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

CHAP. 6] THEORY OF PRODUCTION 125
equilibrium at point D on isoquant I by purchasing 3K and 3L. When TO ¼ $10, the producer attains equilibrium at point M
on isoquant II by buying 5K and 5L. When TO ¼ $14, the producer reaches equilibrium at point P on isoquant III by
purchasing 7K and 7L.
Fig. 6-7
Line OS joining the origin with equilibrium points D, M, and P is the expansion path for this firm. Note that in this case,
the expansion path is a straight line through the origin. This means that as output is expanded, the K/L ratio (the slope of the
expansion path) remains the same. (When the expansion path is a straight line through the origin, the ridge lines will also be
straight lines through the origin, rather than as drawn in Fig. 6-5.)
The line joining points on different isoquants at which the MRTS (slope) is constant is called an isocline. Thus, an
expansion path is the particular isocline along which output expands with factor prices remaining constant.
6.10 FACTOR SUBSTITUTION
If, starting from a position of producer equilibrium, the price of a factor falls, the equilibrium position will
be disturbed. In the process of reestablishing equilibrium, the producer will substitute in production this (now
relatively) cheaper factor for the other factor, until equilibrium is reestablished. The degree of substitutability of
factor L for factor K, resulting exclusively from the change in relative factor prices, is called the elasticity of
technical substitution and is measured by
D K K
L L
(e subst:) LK ¼
D(MRTS LK )=MRTS LK
(See Problems 6.19–6.23.)
6.11 CONSTANT, INCREASING, AND DECREASING RETURNS TO SCALE
We have constant, increasing, or decreasing returns to scale if, when all inputs are increased in a given
proportion, the output of the commodity increases in the same, in a greater, or in a smaller proportion, respectively
(see Problems 6.24 to 6.26).