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Frank Cowell: UB Public Economics Welfare Analysis of Distribution June 2005 Public Economics: University of Barcelona Frank Cowell

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1 Frank Cowell: UB Public Economics Welfare Analysis of Distribution June 2005 Public Economics: University of Barcelona Frank Cowell

2 Frank Cowell: UB Public Economics The role of public economics What is the motivation for our subject? What is the motivation for our subject? What is the reason for intervention by public sector in private economic activity? What is the reason for intervention by public sector in private economic activity? This is a main purpose of this lecture This is a main purpose of this lecture We will: We will:  Examine the rationale of the public sector  Analyse alternative philosophical bases for intervention  Develop a simple model of welfare First: how to characterise the role of the public sector? First: how to characterise the role of the public sector?

3 Frank Cowell: UB Public Economics Economic rôle of government...? Regulator and enforcer Regulator and enforcer  Enforcement of property rights  Prices, quantity, quality standards Spender Spender  Public goods  Public provision of private goods Revenue raiser Revenue raiser  Taxes, user charges... Redistributor Redistributor  Taxes, and spending... A brief agenda....

4 Frank Cowell: UB Public Economics Agenda Previous classification is ad hoc. Previous classification is ad hoc. We seek a reasoned basis for the rôle of public sector. We seek a reasoned basis for the rôle of public sector. Use the standard microeconomic model as context. Use the standard microeconomic model as context. Find the rôle for the public sector in this context. Find the rôle for the public sector in this context. Examine “Equity-efficiency trade-off”. Examine “Equity-efficiency trade-off”. Incorporate social values. Incorporate social values.

5 Frank Cowell: UB Public Economics Overview... A model of intervention Income, welfare, utility The basis for redistribution Risk and welfare Welfare Analysis of Public Economics Roots in basic microeconomics

6 Frank Cowell: UB Public Economics Finding room for public economics We want to ground the public sector within conventional economics. We want to ground the public sector within conventional economics. The public sector should not be seen as a kind of alien invader. The public sector should not be seen as a kind of alien invader. It should follow naturally from the model of the economic system. It should follow naturally from the model of the economic system. In effect we “find room” for the public sector within microeconomics. In effect we “find room” for the public sector within microeconomics. We begin with a standard paradigm. We begin with a standard paradigm.

7 Frank Cowell: UB Public Economics A simple model of the economy The basics: The basics:  A collection of persons  A collection of resources  A collection of firms Private ownership: Private ownership:  Entitlement to the resources  Shares in the firms A market allocation: A market allocation:  Consumption basket for each person  Output/input programme for each firm  A set of prices  Competitive if everyone is maximising A complete description of the economy? Determines incomes in market allocation A complete description of a social state?

8 Frank Cowell: UB Public Economics Market economy: operation Assumptions: Assumptions:  Given property distribution  informed optimisation  Free contracting  Known prices Implications: Implications:  Incomes are automatically generated  Equilibrium (CE) under fairly general conditions Equilibrium system: a fundamental mapping Equilibrium system: a fundamental mapping property distribution  goods allocation individual welfare  Is this a means of steering the economy? Is this a means of steering the economy?

9 Frank Cowell: UB Public Economics Market economy: basic results Using the mapping seems a powerful argument. Using the mapping seems a powerful argument. It is strengthened by appeal to welfare theorems: It is strengthened by appeal to welfare theorems: 1. Any CE is Pareto Efficient (PE) 2. Any PE allocation can be “supported” by a CE Implications: Implications:  Decide on the type of efficient outcome you want.  Use political system to get resource distribution right  Use the competitive system as a delivery vehicle But could there be trouble in this competitive paradise? But could there be trouble in this competitive paradise?

10 Frank Cowell: UB Public Economics Problems with the market ? Why might the delivery system not work? Why might the delivery system not work? Classic issues in market failure: Classic issues in market failure:  externalities  public goods  non-existence of equilibrium Informational problems in redistribution Informational problems in redistribution  unobservable resources  uncertainty about prices Opens up natural discussion of role for public sector Opens up natural discussion of role for public sector

11 Frank Cowell: UB Public Economics Rôle for government? Facilitate the economic system Facilitate the economic system  Enforce property rights Correct “market failure” Correct “market failure”  Externalities  Public goods  Information problems Change the resource distribution Change the resource distribution  But may not be possible without excessive cost Change the relationship between resources and allocations Change the relationship between resources and allocations  A policy trade-off…?

12 Frank Cowell: UB Public Economics Policy options Often depicted as a trade-off. Often depicted as a trade-off. But what kind of trade-off? But what kind of trade-off? Is a trade-off actually necessary? Is a trade-off actually necessary? And how to make the choice from the trade-off options? And how to make the choice from the trade-off options?

13 Frank Cowell: UB Public Economics An standard approach? equity efficiency   A classic trade-off   Social values   An optimum?   Need to define terms...   What is “efficiency”?   What is “equity”?   Need to define terms...   What is “efficiency”?   What is “equity”? ll ll

14 Frank Cowell: UB Public Economics Efficiency-equity trade-off Is there necessarily a trade-off? Is there necessarily a trade-off?  Not if we can redistribute resources without transactions cost. What is efficiency? What is efficiency?  PE provides a criterion for the goal of efficiency itself.  Pareto criterion gives no guidance away from efficient point. Standard approach to efficiency gains and losses: Standard approach to efficiency gains and losses:  A criterion for Public Economics applications such as tax design. What is equity? What is equity?  Raises issues of definition.  Also of the case for egalitarianism (Putterman et al. - JEL98). Putterman et al. - JEL98Putterman et al. - JEL98

15 Frank Cowell: UB Public Economics Components of the policy problem Specification of the technology Specification of the technology  Production of private and public goods  Enables precise definition of efficiency A definition of equity A definition of equity  Also related concepts such as inequality  See later lectures An analysis of the nature of the trade-off An analysis of the nature of the trade-off  Informational problems  See lecture on design issues A statement of social preferences A statement of social preferences  What is the basis for concern with distribution?  We deal with this in the current lecture

16 Frank Cowell: UB Public Economics Welfare approaches Ordinal approaches to welfare Ordinal approaches to welfare  These are of little use  Run into the Arrow (1953) problem  Hence are hopelessly indecisive Welfarism Welfarism  Uses a cardinally measurable and interpersonally comparable approach to welfare.  Usually based on individualism  Provides the basis for a coherent model Need to examine the basic building blocks… Need to examine the basic building blocks…

17 Frank Cowell: UB Public Economics Overview... A model of intervention Income, welfare, utility The basis for redistribution Risk and welfare Welfare Analysis of Public Economics The basic units of analysis

18 Frank Cowell: UB Public Economics Ingredients of an approach A model of individual resources A model of individual resources A measure of individual welfare A measure of individual welfare A basis for interpersonal comparisons A basis for interpersonal comparisons An intellectual base for state intervention An intellectual base for state intervention We will deal with the first three of these now. We will deal with the first three of these now.

19 Frank Cowell: UB Public Economics Individual resources and distribution We adopt two simple paradigms concerning resources: We adopt two simple paradigms concerning resources:  The cake-sharing problem  The general case with production Often distributional analysis can be conducted in terms of typical individuals i and j. Often distributional analysis can be conducted in terms of typical individuals i and j. In some cases one needs a more general distributional notation In some cases one needs a more general distributional notation Fixed total income Incorporates incentive effects Irene and Janet The F-form approach

20 Frank Cowell: UB Public Economics A simple model for the distributional problem   Two persons   The interesting distributions Janet’s income Irene’s income 0 45° ray of equality Income distributions with given total Income distributions with given total   The basic cake-sharing income-distribution problem   The feasible set

21 Frank Cowell: UB Public Economics Limitations of this basic model Just 2 persons Just 2 persons  n  3 persons for the inequality problem Fixed-size cake Fixed-size cake  Economic growth?  Waste through distortion? Costlessly transferable incomes Costlessly transferable incomes  The “leaky bucket” problem  Analysed further in discussion of incentives Incomes or utilities? Incomes or utilities? Essential to first-best welfare economics Essential to first-best welfare economics

22 Frank Cowell: UB Public Economics For welfare purposes we are concerned with utility... What is the relationship of utility to income? What is the relationship of utility to income? What properties does utility have? What properties does utility have?  Is it measurable?  Is it comparable? These properties are independent These properties are independent We usually need both We usually need both Measurability without comparability: Imagine a world where utility is proportional to income, but the constant of proportionality is known to depend on family characteristics which may be unobservable. Double a family’s income and you double each member’s utility; but you cannot compare utilities of persons from different families. Measurability without comparability: Imagine a world where utility is proportional to income, but the constant of proportionality is known to depend on family characteristics which may be unobservable. Double a family’s income and you double each member’s utility; but you cannot compare utilities of persons from different families. Example 1 Comparability without measurability : Imagine a world where access to public services determines utility and the following ordering is recognised: Gas+Electricity Electricity only Gas only Neither It makes no sense to say “U(G+E) =2U(E)”, but you could still compare individuals. Comparability without measurability : Imagine a world where access to public services determines utility and the following ordering is recognised: Gas+Electricity Electricity only Gas only Neither It makes no sense to say “U(G+E) =2U(E)”, but you could still compare individuals. Example 2 We need a simple model of utility....

23 Frank Cowell: UB Public Economics Ingredients a: personal attributes a: personal attributes  Identity  Needs  Abilities  Special “merit” or “desert” y: income y: income  Could be exogenous  Or you can model as a function of attributes: y=y(a)  : individual utility  : individual utility  Several ways of modelling this…  …see below x: “equivalised” income x: “equivalised” income  Dollar/Pound/Euro units…  Can be treated as a version of “utility”

24 Frank Cowell: UB Public Economics Ingredients (2) F : distribution function F : distribution function  Standard tool borrowed from statistics U : utility function U : utility function  A variety of specifications – see below  Gives indicator of how “well-off” a person of given attributes is  : equivalisation function  : equivalisation function  A simple way of accounting for differences in needs  Perhaps too simple?  We will try something different in the next lecture

25 Frank Cowell: UB Public Economics Basic questions about income Is it unique? Is it unique? How comprehensive should it be? How comprehensive should it be? What is the relevant receiving unit? What is the relevant receiving unit? Is it comparable between persons? Is it comparable between persons?

26 Frank Cowell: UB Public Economics Income: Uniqueness? Should we use univariate or multivariate analysis? Should we use univariate or multivariate analysis?  income and expenditure?  income and wealth?  income over time? A relationship between different types of “income”? A relationship between different types of “income”?  covariance of earnings and asset income?  conditional transfers? Several definitions may be relevant? Several definitions may be relevant?  gross income?  disposable income?  other concepts?

27 Frank Cowell: UB Public Economics Income: comprehensiveness? Is income “full income”? Is income “full income”?  final income +  value of leisure +...? Is income a proxy for economic welfare? Is income a proxy for economic welfare?  discount for risk?  valuation over time?.. Can income be zero? Can income be zero?  rental income?... or less than zero?... or less than zero?  business losses?

28 Frank Cowell: UB Public Economics Income: Comparability? Price adjustment Price adjustment  Normalise by price indices Adjustment for needs and household size Adjustment for needs and household size  Usual approach is to introduce equivalence scales The equivalence transformation is The equivalence transformation is x =  ( y, a ) Usually a simplifying assumption is made. Usually a simplifying assumption is made. Write transformation as an income-independent equivalence scale: Write transformation as an income-independent equivalence scale: x = y /  (a) nominal income personal attributes Equivalised income Number of equivalent adults Where does the function  come from? Where does the function  come from?

29 Frank Cowell: UB Public Economics Equivalence Scales We will assume that there is an agreed method of determining equivalence scales. We will assume that there is an agreed method of determining equivalence scales. But there is a variety of possible sources of information for equivalence scales: But there is a variety of possible sources of information for equivalence scales:  From official government sources  From international bodies such as OECD  From econometric models of household budgets. Consider an example of the last of these: Consider an example of the last of these:

30 Frank Cowell: UB Public Economics A model of income and need childless couple couple with children x, y yiyi xixi s food 0 income proxy for “need” From budget studies   Plot share of food in budget against household income   A reference household type...   Engel Equivalence Scale x r  y r

31 Frank Cowell: UB Public Economics Alternative models of utility  = U (y)  Inter-personally comparable utility  = U (y; a)  Individualistic utility  May not be comparable, depending on information about.  May not be comparable, depending on information about a.  = U (y, F)   Concern for distribution as a kind of externality   Need not be benevolent concern   Evidence that people are   Concerned about relative incomes   “upward looking” in their comparisons.   Ferrar-i-Carbonell (2005) Ferrar-i-Carbonell (2005) x  =  (y ; a) = y / (a)  A comparable money-metric utility?

32 Frank Cowell: UB Public Economics The relationship between utility and income:   = U(y) y ^ Increase concavity

33 Frank Cowell: UB Public Economics A simple model As an example take the iso-elastic form: As an example take the iso-elastic form: y 1 –  – 1 U(y) = ————,   1 –  We can think of  as risk aversion We can think of  as risk aversion But it may take on an additional welfare significance But it may take on an additional welfare significance

34 Frank Cowell: UB Public Economics What to do with this information? We need a method of appraising either the distribution of utilities… We need a method of appraising either the distribution of utilities… …or, the system by which they were produced …or, the system by which they were produced This involves fundamentally different approaches to welfare judgments. This involves fundamentally different approaches to welfare judgments.

35 Frank Cowell: UB Public Economics Overview... A model of intervention Income, welfare, utility The basis for redistribution Risk and welfare Welfare Analysis of Public Economics Philosophies, social welfare and the basis for intervention

36 Frank Cowell: UB Public Economics Five intellectual bases for public action …and five social philosophers …and five social philosophers Entitlement theories Entitlement theories  Nozick Unanimity Unanimity  Pareto Utilitarianism Utilitarianism  Bentham Concern with the least advantaged Concern with the least advantaged  Rawls Egalitarianism Egalitarianism  Plato

37 Frank Cowell: UB Public Economics A distributional outcome   Standard cake-sharing model Janet’s income Irene’s income 0 45° ray of equality   N stands for “Nozick” l l N implications for utility possibilities

38 Frank Cowell: UB Public Economics l l N Utility-possibility set ray of equality …and that U is the same function for both Irene and Janet.   Plot utility on the axes   The effect of utility interdependence   Simple cake-sharing Assuming that U is strictly concave... 0 ii jj 45°

39 Frank Cowell: UB Public Economics Should we move from N? What is the case for shifting from the status-quo point? What is the case for shifting from the status-quo point? Answer differs dramatically according to social philosophy: Answer differs dramatically according to social philosophy: Entitlement approach is concerned with process Entitlement approach is concerned with process Other approaches concerned with end-states Other approaches concerned with end-states

40 Frank Cowell: UB Public Economics Entitlement approach Focus on Nozick ( Anarchy, State and Utopia, 1974 ). Focus on Nozick ( Anarchy, State and Utopia, 1974 ). Answer depends crucially on how N came about Answer depends crucially on how N came about Distinguish three key issues: Distinguish three key issues:  fairness in original acquisition  fair transfers  rectification of past injustice Presumption is that there will be little or no role for the State Presumption is that there will be little or no role for the State  “Night watchman”

41 Frank Cowell: UB Public Economics Pareto Criterion Pareto unanimity criterion is an end-state principle Pareto unanimity criterion is an end-state principle  Approve the move from N to another point…  …if at least one person gains  …and no-one loses Individualistic Individualistic Based on utilities Based on utilities  But utility may have a complicated relationship with income  May depend on the income of others See how Pareto applies in the simple example See how Pareto applies in the simple example

42 Frank Cowell: UB Public Economics Pareto improvement: simple case 0 ii jj 45° ray of equality l l N   No case for intervention?   The utility-possibility set again   The initial point   Pareto superior points

43 Frank Cowell: UB Public Economics End-state approaches: beyond Pareto Pareto criterion can be indecisive Pareto criterion can be indecisive Alternative end state approaches use a social welfare function Alternative end state approaches use a social welfare function  Typically get unique solution What principles should this embody? What principles should this embody?  Individualism?  The Pareto principle?  Additivity? Take a simple example that combines them all... Take a simple example that combines them all...

44 Frank Cowell: UB Public Economics Benthamite approach General principle is “Seek the greatest good of the greatest number” General principle is “Seek the greatest good of the greatest number” This is typically interpreted as maximising the sum of individual welfare. This is typically interpreted as maximising the sum of individual welfare. In Irene-Janet terms: In Irene-Janet terms:  1  2  n More generally the SWF is: More generally the SWF is: W B =   dF(  )

45 Frank Cowell: UB Public Economics Distributional implications of utilitarianism Much of public economics uses utilitarianism. Much of public economics uses utilitarianism.  Efficiency criteria  Sacrifice theories in taxation But does utilitarianism provide a basis for egalitarian transfers? But does utilitarianism provide a basis for egalitarian transfers?  Sen has argued that this is a common fallacy  Sen and Foster (1997) Again look at this within the simple model Again look at this within the simple model

46 Frank Cowell: UB Public Economics Benthamite redistribution? 45° ray of equality l l N l l B  i  j = constant   Take a symmetric utility- possibility set   The initial distribution   Benthamite welfare contour   Maximise welfare   Optimum in this case   Implied tax/transfer The general case? 0 ii jj

47 Frank Cowell: UB Public Economics   Incorporates differential incentive effects etc.   Points that Pareto- dominate N The general case... l l N   Anywhere above C might be a candidate   C The voluntary solution?   B. Benthamite solution   Pareto improvements   N. The status quo 0 ii jj l l C   Paretianism leads to multiple solutions   Benthamite utilitarianism leads to a unique, possibly different, solution.   Paretianism leads to multiple solutions   Benthamite utilitarianism leads to a unique, possibly different, solution. l l B

48 Frank Cowell: UB Public Economics General case: discussion A motive for changing distribution? A motive for changing distribution?  Nozickians might still insist that no move from N is justified  unless it came through private voluntary action  Applies even to C Implementation: Implementation:  Private voluntary action might not be able to implement C  Could rise if there were many individuals Case for egalitarianism? Case for egalitarianism?  Clearly Bentham approach does not usually imply egalitarian outcome. Consider two further alternative approaches: Consider two further alternative approaches:  Concern for the least advantaged (Rawls)  Egalitarianism

49 Frank Cowell: UB Public Economics Rawls (1971) Rawls’ distributional philosophy is based on two fundamental principles: Rawls’ distributional philosophy is based on two fundamental principles: 1.each person has equal right to the most extensive scheme of equal basic liberties compatible with a similar scheme of liberties for all 2.society should so order its decisions as to secure the best outcome for the least advantaged Economic focus has usually been on 2 Economic focus has usually been on 2  Argument based on reasoning behind a “veil of ignorance”  I do not know which position in society I have when making social judgment Needs careful interpretation Needs careful interpretation  Avoid confusion with a probabilistic approach we consider later

50 Frank Cowell: UB Public Economics The Rawls approach…? What is meant by the difference principle? What is meant by the difference principle? This is typically interpreted as maximising the welfare of the worst-off person. This is typically interpreted as maximising the welfare of the worst-off person.  Based on simplistic interpretation of veil of ignorance argument  Rawls interpreted it differently  But rather vaguely In Irene-Janet terms: In Irene-Janet terms: min {  1  2  n } So the suggested SWF is: So the suggested SWF is: W R = {min  : F(  )>0}

51 Frank Cowell: UB Public Economics Egalitarianism? Origin goes back to Plato… Origin goes back to Plato… …but reinterpreted by Meade (1974). …but reinterpreted by Meade (1974).  “Superegalitarianism” Welfare is perceived in terms of pairwise differences: Welfare is perceived in terms of pairwise differences: [  i  j ]... Welfare might not be expressible as a neat additive expression involving individual utilities. Welfare might not be expressible as a neat additive expression involving individual utilities.  Finds an echo in more recent welfare developments  Covered in a later lecture

52 Frank Cowell: UB Public Economics 0 ii jj General case (2) l l R l l E Contours of max min function l l N ray of equality   A 'Rawlsian' solution   Superegalitarianism   Maxi-min does not imply equality   Superegalitaranism implies equality

53 Frank Cowell: UB Public Economics Bergson-Samuelson approach But why an additive form of the SWF? But why an additive form of the SWF? We could just use a weaker individualistic form. We could just use a weaker individualistic form. This is the basis of the Bergson-Samuelson formulation This is the basis of the Bergson-Samuelson formulation  A generalisation  Subsumes several welfare concepts In Irene-Janet terms: In Irene-Janet terms: W(  1  2  n ) More generally the SWF is: More generally the SWF is: W BS = W(F)

54 Frank Cowell: UB Public Economics General individualistic welfare The specific welfare functions are special cases of Bergson-Samuelson. The specific welfare functions are special cases of Bergson-Samuelson. Most satisfy the principle of additivity Most satisfy the principle of additivity  Except for the last one (utility differences) In Irene-Janet terms this means we can write: u() u() u() In Irene-Janet terms this means we can write: u(  1 )  u(  2 )  u(  n ) More generally the SWF is: More generally the SWF is: u() W BSa =   u(  ) dF(  ) This is clear for Bentham where u()=But… This is clear for Bentham where u(  )=  But…

55 Frank Cowell: UB Public Economics General individualistic welfare (2) …we can say more …we can say more Again take the iso-elastic form, this time of the (social) u-function: Again take the iso-elastic form, this time of the (social) u-function:  1 –  – 1 u(  ) = ————,   1 –  Bentham corresponds to the case Bentham corresponds to the case  Max-min (“Rawls”) corresponds to the case Max-min (“Rawls”) corresponds to the case  Intermediate cases (0<) are interesting too Intermediate cases (0<  ) are interesting too

56 Frank Cowell: UB Public Economics General case (closeup) llBllB l l W l l R l l E   B. Benthamite (  0)   W. Intermediate (  )   R. 'Rawlsian' (  )   ‘E. Superegalitarianism' (no e value)

57 Frank Cowell: UB Public Economics A brief summary Entitlement theories Entitlement theories  Thatcherism? Unanimity Unanimity  Blairism? Utilitarianism Utilitarianism  A basis for egalitarianism? Concern with the least advantaged Concern with the least advantaged  How to be interpreted? (Super)-egalitarianism (Super)-egalitarianism  Out of fashion in UK.  In Spain...?

58 Frank Cowell: UB Public Economics Overview... A model of intervention Income, welfare, utility The basis for redistribution Risk and welfare Welfare Analysis of Public Economics A reinvention of utilitarianism?

59 Frank Cowell: UB Public Economics But where do the values in the SWF come from...? Consensus Consensus  Runs into the “Arrow Theorem...” High-minded idealism High-minded idealism  Social and private values...? The PLUM principle The PLUM principle  “People Like Us Matter” – a cynical approach The Harsanyi approach The Harsanyi approach  Based on individual rationality under uncertainty take another look...

60 Frank Cowell: UB Public Economics High-minded idealism? Do people care about inequality or other distributional issues? Do people care about inequality or other distributional issues? Multiple values argument Multiple values argument  Suppose that people are “schizophrenic”  They have two sets of values, private and public. Externality argument Externality argument  People treat the income distribution as a “public good”  Hochman and Rodgers (AER 1969) Hochman and Rodgers (AER 1969 Hochman and Rodgers (AER 1969 Motivates the formulation  = U (y, F) Motivates the formulation  = U (y, F)  Individuals care about the income distribution F

61 Frank Cowell: UB Public Economics The PLUM principle Interest groups may determine what the SWF is Interest groups may determine what the SWF is  Champernowne and Cowell (1998) No reason to suppose that it has a direct connection with individual utilities No reason to suppose that it has a direct connection with individual utilities However we may still be able to say something about how values are/should be determined However we may still be able to say something about how values are/should be determined For example they should at least be consistent For example they should at least be consistent

62 Frank Cowell: UB Public Economics An approach based on risk analysis Social welfare is based individual utility Social welfare is based individual utility  Utility is of a representative person  Harsanyi  Harsanyi (Journal of Political Economy 1953, 1955) Each citizen ranks social states on the basis of expected utility Each citizen ranks social states on the basis of expected utility These utilities concern life prospects These utilities concern life prospects  made behind a “veil of ignorance” similar to Rawls  Ignorance concerns income, wealth, social position etc  But what of personal values? We need to reconsider and reinterpret the sum-of-utilities approach. We need to reconsider and reinterpret the sum-of-utilities approach.

63 Frank Cowell: UB Public Economics Reinterpret sum-of-utilities The Irene-Janet version: The Irene-Janet version:  1  2  n This is equivalent to: This is equivalent to: (1/n)  1 + (1/n)  2  (1/n)  n Reinterpreted as: Reinterpreted as:, where := 1/n p 1  1 + p 2  2  p n  n , where p i := 1/n Which is simply E Which is simply E  i

64 Frank Cowell: UB Public Economics Reinterpret sum-of-utilities (2) The formal utility function: The formal utility function:   dF(  ) This is equivalent to: This is equivalent to:   U(y) f(y)dy Reinterpreted as: Reinterpreted as:  U(y(a)) p(a) da Which is simply E Which is simply E  U(y(a)) How do we reach this conclusion…?

65 Frank Cowell: UB Public Economics Welfare and Risk? Expect links between welfare and risk analysis Expect links between welfare and risk analysis  Argument by analogy  Atkinson (JET 1970) on inequality The Harsanyi paradigm (J.Pol.E. 1953, 1955) The Harsanyi paradigm (J.Pol.E. 1953, 1955) Harsanyi’s contribution is fundamental Harsanyi’s contribution is fundamental Consists of two strands. Consists of two strands.  See Amiel et al (2005) See Amiel et al (2005) See Amiel et al (2005)

66 Frank Cowell: UB Public Economics Harsanyi 1 Aggregation theorem Aggregation theorem Consider preferences over set of lotteries L Consider preferences over set of lotteries L Individuals’ preferences V i satisfy EU axioms i=1,…,n Individuals’ preferences V i satisfy EU axioms i=1,…,n Social preference V satisfies EU axioms Social preference V satisfies EU axioms Assume Pareto indifference is satisfied Assume Pareto indifference is satisfied Then there are numbers a i and b such that, for all p  L Then there are numbers a i and b such that, for all p  L

67 Frank Cowell: UB Public Economics Harsanyi 1 (contd) Powerful result Powerful result Does not assume interpersonal utility comparisons. Does not assume interpersonal utility comparisons. If such comparisons ruled out, the a i are based on the evaluator’s value judgments (Harsanyi 1978, p. 227) If such comparisons ruled out, the a i are based on the evaluator’s value judgments (Harsanyi 1978, p. 227)  personal?  arbitrary?  the evaluator? “Judges and other public officials” (1978, p. 226) “Judges and other public officials” (1978, p. 226) Need not be a member of the society Need not be a member of the society Must satisfy some consistency requirements Must satisfy some consistency requirements

68 Frank Cowell: UB Public Economics Harsanyi 2 Impartial observer theorem. Impartial observer theorem. Basic idea already in Vickrey (1945). Basic idea already in Vickrey (1945). Assumes interpersonal comparisons of utility. Assumes interpersonal comparisons of utility. An impartial observer sympathetic to the interests of each member of society makes value judgments. An impartial observer sympathetic to the interests of each member of society makes value judgments. The observer is to imagine himself being person i. The observer is to imagine himself being person i.  i’s objective circumstances  i’s preferences

69 Frank Cowell: UB Public Economics Harsanyi 2 (contd) How to get a representative person? How to get a representative person? Thought experiment Thought experiment  Evaluator imagines he has an equal chance of being any person in society  Equal consideration to each person’s interests. Impartial observer calculates average expected utility of each lottery in L: Impartial observer calculates average expected utility of each lottery in L: I.e. person j’s expected utility I.e. person j’s expected utility

70 Frank Cowell: UB Public Economics Implications of Harsanyi approach The aggregation theorem gives an argument for additivity The aggregation theorem gives an argument for additivity The “representative person” induces a probabilistic approach The “representative person” induces a probabilistic approach Then social welfare is found to be inherited from individual expected utility Then social welfare is found to be inherited from individual expected utility But on what basis do we get the probabilities here? But on what basis do we get the probabilities here? And is “expectations” an appropriate basis for social choice? And is “expectations” an appropriate basis for social choice?

71 Frank Cowell: UB Public Economics Harsanyi: Some difficulties Are preferences known behind the “Veil of ignorance”? Are preferences known behind the “Veil of ignorance”?  Not in the Rawls approach  But Harsanyi assumes that representative person knows others utilities Is it useful to suppose equal ignorance? Is it useful to suppose equal ignorance? Subjective probabilities may be inconsistent Subjective probabilities may be inconsistent Should we be concerned only with expected utility? Should we be concerned only with expected utility? It is not clear that individuals view risk-choices and distributional choices in the same way It is not clear that individuals view risk-choices and distributional choices in the same way  Cowell and Schokkaert (EER 2001). Cowell and Schokkaert (EER 2001) Cowell and Schokkaert (EER 2001)  Carlsson et al (Economica 2005) Carlsson et al (Economica 2005) Carlsson et al (Economica 2005)

72 Frank Cowell: UB Public Economics Identity probability identity | n the veil of ignorance the cynical approach i a general view |1 |1 |2 |2 |3 |3 |

73 Frank Cowell: UB Public Economics A difficulty with expected utility? Suppose the outcomes depend on uncertain events Suppose the outcomes depend on uncertain events   probabilities of Events 1,2 are (p, 1  p) Payoffs for persons (i,j) under two policies are Payoffs for persons (i,j) under two policies are PolicyEvent 1Event 2   Consider choice between policies  and  Consider choice between policies  and  Expected payoffs are:   Under  : (1,0)   Under  : (p, 1  p) Should society be indifferent between  and  ? Mobility may be important as well as expected outcome .  See Diamond (Journal of Political Economy 1967)..(Journal of Political Economy 1967).

74 Frank Cowell: UB Public Economics Views on redistribution Source: Ravallion and Lokshin (JPubE 2000)JPubE 2000 Clearly views on distribution depend on (i) your current position and (ii) your expectations

75 Frank Cowell: UB Public Economics Concluding remarks We can construct a model with an individualistic base for welfare comparisons. We can construct a model with an individualistic base for welfare comparisons. The alternative social philosophies may give support to redistributive arguments, The alternative social philosophies may give support to redistributive arguments, But it raises some awkward questions... But it raises some awkward questions... Should the social basis for redistribution rest on private tastes for equality or aversion to misery? Should the social basis for redistribution rest on private tastes for equality or aversion to misery?  What if people like seeing the poor..? Should it rest on individual attitudes to risk? Should it rest on individual attitudes to risk?  What if people are not risk-averse? We will come back to consider the implications of these questions We will come back to consider the implications of these questions


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