Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006
316 GENERAL EQUILIBRIUM AND WELFARE ECONOMICS [CHAP. 14Welfare Economics14.7 WELFARE ECONOMICS DEFINEDWelfare economics studies the conditions under which the solution to a general equilibrium model can besaid to be optimal. This requires, among other things, an optimal allocation of factors among commodities andan optimal allocation of commodities (i.e., distribution of income) among consumers.An allocation of factors of production is said to be Pareto optimal if production cannot be reorganized toincrease the output of one or more commodities without decreasing the output of some other commodity.Thus, in a two-commodity economy, the production contract curve is the locus of the Pareto optimal allocationof factors in the production of the two commodities. Similarly, an allocation of commodities canbe said to be Pareto optimal if distribution cannot be reorganized to increase the utility of one or moreindividuals without decreasing the utility of some other individual. Thus, in a two-individual economy,the consumption contract curve is the locus of the Pareto optimal distribution of commodities between thetwo individuals.14.8 THE UTILITY-POSSIBILITY CURVEBy mapping the consumption contract curve of Fig. 14-4 from the output space into a utility space, we getthe corresponding utility-possibility curve. This shows the various combinations of utility received by individualsA and B (i.e., u A and u B ) when the simple economy of Section 14.1 is in general equilibrium of exchange.The point on the consumption contract curve at which the MRS xy for A and B equals the MRT xy gives the pointof Pareto optimum in production and consumption on the utility-possibility curve.EXAMPLE 6. If indifference curve A 1 in Fig. 14-4 refers to 150 units of utility for individual A (i.e., u A ¼ 150 utils) andB 3 refers to u B ¼ 450 utils, we can go from point C on the consumption contract curve (and output space) of Fig. 14-4 topoint C 0 in the utility space of Fig. 14-5. Similarly, if A 2 refers to u A ¼ 300 utils and B 2 refers to u B ¼ 400 utils, we can gofrom point D in Fig. 14-4 to point D 0 in Fig. 14-5. And if A 3 refers to u A ¼ 400 utils while B 1 refers to u B ¼ 150 utils, we cango from point E in Fig. 14-4 to point E 0 in Fig. 14-5. By joining points C 0 , D 0 , and E 0 , we derive utility-possibility curve F M 0(see Fig. 14-5). At point D 0 in this figure (which corresponds to point D in Fig. 14-4), this simple economy is simultaneouslyat Pareto optimum in both production and consumption.Fig. 14-5
CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 31714.9 GRAND UTILITY-POSSIBILITY CURVEBy taking another point on the transformation curve, we can construct a different Edgeworth box diagram andconsumption contract curve. From this we can derive a different utility-possibility curve and another point of Paretooptimum in production and consumption. This process can be repeated any number of times. By then joining theresulting points of Pareto optimum in production and exchange, we can drive the grand utility-possibility curve.EXAMPLE 7. Utility-possibility curve F M 0 in Fig. 14-5 was derived from the consumption contract curve drawn frompoint O A to point M 0 on the transformation curve of Fig. 14-4. If we pick another point on the transformation curve ofFig. 14-4, say point N 0 , we can construct another Edgeworth box diagram and get another consumption contract curve,this one drawn from point O A to point N 0 in Fig. 14-4. From this different consumption contract curve (not shown inFig. 14-4), we can derive another utility-possibility curve (F N 0 in Fig. 14-6) and get another Pareto optimum point inboth production and exchange (point T 0 in Fig. 14-6). By then joining points D 0 , T 0 and other points similarly obtained,we can-derive grand utility-possibility curve G in Fig. 14-6. Thus, the grand utility-possibility curve is the locus ofPareto optimum points of production and exchange. That is, no reorganization of the production-distribution process canmake someone better off without at the same time making someone else worse off.Fig. 14-614.10 THE SOCIAL WELFARE FUNCTIONThe only way we can decide which of the Pareto optimum points on the grand utility-possibility curve representsthe maximum social welfare is to accept the notion of interpersonal comparison of utility. We wouldthen be able to draw social welfare functions. A social welfare function shows the various combinations ofu A and u B that give society the same level of satisfaction or welfare.EXAMPLE 8. In Fig. 14-7, W 1 ,W 2 , and W 3 are three social welfare functions or social indifference curves from thissociety’s dense welfare map. All points on a given curve give society the same level of satisfaction or welfare. Societyprefers any point on a higher to any point on a lower social welfare function. Note, however, that a movement along asocial welfare curve makes one individual better off and the other worse off. Thus, in order to construct a social welfarefunction, society must make an ethical or value judgment (interpersonal comparison of utility).
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316 GENERAL EQUILIBRIUM AND WELFARE ECONOMICS [CHAP. 14
Welfare Economics
14.7 WELFARE ECONOMICS DEFINED
Welfare economics studies the conditions under which the solution to a general equilibrium model can be
said to be optimal. This requires, among other things, an optimal allocation of factors among commodities and
an optimal allocation of commodities (i.e., distribution of income) among consumers.
An allocation of factors of production is said to be Pareto optimal if production cannot be reorganized to
increase the output of one or more commodities without decreasing the output of some other commodity.
Thus, in a two-commodity economy, the production contract curve is the locus of the Pareto optimal allocation
of factors in the production of the two commodities. Similarly, an allocation of commodities can
be said to be Pareto optimal if distribution cannot be reorganized to increase the utility of one or more
individuals without decreasing the utility of some other individual. Thus, in a two-individual economy,
the consumption contract curve is the locus of the Pareto optimal distribution of commodities between the
two individuals.
14.8 THE UTILITY-POSSIBILITY CURVE
By mapping the consumption contract curve of Fig. 14-4 from the output space into a utility space, we get
the corresponding utility-possibility curve. This shows the various combinations of utility received by individuals
A and B (i.e., u A and u B ) when the simple economy of Section 14.1 is in general equilibrium of exchange.
The point on the consumption contract curve at which the MRS xy for A and B equals the MRT xy gives the point
of Pareto optimum in production and consumption on the utility-possibility curve.
EXAMPLE 6. If indifference curve A 1 in Fig. 14-4 refers to 150 units of utility for individual A (i.e., u A ¼ 150 utils) and
B 3 refers to u B ¼ 450 utils, we can go from point C on the consumption contract curve (and output space) of Fig. 14-4 to
point C 0 in the utility space of Fig. 14-5. Similarly, if A 2 refers to u A ¼ 300 utils and B 2 refers to u B ¼ 400 utils, we can go
from point D in Fig. 14-4 to point D 0 in Fig. 14-5. And if A 3 refers to u A ¼ 400 utils while B 1 refers to u B ¼ 150 utils, we can
go from point E in Fig. 14-4 to point E 0 in Fig. 14-5. By joining points C 0 , D 0 , and E 0 , we derive utility-possibility curve F M 0
(see Fig. 14-5). At point D 0 in this figure (which corresponds to point D in Fig. 14-4), this simple economy is simultaneously
at Pareto optimum in both production and consumption.
Fig. 14-5
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