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

CHAP. 14] GENERAL EQUILIBRIUM AND WELFARE ECONOMICS 315
14.5 THE SLOPE OF THE TRANSFORMATION CURVE
The slope of the transformation curve at a particular point gives the marginal rate of transformation of X for
Y (MRT xy ) at that point. It measures by how much this economy must reduce its output of Y in order to release
enough L and K to produce exactly one more unit of X.
EXAMPLE 4. At point M 0 in Fig. 14-3, the slope of the transformation curve, or MRT xy , is 1. This means that at point M 0 ,
by reducing the amount of Y produced by one unit, enough L and K are released from the production of Y to allow exactly
one additional unit of X to be produced. Note that as we move down the transformation curve, say from point M 0 to point N 0 ,
its slope, or MRT xy , increases. This means that we must give up more and more of Y to get each additional unit of X. That is,
this economy incurs increasing costs (in terms of the amounts of Y it has to give up) to produce each additional unit of
X. This is an instance of imperfect factor substitutability. Because of it, the transformation curve in Fig. 14-3 is concave
to the origin rather than a straight line.
14.6 GENERAL EQUILIBRIUM OF PRODUCTION AND EXCHANGE
We now combine the results of Sections 14.2 to 14.5 and examine how our simple economy can achieve
simultaneous general equilibrium of production and exchange.
If we take a particular point on the economy’s production transformation curve, we specify a particular
combination of X and Y produced. Given this particular combination of X and Y, we can construct an Edgeworth
box diagram and derive the consumption contract curve. The economy will then be simultaneously in
general equilibrium of production and exchange when MRT xy ¼ (MRS xy ) A ¼ (MRS xy ) B .
EXAMPLE 5. The transformation curve in Fig. 14-4 is that of Fig. 14-3. Every point on such a transformation curve corresponds
to a point of general equilibrium of production. Suppose that the output of X and Y produced by this economy
is given by point M 0 (i.e., 12X and 12Y) on the transformation curve. By dropping perpendiculars from point M 0 to both
axes, we can construct in Fig. 14-4 the Edgeworth box diagram of Fig. 14-1 for individuals A and B. Every point on consumption
contract curve O A CDEO B is a point of general equilibrium of exchange. However, this simple economy will be simultaneously
in general equilibrium of production and exchange at point D, where (MRS xy ) A ¼ (MRS xy ) B ¼ MRT xy .If
(MRS xy ) A ¼ (MRS xy ) B = MRT xy , the economy would not be in general equilibrium of production and exchange. For
example, if the (MRS xy ) A ¼ (MRS xy ) B ¼ 2 while the MRT xy ¼ 1, individuals A and B would be willing (indifferent) to
give up two units of Y of consumption for one additional unit of X, while in production only one unit of Y must be given
up in order to get the additional unit of X. Thus more of X and less of Y should be produced until
(MRS xy ) A ¼ (MRS xy ) B ¼ MRT xy .
We conclude the following about this economy when in general equilibrium of production and exchange: (1) it produces
12X and 12Y (point M 0 in Fig. 14-4); exactly how this society decides on this level of production is discussed in
Section 14.11; (2) individual A receives 7X and 5Y while individual B receives the remaining 5X and 7Y (point D in
Fig. 14-4); (3) to produce the 12X, 8L and 5K are used while to produce the 12Y, the remaining 6L and 7K are used
(see point M in Fig. 14-2). (For a discussion of equilibrium P L , P K , P x , and P y , see Problems 14.13 and 14.14; the conditions
for general equilibrium of production, of exchange, and of production and exchange simultaneously, for an economy of
many factors, commodities and individuals, are examined in Problem 14.15.)
Fig. 14-4