GWLecture9 - Part IIa Paper 1 General Equilibrium and...

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Unformatted text preview: Part IIa: Paper 1 General Equilibrium and Welfare Economics Dr Sönje Reiche 1 First half of course … • To show how to analyse problems in a general equilibrium framework – Varian Ch. 31, 32 – Cowell Ch. 6.3, 6.4, 7 • To use this framework to address questions in trade – Krugman & Obstfeld Ch. 2, 3, 4, 6, 8 • NOT Ch. 5, 7, 9, 10 and further – Heffernan & Sinclair Ch. 2 • But: simplistic welfare analysis and lack of consideration of distributional consequences 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 Outline: Welfare Economics • • • • Concepts of Welfare Economics Basic Value Judgements Bergson-Samuelson Social Welfare Functions Utilitarianism vs Rawlsian SWF • Books – Varian Ch. 33 – Cowell Ch. 9.1, 9.4, 9.5 4 Concepts of Welfare Economics • Want “social preference ordering” over states – complete (defined over all states) – transitive x y y z ⇒x z • Less controversial at individual level, but what does this imply at society level? 5 • Distinguish: Bergson-Samuelson Social Welfare Function – Social welfare function (which corresponds to individual utility function) – Mechanism for achieving this social welfare function (through combining individual preferences) Arrow: Social Choice Rule, Social Welfare Functional or 6 Constitution Basic Value Judgements Individualism 1. 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 Individualism 2. 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 Alternative: Society as an Organism (Plato, Marx, Hobbes) • Rulers determine goals for the organism (e.g. conquest, glory of God, triumph of ideology) • Individuals matter only insofar as they can be used as tools to achieve those goals A heart muscle cell has no independent importance beyond helping pump blood Examples: • “Divine right of kings”: Britain (formerly!) • Communism • Fascism 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 Implications • Define a utility function to represent an individual’s preferences over resource allocations • This is an ORDINAL utility function 1. Ordinally measurable – utility numbers for an individual convey information about that individual’s welfare BUT only convey information on the order, not intensity 1. Noncomparable (across individuals) – utility numbers generated by different individuals’ utility functions cannot be compared 11 Key: an ordinal utility function is unique up to a positive, monotonic transformation u1a = xy u1b = log x + log y u1c = x 3 y 3 … all represent the same preferences The units have no meaning: convey no information about the intensity of individual 1’s preference Hence, the units used for individual 1 convey no information that can compare utility to individual 2’s level of utility 12 Utility Possibility Set Different resource allocations between person 1 and 2 lead to different utility levels for each (mapping from contract curve into utility space) Pareto principle u2 Allows comparison between some allocations (A and B) Not between others (A and C) C B A INCOMPLETE ORDERING BUT: Pareto improvement possible from interior, so necessary condition u1 13 (although precise shape of UPS depend on the particular representation) 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 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 W ( x ) = W ( u1 ( x ) , u2 ( x ) ,..., u N ( x ) ) x y if and only if W ( x) > W ( y) Cardinal utility function! 15 Properties ∂W ≥0 ∂uh • Paretian • Anonymous: identity of individual does not matter • Weak preference for equality (quasi-concave) u2 u1 16 Forms of B-S SWF: Utilitarianism N W = u1 + u2 + ... + u N = ∑ uh h =1 Utility of 1 is a perfect substitute for the utility of 2 u2 u1 This does not imply that giving £1 to individual 1 has the same benefit as giving £1 to individual 2 17 Forms of B-S SWF: Rawlsian Maximise the welfare of the worst off person in society W = min[ u1 , u 2 ,..., u N ] u2 u1 Utility of individual 1 is a perfect complement for the utility of 18 individual 2 B-S SWF Basis for showing how attitudes to inequality affect optimal allocations u2 Utilitarian Rawlsian Egalitarian 45 UPF u1 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 ...
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This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.

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