Welfare economics. Utilitarism.

1. Welfare economics. Utilitarism. Lecture 4 17/11/2011 POVERTY, INEQUALITY AND INCOME DISTRIBUTION (30195) Academic year 2011/2012 Second Part Prof. Renata Targetti Lenti (targetti@unipv.it)

2. - *Zamagni S., Microeconomic Theory. An Introduction, Basil Blackwell, 1987, pp. 528-545.

3. The analysis of poverty and inequality involves both descriptive and prescriptive issues. • Principles of justice are central for judging different distributions of income. T • he degree of inequality that a society is willing to accept depends on the so called “aversion to inequality”

4. 1) The choice between alternatives allocations of wealth and of income requires the introduction of a welfare function based on some principles of justice • 2)The choice of indexes suitable to measure inequality depends on their features from a normative point of view: the assiomatic approach, as already stressed, for building inequality measures is based on the acceptance of some principles of justice (Pigou Dalton principle). • 3) Intersecting Lorenz curves may generate conflicting judgements which can be solved only referring to a shared idea of justice. • 4) ‘Better off’ and ‘worse off’ refers to each individual’s subjective evaluation of the change, or, in other words to subjective concepts of justice.

5. The first theorem of welfare economics • The first theorem of welfare economics refers to the conditions which allow to identify the point that can be considered an optimum one from the consumption and from the production point of view. • The concept of optimality corresponds to the more efficient position. According to Pareto’s the exchange and the production equilibrium must refers to: • (a) an efficient distribution of goods produced among consumers (consumption optimum); • (b) an efficient allocation of productive resources among firms (production optimum); • (c) an efficient composition of the final product (general optimum).

6. Arrow and Debreu in 1951 demonstrated what are called the two fundamentals theorems of welfare that is: • 1) “there is a close correspondence between an allocation of resources that satisfies the Pareto conditions and the allocation that results from a perfectly competitive price system”; • 2) the final position depends on the initial distribution of resources. It could be efficient but unequal. The second theorem of the welfare economics shows that it is possible to reach a more equitable position introducing positive (to poorest) and negative transfers (from the richest).

7. The three conditions of paretian optimum

8. The first Pareto principle

9. For any given amounts of the two goods, represented by any point inside the box in the Edworth box, there exist a high number of possible consumption optima (all those which lie on the contract curve OA – OB), e.g. the points at which both the two consumers’ marginal rates of substitution between the goods X and Y are equal to the price ratio px/ py . • Note that the slopes of the tangents at points D and F are equal. The position of the point on the consumption contract curve depends in the final instance on the initial distribution of goods between the two individuals, and from the contractual strength of each of them.

10. The Edgworth for the production

11. The “production possibility frontier” • The “production possibility frontier”. This curve is the contract curve transferred onto a graph in which the coordinates measure the quantities of the two outputs x and y. • It follows, therefore, that the production possibility curve is the locus of points which define the Pareto efficient combinations of output, given the endowment of factors (and obviously the state of technology). • The slope at any point of the transformation curve defines the marginal rate of transformation between outputs, i.e. the quantity of Y which must be sacrificed in order to produce an additional unit of X.

17. The third Pareto condition

20. The curve of the possible utilities • If we recall that the indifference curves correspond to different level of utility for the two consumers we can derive a new curve which represent all the combinations of utilities which correspond to all the possible distributions of goods for the two consumers. This curve is called the “curve of the possible utilities”. • All point are points of relative optimum. The problem now becomes: how to determine an absolute optimum that maximizes the welfare of the society. The solution can be obtained in alternative ways: 1) introducing a welfare function to be confronted with this curve; 2) introducing some principles of justice.

22. Whenever there is a utility conflict among households such as created by a move along the utility possibilities frontier we need a rule that can consistently rank all points on the utility possibility frontier. Such a complete and consistent ranking of social states is called a social welfare ordering, and is much like a household’s preference ordering. • If the social welfare ordering is continuous, it can be translated into a social welfare function. This is simply a function f(U1 ,U2), of the utility levels of all (both) households such that a higher value of the function is preferred to a lower one. • In literature, however, we find at least 4 different approaches to the problem of the determination of a welfare function: 1) Utilitarism; 2) Theory of rights (Nozick, Von Hayeck); 3) Neo-contractualism (Rawls); 4) Sen approach.

23. The final distribution resulting from the competitive mechanism is determined by the initial allocation and can be far from the optimum. • The point iii on the curve of possible utilities can be considered an absolute optimum. The second theorem of the welfare economics shows that it is possible to reach this more equitable position introducing positive (to poorest) and negative transfers (from the richest).

24. Let ω be the initial configuration of the endowments of goods. As can be seen in figure 5, Ω is greatly to the advantage of individual A. The competitive equilibrium relative to ω is Z However, an allocation such as V which lies on the contract curve, seems preferable to Z on the grounds of equity. • This raises the following question: given ω, can the competitive mechanism lead the economy to an allocation such as V? The answer is supplied by the second fundamental theorem of welfare economics.

26. Assume that we are able to modify the competitive mechanism in such a way that a central authority (e.g. the State) carries out lump sum transfers between individuals. Each consumer has an account which lists all the goods in his possession. The initial value of this account will be given by: pX ω iX + pY ω iY i = A,B • The State can modify the accounts of the two individuals redistributing a quantity T, which can be either positive or negative. Accordingly, the budget constraint of individual i now becomes pX xiX + pY xiY ≤ pX ω iX + pY ω iY + T • Clearly, the State will attempt to favour a more equitable allocation by assigning values of Ti > O to those disadvantaged by the initial allocation and values of Ti <O to those judged to be ‘too rich’.

27. Once these transfers have been made the consumers can again trade between themselves and the market mechanism can resume its efficient function. In general, the problem can be expressed in the following terms. • Given an initial allocation ω = (ω1, ω2……, ωn ) and a desired allocation = (y1, y2……,yn ) does there exist a transfer vector T = (T1, T2……, Tn ) and a price vector p = (p1, p2……, pn) such that each individual maximizes his utility function Ui (i = 1, 2,.. . , n) with respect to the constraint pyi ≤ pωi + Ti? • The affirmative answer is the content of the second fundamental theorem of welfare economics. Let y be any Pareto-optimal allocation for which yij ≥ 0 for all i and j. There will therefore exist a transfer vector T and a price vector p such that, given those transfers (y, p) the point V is a competitive equilibrium.

28. The two fundamentals theorems of welfare economics show that there is a trade-off between distributive justice and Pareto-efficiency. The faith in the self-regulating nature of the market mechanism was a pillar of the neoclassical paradigm and legitimized a policy of laissez-faire. • The tasks of State are the maintenance of order and property rights. However, the existence of the trade-off should not impeding governments from intervening in the economy in order to reduce the degree of inequality due to an initial unequal distribution of endowments.

29. However historical experience has shown the limits of ex-post redistribution: inasmuch as the pre-intervention situation may be efficient, the adoption of income taxes or transfers for redistribution purposes would distort resource allocations. • The magnitude of such distortion may be disputable, yet the perception of redistributions costs may — as in fact it did — represent a powerful factor limiting in practice the use of taxes and transfers.

30. Utilitarism • Utilitarianism is the theory of social welfare more deeply founded in economics. It is based on three fundamental principles: i) The first principle concerns the variable which is the evaluation space of alternative situations: the focus of the utilitarian evaluation is on the individual utilities (“welfarism”). ii) The second principle concerns the basis of choice of actions, and states that actions can only be compared or evaluated with respect to the consequences of such actions, without any consideration of the intentions of the individual or moral imperatives iii) The third principle concerns the aggregation of the welfare of individuals, and states that the aggregation criterion must be that of summing individual welfares (consequentialism).

31. The welfarist approach has been developed: • In the cardinal approach as a framework for the determination of the welfare function of a society. • In the ordinal (Paretian) approach as a framework for the determination of the efficiency of a competitive setting.

33. We can say that state x is at least as good as state y (in symbols xRy) if and only if n n ∑ Ui(x) ≥ ∑ Ui(y) i=1 i=1 • The only criterion used to judge between alternative situations or economic configurations is that of the maximization of the sum of individual utilities. There is no space for distributive goals. The assumption is the concrete possibility of interpersonal comparisons of utility, i.e. society must be able to attribute different degrees of importance to different individuals.

34. A separable form of welfare function is, for instance, used in Atkinson’s classic formulation of ethical measurement of income inequality: n W= ∑ui i • The extent of income inequality is judged by an index A, given by the percentage difference between the actual mean income (y), and the mean of a “income equivalent equally distributed”, that is of the income yeed that would permit the same social welfare to be achieved through an optimal (in this case, equal) distribution.

35. The Atkinson index • Starting from The Atkinson index will be yeed OB-OC CB • IA = 1 - ----------- IA = ----------- = ---------  OB OB

36. Curves of social welfare function and the Atkinson index y2 W0 μ B C ye A y2* 45˚ 45˚ y1* 0 μ ye y1

37. 1) The ordinal approach, when interpersonal comparison of individual utilities is excluded, the welfare function can be defined only as a binary preference relation based on the individual orderings and it is represented as a map of indifference curves. • 2) Social welfare indifference curves, just like the household’s indifference curves, are negatively sloped; if one household is made worse off, then another household must be made better off to maintain the same level of social welfare. • 3) Thirdly, the intensity of this trade-offs usually it is assumed to depend on the degree of inequality.

38. The ‘new’ welfare economics introduced, with the map of indifference curves, the ordinal approach. The basic rule of the ordinalist approach is known as the Pareto principle. • This criterion permits statements on social welfare without, however, implying interpersonal comparisons of utility. • By this criterion, a policy change is socially desirable if everyone is made better off (the weak Pareto criterion) or at least some are made better off while no one is made worse off (the strong Pareto criterion).

39. It is necessary to enlight some important limitations of the welfarist approach in the ordinal space: • 1) The first major limitations of this approach lies in the fact that the same collection of individual welfares may correspond to very different social arrangements, opportunities and freedoms. • 2) Deprivations are not adequately recognized in the basal space of utilities. • 3) It is totally insensitive to interpersonal differences.

40. If we accept the assumption that it is impossible to compare individual preference immediately rises this important question: so that according to which criteria is it possible to obtain a social ordering starting from the individual one and to determine whether one alternative is socially superior to another? • Each individual possess some ordering of preferences over a set of social states. These orderings are expressions of the system of the individual values that generally do not coincide each others.

41. Social choice theory has so far reached only negative conclusions in this respect and indeed it has been demonstrated by Arrow’s (1951) and by Sen the impossibility of determining rules for collective choice. • In particular Arrow demonstrated that there is no social-choice function capable of satisfying contemporary principles which satisfy the minimum requirements of coherence (the transitivity condition) and ethical acceptability

42. First of all it is possible to show that the problem cannot be solved with a voting process with a simple example. Three individual A, B, C have preferences that satisfy the transitivity condition, where P means prefers: • A: xPyPz • B: yPzPx • C: zPxPy • Voting with the majority rule the society prefers x to y (x has two votes in favour). It prefers also y to z, but prefers z to x, instead of x to z. The preferences of the society does not satisfy the transitivity condition.

43. How to overcome the difficulties of the Utilitarian approach? One solution is to put the assumption that the State possess information which allow to determine a function of social choice. In this case the State has information on the needs of the citizens and can undertake redistributive policies. The alternatives theories of justice can help in this task. • The following figure 9 shows different maps which correspond to 3 different welfare approaches: i) the Rawls’ approach; 2) the Bentham’s approach where there is substitutability between the levels of utility of the two individual; 3) the assumption of a welfare function of Cobb-Douglas type.