Download - 6 Consumer Welfare
-
8/4/2019 6 Consumer Welfare
1/21
Lecture 6: Consumer Welfare
-
8/4/2019 6 Consumer Welfare
2/21
Outline1. Consumer Welfare2. Consumer Surplus
3. Expenditure Function and Consumer
Welfare4. Effects of Government Policies on
Consumer Welfare
-
8/4/2019 6 Consumer Welfare
3/21
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
-
8/4/2019 6 Consumer Welfare
4/21
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.
-
8/4/2019 6 Consumer Welfare
5/21
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
-
8/4/2019 6 Consumer Welfare
6/21
Consumer Surplus
Consumer surplus(CS) is the areaunder the inverse
demand curve andabove the marketprice up to thequantity purchasedby the consumer.
Smooth inversedemand function
-
8/4/2019 6 Consumer Welfare
7/21
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
-
8/4/2019 6 Consumer Welfare
8/21
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
===
-
8/4/2019 6 Consumer Welfare
9/21
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)
-
8/4/2019 6 Consumer Welfare
10/21
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*:
-
8/4/2019 6 Consumer Welfare
11/21
Expenditure Function andConsumer Welfare
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 =
-
8/4/2019 6 Consumer Welfare
12/21
Expenditure Function andConsumer Welfare
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.
-
8/4/2019 6 Consumer Welfare
13/21
Compensating Variation andEquivalent Variation
Indifferencecurves can beused todetermine
compensatingvariation (CV)andequivalent
variation(EV).
-
8/4/2019 6 Consumer Welfare
14/21
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
-
8/4/2019 6 Consumer Welfare
15/21
Three Measures: CS, CV, andEV
Relationship betweenthese measures fornormal goods:
|CV| > |CS| > |EV|
For small changes inprice, all threemeasures are verysimilar for most goods.
-
8/4/2019 6 Consumer Welfare
16/21
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
-
8/4/2019 6 Consumer Welfare
17/21
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
-
8/4/2019 6 Consumer Welfare
18/21
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.
-
8/4/2019 6 Consumer Welfare
19/21
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.
-
8/4/2019 6 Consumer Welfare
20/21
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
-
8/4/2019 6 Consumer Welfare
21/21
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