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

330 GENERAL EQUILIBRIUM AND WELFARE ECONOMICS [CHAP. 14
Fig. 14-14
Fig. 14-15
(a)
(b)
(c)
Point C 0 in Fig. 14-14 corresponds to point C (on A 1 and B 3 ) in Fig. 14-13, point D 0 corresponds to point D
(on A 2 and B 2 ), and point E 0 corresponds to point N (on A 3 and B 1 ). Other points could be similarly obtained.
Joining these points, we get utility-possibility curve (F M 0) shown here. Thus, the utility-possibility curve is
obtained from mapping the consumption contract curve from the output space into a utility space.
Notice that the scale along the horizontal axis refers only to individual A, while the scale along the vertical
axis refers only to B. That is, the numbers along the axes are purely arbitrary as far as interpersonal comparisons
of utility are concerned. For example, u A ¼ 450 utils is not necessarily greater than u B ¼ 300 utils,
though u A ¼ 450 . u A ¼ 300. Also note that the utility-possibility curve need not be as regularly shaped as
shown in Figs. 14-14 and 14-15.
The utility-possibility curve, or frontier, is the locus of points of maximum utility for one individual for any
level of utility for the other individual. So it is the locus of general equilibrium and Pareto optimality in
exchange or consumption. A point inside the utility-possibility curve, say, point H 0 (which corresponds
to point H in Fig. 14-13), represents a nonoptimal distribution of commodities. A point such as Q in
Fig. 14-13 cannot currently be achieved with the available X and Y.
Of all the points of Pareto optimality of exchange along the utility-possibility curve of Fig. 14-14, only point
D 0 (which corresponds to point D in Fig. 14-13) is also a point of Pareto optimality in production. That is, at
point D 0 ,(MRS xy ) A ¼ (MRS xy ) B ¼ MRT xy .
14.17 From Fig. 14-13, (a) derive the grand utility-possibility curve. (b) What do points on the grand utilitypossibility
curve represent?
(a)
(b)
F M 0 in Fig. 14-15 is the utility-possibility curve of Fig. 14-14 and point D 0 is the point of Pareto optimality in
production and exchange. If we picked another point, say N 0 , on the transformation curve of Fig. 14-13, we
can construct a different Edgeworth box diagram (from point N 0 ) and get a different consumption contract
curve, this one drawn from point O A to point N 0 in Fig. 14-12. From this different consumption contract
curve, we can derive another utility-possibility curve (FN 0 in Fig. 14-15) and get another Pareto optimum
point of production and exchange (point T 0 here). This process can be repeated any number of times. By
then joining the resulting points (such as D 0 and T 0 ) of Pareto optimum in production and exchange, we
can derive grand utility-possibility curve G of Fig. 14-15. This is an envelope of the utility-possibility
curves associated with each point on the transformation curve.
The grand utility-possibility curve or frontier is the locus of Pareto optimum points of production and
exchange. Thus, the marginal conditions for Pareto optimality do not give us a unique solution for
maximum social welfare. Each point on the grand utility-possibility frontier refers to: (1) a particular point
on the transformation curve (i.e., combination of X and Y produced), (2) a particular point on the relevant
consumption contract curve (i.e., distribution of X and Y or real income between individuals A and B),
and (3) a particular point on the relevant production contract curve (i.e., allocation of L and K between X