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

314 GENERAL EQUILIBRIUM AND WELFARE ECONOMICS [CHAP. 14
If this economy were initially at point R, it would not be maximizing its output of X and Y, because at point R the slope
of X 1 exceeds the slope of Y 1 (i.e., the MRTS LK in the production of X exceeds the MRTS LK in the production of Y). By
simply transferring 8K from the production of X to the production of Y and 1L from the production of Y to the production of
X, this economy can move from point R (on X 1 and Y 1 ) to point J (on X 1 and Y 3 ) and increase its output of Y without reducing
its output of X. On the other hand, this economy can move from point R to point N (and increase its output of X without
reducing its output of Y) by transferring 2K from the production of X to the production of Y and 8L from Y to X. Or, by
transferring 5K from the production of X to the production of Y and 5L from Y to X, this economy can move from point R
(on X 1 and Y 1 ) to point M (on X 2 and Y 2 ) and increase its output of both X and Y. At points J, M, and N, an X isoquant is
tangent to a Y isoquant and so (MRTS LK ) x ¼ (MRTS LK ) y .
If we join such tangency points, we get the production contract curve O x JMNO y in Fig. 14-2. Thus, by simply transferring
some of the given and fixed quantities of the L and K available between the production of X and Y, this economy can
move from a point not on the production contract curve to a point on it and so increase its output. Once on its production
contract curve, there is no further net gain in output to be obtained, and the economy is in general equilibrium of production.
14.4 THE TRANSFORMATION CURVE
By mapping the production contract curve of Fig. 14-2 from the input space into an output space, we get the
corresponding product transformation curve. The transformation curve shows the various combinations of X
and Y that this economy can produce by fully utilizing all of its fixed L and K with the best technology available.
EXAMPLE 3. If isoquant X 1 in Fig. 14-2 refers to 4 units of output of commodity X and Y 3 refers to 18Y, we can go from
point J on the production contract curve (and input space) of Fig. 14-2 to point J 0 in the output space of Fig. 14-3. Similarly,
if X 2 ¼ 12X and Y 2 ¼ 12Y, we can go from point M in Fig. 14-2 to point M 0 in Fig. 14-3 and if X 3 ¼ 18X while Y 1 ¼ 4Y,
we can map point N of Fig. 14-2 as point N 0 in Fig. 14-3. By joining points J 0 , M 0 , and N 0 , we derive the transformation curve
for X and Y in Fig. 14-3.
Fig. 14-3
The transformation curve shows the various combinations of X and Y that this economy can produce when in general
equilibrium of production. Point R 0 inside the transformation curve corresponds to point R in Fig. 14-2 and indicates that the
economy is not in general equilibrium of production. By simply reallocating some of the fixed L and K between the production
of X and Y, this economy can increase either its output of Y (point J 0 ) or its output of X (point N 0 ) or its output
of both X and Y (point M 0 ). With the fixed L and K available and the technology existing at a particular point in time,
this economy cannot currently achieve points above its transformation curve.