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Session 2 Welfare Economics Welfare Economics Welfare Economics – branch of economic theory concerned with the social desirability of alternative economic states Pure Economy Exchange • Assume a given amount of commodities exist – No Production – Two people and two commodities • Problem is to efficiently allocate these commodities among households – An allocation of existing commodities is efficient if no one household can be made better off without making some other household worse off Edgeworth Box • A device used to depict the distribution of two goods in a two good –two person world. • We look at the possible distribution of apples and fig leaves between Adam and Eve. • Constructed from utility functions from two households – Utility functions have the usual properties… • Every point in the Edgeworth box is a feasible allocation • Size of Edgeworth box determined by the total initial endowment. Edgeworth Box Eve y 0’ Fig leaves per year r v u 0 Adam w s x Apples per year Edgeworth Box Edgeworth Box • Adam and Eve , each has a set of indifference curves that reflect their preferences for fig leaves and apples. • Adam is happier the farther he can move toward the top-right corner of the box. • Eve attains higher utility as she moves toward the lower-left corner Indifference curves in Edgeworth Box Eve r 0’ E1 Fig leaves per year E2 E3 A3 A2 A1 s 0 Adam Apples per year Edgeworth Box Making Adam better off without Eve Eve becoming worse off 0’ r Fig leaves per year Eg g h A Pareto Efficient Allocation p Ap Ah Ag s 0 Adam Apples per year Edgeworth Box Making Eve better off without Adam Eve becoming worse off 0’ r Fig leaves per year Eg g p Ep1 p1 A Pareto Efficient Allocation Ag s 0 Adam Apples per year Edgeworth Box Making both Adam and Even better off Eve 0’ r Fig leaves per year Eg g • Pareto efficient • Pareto improvement Ep2 p p2 p1 Ap2 Ag s 0 Adam Apples per year Edgeworth Box Starting from a different initial point Eve 0’ r Fig leaves per year Eg g k p4 Ep2 p p3 p2 p1 Ap2 Ag s 0 Adam Apples per year Edgeworth Box The Contract Curve Eve 0’ r Fig leaves per year Eg g The contract curve p4 Ep2 p p3 p2 p1 Ap2 Ag s 0 Adam Apples per year Edgeworth Box Pareto-Efficient Allocation • Allocation where there is no way to make all households better off • No way to make some households better off without making someone else worse off – All gains from trade are exhausted… • Definition of Pareto-Efficient Allocation: – Allocation for which it is not possible to make any person better off without making someone else worse off… Pareto Efficiency in Consumption • • • • MRSAdamaf = MRSEveaf A point at which the indifference curves for Adam and Eve are barely touching (tangent). The slopes of the indifference curves are equal. Pareto efficiency is used as a standard for evaluating the desirability of an allocation of resources. If the allocation is not Pareto efficient, it is wasteful. Pareto improvement • A reallocation of resources that makes one person better off without making anyone worse-off. • Contract curve- The locus of all Pareto efficient points. Fig leaves per year Production Possibilities Curve C │Slope│ = marginal rate of transformation w y 0 C x z Apples per year Marginal Rate of Transformation • MRTaf = Marginal rate of transformation of apples for fig leaves • MRTaf = MCa/MCf • MRT is the rate at which the economy can transform one good into another good- it is the slope of the PPF. • MC-Marginal cost- is the incremental cost of producing one more unit of output Efficiency Conditions with Variable Production Adam Eve MRTaf = MRSaf = MRSaf Adam Eve MCa/MCf = MRSaf = MRSaf The First Fundamental Theorem of Welfare Economics – In a perfectly competitive price system, correspondence between Paretoefficient allocation of resources and perfectly competitive price system is exact • Market forces in a competitive market lead to (Pareto) efficient outcomes. • Thus, if supply equals demand (equilibrium), prices are at equilibrium, and consumers cannot be made The First Fundamental Theorem of Welfare Economics MRSAdam af = Pa/Pf MRSEve af = Pa/Pf MRSaf = MRSaf Adam = P Eve MCa/MC f a/Pf MRTaf = Pa/Pf Pa/Pf = MCa/MCf • A competitive economy automatically allocates resources efficiently. 2nd Fundamental theorem: Efficiency versus Equity 0’ Fig leaves per year r p3 p5 q s 0 Adam Eve Apples per year Edgeworth Box Efficiency versus Equity • Point p5 is Pareto efficient but q is not. • But society may prefer point q becoz it provides a more equal distribution of the two goods. • The main argument is that Pareto efficiency alone is not enough to rank alternative allocations. • Explicit value judgements are required on the fairness of the distribution of utility Adam’s utility Utility Possibilities Curve U p3 p5 q U Eve’s utility Utility Possibilities Curve • A graph showing the maximum amount of Adam’s utility given each level of utility attained by Eve. • We derive it from the contract curve • All points on or below the utility possibilities frontier are attainable by society. • All points on UU are Pareto efficient, although they represent different distributions of real income btn Adam and Eve. • Which distribution is the best? • We assume social welfare function • W = F(UAdam, UEve) Adam’s utility Social Indifference Curve W = F(UAdam, UEve) Increasing social welfare Eve’s utility Social Indifference Curve • The welfare function embodies society’s preferences on the relative deservedness of Adam and Eve. • Society’s welfare depends on the utilities of each of its members. • Society is better off when any of its members becomes better off. • The social welfare function leads to a set of social indifference curves between people’s utilities. Adam’s utility Maximizing Social Welfare i iii ii Eve’s utility 2nd Fundamental theorem • Point iii is preferred to i and ii becoz it is both efficient and fair. • Govt intervention may be necessary to achieve a fair distribution of utility. • Society can attain any Pareto efficient allocation of resources by making a suitable assignment of the initial endowments and then letting people freely trade with each other. Market Failure • An economy can be inefficient becoz of 2 reasons: Market Power and Nonexistence of Markets • Market Power – Monopoly- firms are price makers not price takers violating the 1st Theorem. P can be >MC • Nonexistence of Markets – E.g. there is no market for poverty insurance. – There are 3 types of inefficiencies from non-existent markets: • asymmetric information - one part in a transaction has information that is not available to others • Externality- one person’s behaviour affects the welfare of others – MC<MSC • public good – A good that is non-rival and non-excludable in consumption. Buying into Welfare Economics • Individualistic outlook – merit goods • Results orientation • Coherent framework for analyzing policy – Will it have desirable distributional consequences? – Will it enhance efficiency? – Can it be done at a reasonable cost?