Measuring Welfare Changes of Individuals Exact Utility Indicators

Measuring Welfare Changes of Individuals  Exact Utility Indicators

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! Indifference Curves X2 M2 M1 M0 U3

U2 U 0 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 P 0 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 P 0 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 P 0

P1 X CV for a Price Increase Y CV U0 U1 P

1 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 P

0 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 P 1 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. 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

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