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

1. 1 Lecture 6 Part IIa: Paper 1General Equilibrium and Welfare EconomicsDr Hamish Low

2. 2 Outline: Efficiency and Equity Conditions for Pareto Efficiency First Fundamental Theorem Efficiency vs Equity and the Second Fundamental Theorem First Best vs Second Best Lump sum taxes

3. 3 Necessary Conditions for Pareto Efficiency First Best: an allocation which is Pareto efficient subject only to overall resource constraints and technology constraint Second Best an allocation which is Pareto efficient subject to resource constraints and additional constraints (eg. imperfect information)

4. 4 First Best Pareto Efficiency Nothing about prices in defining first-best allocation All goods are private: rivalrous (if one person consumes a good, this uses up the good and so no one else can consume it) excludable (one person can stop another from consuming the good) Conditions for Pareto Efficiency: Production efficiency Consumption efficiency Overall efficiency

5. 5 Production Efficiency

6. 6 Production Efficiency

7. 7 Consumption Efficiency

8. 8 Overall Efficiency

9. 9 Fundamental Theorems of Welfare Economics Introduce prices: what are the welfare properties of the market? Assumption 1: Competitive Markets Consumers and firms take prices as given Consumers and firms optimise

10. 10 Assumption 2: Complete Markets Enforcability of contracts and complete allocation of property rights A market exists for all goods which influence either individual utilities or firm production

11. 11 (Aside on externalities) Consumption externality Assumption is NOT that this sort of utility function is ruled out Rather the assumption is that there is a price for each good

12. 12 First Fundamental Theorem If assumption of complete and competitive markets holds, then a general competitive equilibrium is first-best Pareto efficient Intuition: Optimising consumers each set : So, if all consumers face the same prices, then consumption efficiency Similarly with optimising firms: each sets Allocation of production between firms:

13. 13 Equity vs Efficiency FT1: market leads to the Pareto frontier Last week: which point on the Pareto frontier maximises social welfare Is there a cost between moving to a point on the frontier which improves social welfare? ie a trade-off between efficiency and equity

14. 14 Assumption 3: Convexity Individual indifference curves are convex rules out a preference for extremes (over mixtures) Firm production sets are convex rules out increasing returns to scale (Assumptions necessary for existence of competitive equilibrium)

15. 15 Assumption 4: Ideal Lump-sum Taxes A lump sum tax or transfer is where the payment (or receipt) is independent of individual choices Transfer based on an individual’s “endowment” (individual specific) Key: imposition of a lump-sum tax leaves all individuals facing common prices but those common prices may depend on the lump sum taxes because of wealth effects

16. 16 Assumption 4: Ideal Lump-sum Taxes The poll tax introduced by Margaret Thatcher was not a lump-sum tax tax was paid “per head” could avoid the tax by not registering to vote amount of the tax did not vary with endowment A tax on labour income is not lump-sum: the price paid by the firm is different from that received by the worker individuals can change their tax burden by changing their behaviour

17. 17 Second Fundamental Theorem If assumptions 1 to 3 hold, then any Pareto efficient allocation can be achieved by appropriate redistribution through an ILST and leaving the competitive market to find prices.

18. 18 FT2 in an Exchange Economy

19. 19 When do reallocations in wealth have no effect on aggregate demand (and hence on prices)? Reallocation of income from person i to j means demand from j increases, i decreases. Exactly offset if both have equal income elasticities Implies income elasticity must be constant across individuals with different levels of income homothetic prefences necessary for representative agent models (Aside on aggregation)

20. 20 Implications of FT2 Decentralisation result: redistribute with limited government informational requirements decentralised decisions will lead to a first-best Pareto allocation (satisfy the marginal conditions) Separate out equity from efficiency: any point on the Pareto frontier can be achieved. there is no conflict between redistribution and achieving a first-best Pareto allocation

21. 21 Implications There are two distinct reasons for government intervention (under the assumptions of the FT2): To redistribute: competitive market may not lead to the Pareto efficient point that maximises social welfare To correct market failure (due to failure of one of assumptions 1 to 3) to return to first best (eg use of Pigouvian taxes to correct externalities)

22. 22 Value of FT2 FT2 provides rationale for why government intervention may be desirable Assumptions (particularly on information) are very strong: FT2 is not valuable to understand what form interventions should take second best analysis of policy intervention

23. 23 Focus on FB vs SB for efficiency (ie keep assumption 4 that LST feasible) Distortion to FB: there is one good where price does not equal marginal cost (eg price of using a road is zero) Competitive equilibrium will not be first best First best solution: is it possible to remove the distortion directly? If so, then move back to the first best. If not: try to satisfy as many Pareto conditions as possible (ie ensure efficiency in all other markets ignoring distortion ) or introduce offsetting distortion (second best policy) First Best vs Second Best

24. 24 Car use (when congestion): First best: directly price externality (road pricing set at marginal cost imposed on others) – Pigouvian solution Second best: what is the price for public transport? Price at marginal cost: public transport is at Pareto efficient level But cars and public transport are substitutes: price below marginal cost induces switch away from car use 1 car user switches: saving of deadweight loss in car market, p-mc imposes deadweight loss in public transport, but negligible since p=mc Example

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26. 26 Information and LST Redistribution requires lump sum payments to vary across individuals according to their characteristics (eg endowments of ability) These characteristics are private information to the individual. Government only observes behaviour. Needs to be in interests of the individuals to reveal information on characteristics through behaviour

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28. 28 Government chooses Th and TL to maximise a Utilitarian SWF. Equivalently, government chooses consumption and leisure bundles for each person.

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30. 30 If ability is unobservable, base tax on observed income First best requires that higher income individuals pay T and lower income individuals receive T, such that consumption equalises high ability lose incentive to work, instead earn low income to mimic low ability individuals

31. 31 Impossible to differentiate lump-sum taxes by unobservable characteristics! Taxes must be based on observed behaviour (or characteristics) When characteristics are private information, redistribution must involve taxes that are distortionary. Policy prescriptions cannot be based on Second Welfare Theorem: cannot separate out efficiency from equity Implications

32. 32 Summary Necessary conditions for Pareto efficiency First Welfare Theorem: competitive market leads to Pareto efficiency Second Welfare Theorem: any Pareto efficient point is achievable by LST and competitive markets allows us to separate out efficiency from equity 2nd Best: if distortion in one market, maybe optimal to introduce an extra distortion elsewhere to offset the first one (rather than trying to satisfy Pareto conditions) Unable to use lump sum taxes because of private information about endowments (of ability). Should not try to maintain separation between equity and efficiency