kindtransfers or acomparable amount of

cash to low-incomeindividuals. Example: food stamps

$100 in food stamps (in-

kind) generates kinkedbudget line.

$100 cash transferincreases opportunity setfurther.


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Effects of Government Policies Because food stamps can only be used on food,

consumers are potentially worse off if they wouldfind it optimal to consume less food and more othergoods than allowed by the program.

Despite this, food stamps are used rather thancomparable cash transfers in order to:

reduce expenditures on drugs and alcohol

encourage appropriate expenditure on food from anutrition standpoint

maintain program support from taxpayers, who feelmore comfortable providing in-kind rather thancash benefits


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Effects of Government Policies Subsidieseither lower

prices or provide lump-sum payments to low-income individuals.

Example: child caresubsidy

Reducing price of childcare rotates budget line out

Unrestricted lump-sum

payment (equal totaxpayers cost of thesubsidy) shifts budget lineout in a parallel fashion andincreases opportunity set

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6 Consumer Welfare