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Part IIa: Paper 1 General Equilibrium and Welfare Economics Dr Hamish Low

2. Motivation. Casual use of Social Indifference curvesWhere do these come from? How are the interests of different individuals weighed up in creating such social indifference curves?With trade, some winners and some losersWant a mechanism for evaluating policyNormative issues (rather than po

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Part IIa: Paper 1 General Equilibrium and Welfare Economics Dr Hamish Low

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    1. 1 Lecture 5 Part IIa: Paper 1 General Equilibrium and Welfare Economics Dr Hamish Low

    2. 2 Motivation Casual use of Social Indifference curves Where do these come from? How are the interests of different individuals weighed up in creating such social indifference curves? With trade, some winners and some losers Want a mechanism for evaluating policy Normative issues (rather than positive analysis of GE)

    3. 3 Outline: Welfare Economics Concepts of Welfare Economics Basic Value Judgements Bergson-Samuelson Social Welfare Functions Utilitarianism vs Rawlsian SWF Arrow’s Impossibility Result Resolutions of Arrow

    4. 4 Concepts of Welfare Economics Want “social preference ordering” over states complete (defined over all states) transitive

    5. 5 Distinguish: Social welfare function (which corresponds to individual utility function) Mechanism for achieving this social welfare function (through combining individual preferences)

    6. 6 Basic Value Judgements Individualism Resource allocations should be judged only through their effects on individuals in the economy Society is a collection of individuals Goal of government is to achieve well-being of the individuals who compose society Individual rights crucial for well-being Locke, Adam Smith, Mill

    7. 7 Individualism Individuals are the best judges of their own welfare The effects of different resource allocations on an individual depend only on that individual’s preference orderings

    8. 8

    9. 9 Basic Value Judgements Pareto Principle Resource allocation Y is socially preferred to allocation Z if all individuals are at least as well off in Y as in Z, and at least one individual strictly prefers Y to Z.

    10. 10 Implications Define a utility function to represent an individual’s preferences over resource allocations This is an ORDINAL utility function Ordinally measurable utility numbers for an individual convey information about that individual’s welfare BUT only convey information on the order, not intensity Noncomparable (across individuals) utility numbers generated by different individuals’ utility functions cannot be compared

    11. 11 Key: an ordinal utility function is unique up to a positive, monotonic transformation

    12. 12 Utility Possibility Set

    13. 13 Compensation Tests Cannot rank Pareto efficient allocations defines set of all “efficient” allocations Need additional criteria (if equity matters) One allocation is more desirable than another if the gainers could hypothetically compensate the losers and still be better off (potential Pareto improvement) Uses willingness to pay (CV) But: Only hypothetical reallocation. Implicit assumption that value of £1 being is worth the same to all individuals (so it does not matter who actually benefits) Non-transitive

    14. 14 Bergson-Samuelson Social Welfare Functions Criteria to rank different allocations using explicit distributional value judgements (ie degree of concern for equity) Benevolent social planner, defines preference ordering using particular utility representation of individual preferences

    15. 15 Properties Paretian Anonymous: identity of individual does not matter Weak preference for equality (quasi-concave)

    16. 16 Forms of B-S SWF: Utilitarianism

    17. 17 Forms of B-S SWF: Rawlsian

    18. 18 B-S SWF

    19. 19 Summary Evaluation of value to society of different allocations Individualistic Pareto Pareto does not provide complete ranking Compensation criterion: potential Pareto, implicit equal weight Bergson-Samuelson: compares across individuals

    20. 20 Outline: Arrow Definition Desirable Properties Three possible resolutions of impossibility! Focus on information requirements for individual utility functions

    21. 21 Arrow (1951): Social Choice Rule Where does Bergson-Samuelson Social Welfare function come from? how does society aggregate individual preferences into a social ordering? B-S SWF: mechanism for making decisions about which allocation is optimal given preferences about inequality Arrow Social Choice Rule: is there a function (or rule) which generates these social preferences? (Social Welfare Functional or Constitution)

    22. 22 Impossibility Theorem Does there exist a social choice rule, F, that satisfies certain desirable requirements? Needs to generate a social preference ordering from individual preference orderings ordinal utility / ordinal social welfare

    23. 23 Impossibility Theorem: Requirements Universality (unrestricted domain) [U] F must be defined over all possible sets of individual preference orderings Pareto principle [P] if all individuals prefer allocation Y to Z, then social preference ordering must rank Y above Z Independence of irrelevant alternatives [IIA] the social preference of Y compared to Z depends only on individual orderings of Y and Z and does not depend on other orderings of other allocations Non-dictatorship [D] there is no individual whose preference ordering determines the social preference ordering

    24. 24 Majority Voting as the Social Choice Rule? Condition U means these preferences must be admissable Condition P: would be satisfied! Conditions IIA and D satisfied if social choice between any pair of allocations is made by majority voting between that pair

    25. 25 Solutions to Impossibility Relax universality Majority voting works if single-peaked preferences difficulties if multi-dimensional preferences Relax independence of irrelevant alternatives Impose some cardinality of utility

    26. 26 Relaxing IIA First-past-the-post: largest number of votes wins adding extra competitors affects the result (Ross Perot in US, Le Penn in France) Borda voting assign a score to each vote (eg. 1 to the worst, 2 to the second worst etc) rank states according to the score given particular point system matters (eg. 1,2,4,8 instead) discarding the worst and recalculating may affect the outcome

    27. 27 Imposing Cardinality The only information for each individual allowed by Arrow is that individual’s preference ordering Corresponding utility functions are ordinally measurable non-comparable [ ONC ]

    28. 28

    29. 29

    30. 30 Relaxing ONC What extra measurability and comparability assumptions are necessary to resolve Arrow? Suppose individual utility: cardinally measurable for each i fully comparable across i (same transformation has to be applied to all individuals) Social choice rule exists and satisfies all 4 conditions: need extra information on intensity and comparability

    31. 31 Summary Arrow: how are individual preference orderings aggregated to give society’s preference ordering? Impossible under minimal assumptions (U,P,IIA,D) Limited information on individual preferences: only ordinal information, so no intensity or comparability Extra information enables aggregation to B-S SWF

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