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

CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 327
(c)
By joining the points of tangency of A’s to B’s indifference curves, we get consumption contract curve
O A CDEO B (see Fig. 14-12). Such points of tangency are assured because indifference curves are convex
and dense. A movement from a point not on the consumption contract curve to a point on it benefits A,
B, or both. Once on the consumption contract curve, one of the two individuals cannot be made
better off without making the other worse off. Thus, the consumption contract curve is the locus of
points of general equilibrium and Pareto optimality of consumption. Different points on the consumption
contract curve refer to different distributions of real income (i.e., of X and Y) between individuals
A and B.
14.10 (a) Give the equilibrium condition that holds along the consumption contract curve, and (b) express the
equilibrium condition that holds along the consumption contract curve in utility terms. (c) What is the
value of the MRS xy at point D and at point C in Fig. 14-12?
(a)
(MRS xy ) A ¼ (MRS xy ) B
(b)
Since MRS xy ¼ MU x /MU y (see Problem 4.28), the conditions that hold along the consumption contract curve
can be restated in utility terms as
MU x
¼
MU y A
MU
x
MU y
B
(c)
The value of the MRS xy at point D is given by the common absolute slope of indifference curves A 2 and B 2 at
point D. Thus, at point D, the slope of A 2 (or the MRS xy for A) ¼ the slope of B 2 (or the MRS xy for B) ¼ 1/2
(see Fig. 14-12). At point C, the MRS xy for A and B ¼ 1.
14.11 Superimpose the Edgeworth box diagram of Fig. 14-12 on the transformation curve of Fig. 14-11, and
determine the general equilibrium and Pareto optimal point of production and distribution.
This simple economy will be simultaneously in general equilibrium of (and at Pareto optimum in) production
and distribution at point D, where (MRS xy ) A ¼ (MRS xy ) B ¼ MRT xy ¼ 1/2. We can verify this solution by showing
that, with output at point M 0 , point C and point E cannot be points of general equilibria of production and distribution.
For example, at point C, (MRS x ) A ¼ (MRS xy ) B ¼ 1 . 1/2 ¼ MRT xy (see Fig. 14-13). This means that individuals
A and B would be willing (indifferent) to give up one unit of Y of consumption for one additional unit of X,
while in production, two additional units of X can be obtained by giving up one unit of Y. If this were the case, this
society would not have chosen the combination of X and Y given by point M 0 , but rather a point further down on its
transformation curve (involving more X and less Y). At point E, the exact opposite is true. Thus, with the output of
X and Y given by point M 0 , individuals A and B will have to be at point D, so that (MRS xy ) A ¼ (MRS xy ) B ¼ MRT xy ,
in order for this simple economy to be simultaneously in general equilibrium of (and at Pareto optimum in) production
and distribution. [Exactly how this society chooses to produce at point M 0 will be discussed in Problem
14.19(a).]
14.12 Given that the society of Problems 14.5, 14.7, 14.9, and 14.11 decides to produce at point M 0 on
its transformation curve, determine (a) how much X and Y it produces, (b) how this X and Y is
distributed between individuals A and B, and (c) how much L and K is used to produce X and
how much to produce Y. (d) What questions have been left unanswered m this general equilibrium
model?
(a) This society produces 60X and 70Y (given by point M 0 on the transformation curve of Fig. 14-13).
(b) Individual A receives 35X and 35Y, while individual B receives the remaining 25X and 35Y (given by point D
in Fig. 14-13).