The Compensation Principle and Social Welfare Function

1. The Compensation Principle and Social Welfare Function Chapter 3

2. Incompleteness of Pareto Criterion • Pareto criterion is useless as a criterion for social choices in many real-world situations since most policy changes produce both gainers and losers • We employ two approaches to handle the inability of Pareto criterion to handle mixed outcomes • Compensation principle • Social welfare function

3. The Compensation Principle • Hicks (1939) and Kaldor (1939) • Consider a project that moves economy from state A to state B • This movement produces both gainers and losers • Incomes can be costlessly redistributed across individuals

4. Kaldor Compensation Criterion The project is desirable according to Kaldor compensation criterion if gainers can compensate losers in state B in such a way that everyone becomes better off compared to state A

5. Kaldor Criterion: An Example State B after redistribution State A State B $150 Since both John and Bill are better off in state B after the redistribution compared to state A, the project that replaces state A with state B is desirable according to the Kaldor criterion

6. Hicks Compensation Criterion The project is desirable according to Hicks compensation criterion if the would-be losers are unable to bribe the would-be winners not to make the move from state A to state B

7. Pareto and Compensation Criteria • The compensation principle is stated in terms of potential compensation rather than actual compensation • If compensation were required, the compensation principle would be equivalent to Pareto principle (consider example for Kaldor compensation criterion) • Considering the hypothetical compensation allows one to focus on the efficiency aspects of the policy change • In other words, a policy change is desirable according to the compensation criterion if total revenue resulting from the policy change exceeds total cost

8. Compensation Principle and General Equilibrium We can further illustrate the meaning and limitations of the compensation principle by considering redistributions of income between two households in the framework of general equilibrium

9. Utility Possibilities Frontier V U = utility of household 1 V = utility of household 2 AA = budget line in state A BB = budget line in state B Utility Possibilities Frontier VA Good 2 VB VB U A UB UB UA UA VA A Good 1

10. Utility Possibilities Frontier: Properties • All points on the utility possibilities frontier satisfy the Pareto condition, i.e. you cannot increase both households’ utilities by moving along this frontier away from any point on it • Any movement along the frontier involves redistribution of wealth (any improvement in one household’s welfare necessarily requires a reduction in the other household’s welfare) • No two points on the utility possibilities frontier can be compared by Pareto or the compensation criterion

11. Compensation Criterion in General Equilibrium Setting V 1. Initially economy is at point O, which is Pareto-inefficient since it is not on the utility possibilities frontier A 2. A move to point B is a Pareto improvement for both households B 3. A move to point A or C is a Pareto improvement for at least one of the households C O D Utility Possibilities Frontier What about movement to point D? U

12. Compensation Criterion in General Equilibrium Setting V 1. A movement from O to D is NOT a Pareto-improvement since utility of household 2 (or V) goes down 2. According to (Kaldor) compensation criterion, a movement from O to D is an improvement because we can move along the utility possibilities frontier (by redistributing wealth among the two households) to point B, which is a Pareto improvement compared to O A B 3. Remember: those compensations are hypothetical! The move from O to D is still NOT a Pareto improvement C O D Utility Possibilities Frontier U

13. Compensation Principle: Limitations V 1. Frontier PP represents the old technology, while frontier RR represents the new one R C 2. B is preferred to A according to the new technology since a movement along the RR utility possibilities frontier to C will result in a Pareto improvement relative to A P 3. However, A is also preferred to B since a movement along the PP frontier to D will result in a Pareto improvement as well A D 5. Thus, the compensation principle cannot completely order social states B R P U

14. Social Welfare Function • Whenever there is a utility conflict among households, we need more than a Pareto or compensation principle in order to be able to rank social states • Such a complete and consistent ranking of social states is called a social welfare ordering • If the social welfare ordering is continuous, it can be translated into a social welfare function • Social welfare function relates individual utility levels to one number called social welfare level so that the combinations of individual utility levels that translate into higher levels of social welfare are preferred to the combinations that result in lower levels of social welfare.

15. Social Welfare Functions: Properties • Welfarism: social welfare depends only on the utility levels of the households • Social welfare function is increasing in each household’s utility level (ceteris paribus), so that an isolated increase of any household’s utility level increases welfare of the whole societysocial welfare indifference curves are negatively sloped • Social welfare indifference curves are convex to the origin • Anonymity: It does not matter who gets a high or low level of utility

16. Social Welfare Indifference Curves V 1. Social welfare increases as we move North-East from the origin so that a move from A to B increases social welfare 2. Note that even if moving from A to B makes household 2 lose (V decreases) and no actual or hypothetical compensation is paid, the move is still socially desirable A B W3 W2 W1 U

17. Social Choice using Utility Possibilities Frontier and Social Welfare Function V 1. Maximum achievable welfare is attained at the tangency of the utility possibilities frontier and the highest attainable social welfare indifference curve A 2. Using the social welfare function, we have reduced the infinite number of possible general equilibria to a single equilibrium point Utility possibilities frontier U