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

U0U0 U2U2 X2X2 X1X1 U1U1 U3U3 Indifference Curves M0M0 M1M1 M2M2

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 U0U0 U1U1 X Y P0P0 P1P1 EV

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 U0U0 U1U1 X Y P0P0 P1P1 CV

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 U0U0 U1U1 X Y P0P0 P1P1 EV

CV for a Price Increase U1U1 U0U0 X Y P1P1 P0P0 CV

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 U0U0 U1U1 X Y P0P0 P1P1 X0X0 X 1M X 1H Price decrease

Marshallian and Hicksian Demand Curves QxQx PxPx P0P0 x X0X0 P1P1 x X 1M DMDM x X 1H DHDH Price decrease

Marshallian and Hicksian Demand Curves U1U1 U0U0 X Y P1P1 P0P0 X 1M X0X0 X 1H Price Increase

Marshallian and Hicksian Demand Curves QxQx PxPx P1P1 x X 1M P0P0 x X0X0 DMDM x X 1H DHDH Price Increase

Marshallian and Hicksian Demand Curves QxQx PxPx P1P1 P0P0 DMDM D H | U(P1) D H | U(P0)

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 QxQx PxPx P1P1 P0P0 DMDM D H | U(P1) D H | U(P0) CV EV CS

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