Measuring Welfare Changes of
Individuals
• Exact Utility Indicators
– Equivalent Variation (EV)
– Compensating Variation (CV)
• Relationship between Exact Utility
Indicators and Consumer Surplus (CS)
• How accurate an approximation of utility
change is CS?
See Zerbe and Dively, Chapter 5
Money Measure of Individual Utility
• Each indifference curve of an individual
consumer corresponds to a unique level of
income
– If prices are fixed!
• The change in utility of an individual from a
policy that provides a direct cash transfer,
without changing any prices, can be
measured by the value of the transfer
Indifference Curves
X2
M2
M1
M0
U3
U2
U0
U1
X1
Equivalent Variation
• Consider an action which will cause a price
to change.
• This price change will change the utility of
the consumer
Equivalent Variation
• How much money would have to be given
to or taken away from the consumer to give
them the equivalent utility of the proposed
action.
– Consumer moves to new utility level, but the
action not undertaken (prices do not change)
Equivalent Variation
Y
EV
U1
U0
P0
P1
X
Compensating Variation
• After introducing a change, how much
money would have to be given to or taken
away from a consumer (compensation) to
place them at their original level of utility
– Action is undertaken but income provided to or
taken away to place the consumer at the
previous level of utility. (prices do change)
Compensating Variation
Y
CV
U1
U0
P0
P1
X
Equivalence of EV and CV
EV for price decrease = CV for price increase
CV for price decrease = EV for price increase
EV for a Price Decrease
Y
EV
U1
U0
P0
P1
X
CV for a Price Increase
Y
CV
U0
U1
P1
P0
X
Marshallian vs Hicksian Demand
Curves
• Marshallian demand curve:
• Shows quantities demanded for different
price levels, holding money income
constant.
– Slutsky decomposition of effect of a price
change:
• Pure substitution effect
• Income effect
Marshallian vs Hicksian Demand
Curves
• Hicksian, or compensated demand curve
• Shows quantities demanded at different
price levels, holding utility constant.
– Only the pure substitution effect
– Smaller response to price change (less elastic),
than Marshallian demand curve - for normal
goods.
Marshallian and Hicksian Demand
Curves
Y
Price decrease
U1
U0
P0
X0 X1H X1M
P1
X
Marshallian and Hicksian Demand
Curves
Price decrease
Px
P0
x
P1
x
x
DM
DH
X0
X1H
X1M
Qx
Marshallian and Hicksian Demand
Curves
Y
Price Increase
U0
U1
P1
X1M X1H X0
P0
X
Marshallian and Hicksian Demand
Curves
Price Increase
Px
P1
x
x
P0
x
DM
DH
X1M
X1H
X0
Qx
Marshallian and Hicksian Demand
Curves
Px
P1
P0
DM
DH|U(P1)
DH|U(P0)
Qx
CV, EV, & CS
• CV and EV are measured on Hicksian
(compensated) demand curves
• CS is measured on Marshallian demand
curve
– CS is only approximation of welfare change
– It is “average between CV and EV
– Willig – under wide range of conditions CS is
close approximation of CV, EV.
Marshallian and Hicksian Demand
Curves
Px
P1
CV
EV
P0
CS
DM
DH|U(P1)
DH|U(P0)
Qx
Comparison of CS, EV CV
• Empirically, we are able to estimate CS, but
not EV or CV.
• How close an approximation is CS to EV or
CV?
– Depends on magnitude of the income effect
– Differences are small for small price changes
– Differences are small if (Marshallian) demand
curve is inelastic