1. 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

2. Money Measure of Individual Utility
Each indifference curve of an individual consumer corresponds to a unique level of income
If prices are fixed!

3. Indifference Curves X2 M2 M1 M0 U3 U2 U1 U0 X1

4. Equivalent Variation
Consider an action which will cause a price to change.
This price change will change the utility of the consumer

5. 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)

6. Equivalent Variation Y EV U1 U0 P1 P0 X

7. 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)

8. Compensating VariationY CV U1 U0 P1 P0 X

9. Equivalence of EV and CV
EV for price decrease = CV for price increase
CV for price decrease = EV for price increase

10. EV for a Price Decrease Y EV U1 U0 P1 P0 X

11. CV for a Price Increase Y CV U0 U1 P0 P1 X

12. 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

13. 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.

14. Marshallian and Hicksian Demand CurvesY
Price decrease U1 U0 P1 P0 X0
X1H
X1M X

15. Marshallian and Hicksian Demand Curves
Price decrease Px P0 x P1 x x DM DH X0
X1H
X1M Qx

16. Marshallian and Hicksian Demand CurvesY
Price Increase U0 U1 P0 P1
X1M
X1H X0 X

17. Marshallian and Hicksian Demand Curves
Price Increase Px P1 x x P0 x DM DH
X1M
X1H X0 Qx

18. Marshallian and Hicksian Demand CurvesPx P1 P0 DM
DH|U(P1)
DH|U(P0) Qx

19. 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.

22. 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