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

CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 325
Fig. 14-11
(a)
(b)
Point J 0 in Fig. 14-11 corresponds to point J (on X 1 and Y 3 ) in Fig. 14-10; point M 0 corresponds to
point M (on X 2 and Y 2 ), and point N 0 corresponds to point N (on X 3 and Y 1 ). Other points could be
similarly obtained; Joining these points, we get the transformation curve shown here. Thus, the transformation
curve is obtained from mapping the production contract curve from the input space into the
output space. The transformation curve is the locus of points of the maximum output of one commodity
for a given output of the other. So it is the locus of general equilibrium and Pareto optimally in
production. Another name for the transformation curve is the production-possibility curve or frontier.
A point inside the transformation curve, say point R 0 (which corresponds to point R in Fig. 14-10), represents a
nonoptimal allocation of resources. A point such as P in Fig. 14-11 cannot currently be achieved with the
available L and K and technology. It can be reached only if there is an increase in the amounts of LorKavailable
to this economy, if there is an improvement in technology, or both.
14.8 (a) Interpret the slope of the transformation curve. Evaluate the slope of the transformation curve of
Fig. 14-11 at point M 0 .(b) Why is the transformation curve concave to the origin? (c) What would a
straight-line transformation curve indicate?
(a)
(b)
(c)
The slope of the transformation curve gives the MRT xy , or the amount by which the output of Y must
be reduced in order to release just enough L and K to be able to increase the output of X by one
unit. Note that MRT xy ¼ MC x /MC y also. For example, if MRT xy ¼ 1/2, this means that by giving up
one unit of Y, we can produce two additional units of X. Thus, MC x ¼ (1/2)MC y and so MRT xy ¼
MC x /MC y . Specifically, between points J 0 and M 0 in Fig. 14-11, the average MRT xy equals the absolute
slope of chord J 0 M 0 ¼ DY/DX ¼ 10/30 or 1/3. Similarly, between points M 0 and N 0 , the average MRT xy
equals the slope of chord M 0 N 0 , which is 2/3. As the distance between two points on the transformation
curve decreases and approaches zero in the limit, the MRT xy approaches the slope of the transformation
curve at a point. Thus, at point M 0 , MRT xy ¼ 1/2 (see Fig. 14-11).
The transformation curve of Fig. 14-11 is concave to the origin (i.e., its absolute slope, or MRT xy , increases as
we move downward along it) because of imperfect factor substitutability. That is, as this economy reduces its
output of Y, it releases L and K in combinations which become less and less suitable for the production of
more X. Thus, the economy incurs increasing MC x in terms of Y.
A straight-line transformation curve has a constant slope of MRT xy and thus refers to the case of constant,
rather than increasing, costs.
14.9 Suppose that there are only two individuals (A and B) in the economy of Problems 14.5 and 14.7 and
they choose the combination of X and Y indicated by point M 0 (60X, 70Y) on the transformation
curve of Fig. 14-11. Suppose also that the indifference curves of individuals A and B are given by
A 1 ,A 2 ,A 3 and B 1 ,B 2 ,B 3 , respectively. (a) Draw the Edgeworth box diagram for individuals A and