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

324 GENERAL EQUILIBRIUM AND WELFARE ECONOMICS [CHAP. 14
Fig. 14-10
(c)
increased without reducing the output of the other. Such points of tangency are assured by convexity
and because the fields of isoquants are dense.
The line joining point J to points M and N gives a portion of the production contract curve. By sketching many
more isoquants for X and Y and joining all the points of tangency, we could obtain the entire production contract
curve. Such a curve would extend from O x to O y (see Fig. 14-10). A movement from a point not on the
production contract curve to a point on it results in an increase in the output of X, Y, or both, without using
more L or K. Thus, the production contract curve is the locus of general equilibrium and Pareto optimal points
of production.
14.6 (a) Give the equilibrium condition that holds along the production contract curve and (b) express in
marginal productivity terms the equilibrium condition that holds along the production contract curve,
(c) What is the value of the MRTS LK at point M in Fig. 14-10?
(a)
(MRTS LK ) x ¼ (MRTS LK ) y
(b)
Since MRTS LK ¼ MP L /MP K (see Section 6.8), the equilibrium condition that holds along the production
contract curve can be restated in productivity terms as
MP L
¼
MP
L
MP K x
MP K y
(c)
The value of the MRTS LK at point M is given by the common absolute slope of isoquants X 2 and Y 2 at point
M; this value is 3/2 (see Fig. 14-9).
14.7 If, in Fig. 14-10, X 1 ¼ 30X, X 2 ¼ 60X, X 3 ¼ 90X and Y 1 ¼ 50Y, Y 2 ¼ 70Y, Y 3 ¼ 80Y; (a) derive the
transformation curve corresponding to the production contract curve of Problem 14.5(a). (b) What does
a point inside the transformation curve stand for? A point outside?