The Social welfare function

The Social welfare function

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  PROF. PRABHA PANTH, OSMANIAUNIVERSITY, HYDERABAD
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  Bergson and Samuelson’sSocial Welfare Function  Hicks and Kaldor’s Compensation principle – does not show a unique equilibrium point, where individuals’ and social welfare is maximised.  If Ps of the two goods change, then equilibrium point also changes.  Does the new equilibrium give greater welfare than the old?  Also they have indirectly brought in Cardinal Utility, which is not measureable. 2Prabha Panth
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   Each economicunit wants to maximise its welfare.  Consumers’ welfare = maximise utility,  Producers’ welfare = maximise profits,  Factors’ welfare = maximise incomes. Is the sum of maximum individual welfare = maximum social welfare? i.e.  Ui = SW (i = 1,2,….. N) Welfare Economics is based on  Normative Economics,  Equity Principles,  Value Judgments Prabha Panth 3
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  Pareto Optimality  ParetoOptimality: Each individual economic unit maximises its welfare.  But if X’s welfare increases, and Y’s welfare decreases, what happens to Social Welfare (SW)?  Does it increase or decrease?  In the Pareto system there is no unique equilibrium.  If relative prices change, leads to new equilibrium.  Does this new equilibrium denote improvement in SW?  See Figure 1. Prabha Panth 4
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  5 CommodityB F Commodity A 0 E •Original equilibriumis at E, on the blue PPC. •Price ratio is PA/PB. • Due to change in economic conditions, PPC may change to the Red curve. •Price ratios have also changed to P1A/P1B. •New equilibrium is at F. •What has happened to efficiency? •Equity? •Social welfare at F compared to E? •Is there any improvement? •PPC shows only production efficiency, not of consumption. FIGURE 1
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  Social Welfare Function- SWF  Bergson: SWF is an ordinal index of society’s welfare.  It is a function of the utility levels of all individuals in society.  Brings in optimisation of consumption welfare also. Pareto optimum reflected only production optimisation.  Based on  Value Judgment of each individual,  Reflected in consumption,  Choices are transitive and consistent. SWF = W(U1, U2, ............... UN) Prabha Panth 6
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  The Social IndifferenceCurve 7 N’sutilityindex M’s utility index0 W1 W2 W3 Q T R S The Social Indifference Curve: is a locus of various combinations of UM and UN, which results in equal level of Social Welfare. In the figure, W1, W2, W3, are Social Indifference Curves. Each curve shows equal different combinations of utility of the two consumers M and N, which give the same level of Social Welfare. The Ws have same properties as ordinary Indifference Curves. All combinations on each W, have same level of Social Welfare. Higher W has higher level of Social Welfare. From R on W1 to T on W2  N’s U, M’s . But on higher W, so Social Welfare increases. Same case of movement from T to Q on W3. M’s U and N’s U. But Social Welfare  as shift to higher W. From T to S, SW constant, as they are on same W. FIGURE 2
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  Utility Possibility Curve InFig.3, the contract curve of consumers 0A 0B, shows equilibrium points of the two consumers. Moving from point 1 to 4, as UX , UY Plotting the contract curve on a diagram, gives the Utility Possibility Curve or Frontier for a given set of Ps. Figure 4. If Ps change, so will the Utility Possibility curve, 8 IC 1X IC2 X IC3 X IC4X BY IC2Y IC3Y IC4Y AX IC1Y 1 2 3 4 AY BX 0B 0A UX3 UX1 UX2 UY4 O UY UY1 UY2 UY3 UY4 1 2 3 4 Figure 3 Figure 4 Utility Possibility Frontier
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  Grand Utility PossibilityFrontier 9 O UY F1 G1 H1 F1 UX G1 H1 Figure 5 The Grand Utility Possibility Frontier • When Ps change, the contract curve changes, and the Utility Possibility Curve also changes.(F1F1, G1G1, and H1H1). • The Outer Envelope of the different Utility Possibility Frontier curves is called “The Grand Utility Possibility Frontier.” • It is the locus of all the possible contract curves or Utility Possible curves from changes in the prices of the two goods. • Satisfies the marginal conditions: MRTS = MRS for each commodity mix. • Satisfies Pareto marginal conditions of a) efficiency in production, b) efficiency in distribution, and c) efficiency in product composition.
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  Point of ConstrainedBliss  But again this does not give a Unique Point of Social Welfare.  If the SWF and Grand Utility Possibility Frontier are combined, then the point of maximum Social and Individual together can be found’  This point is called the Point of Constrained Bliss.  Because a movement away from it will reduce Social Welfare. Prabha Panth 10
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  Prabha Panth 11 O UY W* G H U*Y UX U*XH1 Constrained Bliss Point W1 W2 W3 W4 Figure 6 In Fig.6 the Grand Utility Frontier is combined with a set of social indifference curves (Ws). Social welfare is maximised at W*, where Grand Utility Possibility Frontier is a tangent to the highest possible Social Indifference curve W3. The two consumers enjoy the highest levels of welfare of U*Y and U*X. Point G on W1 is on the Grand Utility Frontier, but not unique equilibrium point. Similarly H on a higher Social Welfare curve than G, but not an equilibrium point. W* is the maximum social welfare possible, given factor endowments, state of technology, and individual’s preferences. At W*, Social Justice condition: Slope of Iso welfare curve = Slope of Utility Frontier