Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 317
14.9 GRAND UTILITY-POSSIBILITY CURVE
By taking another point on the transformation curve, we can construct a different Edgeworth box diagram and
consumption contract curve. From this we can derive a different utility-possibility curve and another point of Pareto
optimum in production and consumption. This process can be repeated any number of times. By then joining the
resulting 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 from
point O A to point M 0 on the transformation curve of Fig. 14-4. If we pick another point on the transformation curve of
Fig. 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 in
Fig. 14-4), we can derive another utility-possibility curve (F N 0 in Fig. 14-6) and get another Pareto optimum point in
both 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 of
Pareto optimum points of production and exchange. That is, no reorganization of the production-distribution process can
make someone better off without at the same time making someone else worse off.
Fig. 14-6
14.10 THE SOCIAL WELFARE FUNCTION
The only way we can decide which of the Pareto optimum points on the grand utility-possibility curve represents
the maximum social welfare is to accept the notion of interpersonal comparison of utility. We would
then be able to draw social welfare functions. A social welfare function shows the various combinations of
u 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 this
society’s dense welfare map. All points on a given curve give society the same level of satisfaction or welfare. Society
prefers any point on a higher to any point on a lower social welfare function. Note, however, that a movement along a
social welfare curve makes one individual better off and the other worse off. Thus, in order to construct a social welfare
function, society must make an ethical or value judgment (interpersonal comparison of utility).