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

142 THEORY OF PRODUCTION [CHAP. 6
equilibrium point T on isoquant II and isocost 4 0 . Thus,
Total effect ¼ Substitution effect þ Output effect
NZ ¼ NT þ TZ
(b)
The movement along isoquant II from N to T is the substitution effect and results exclusively from the
change in relative factor prices. Thus, as P L falls in relation to P K , the firm substitutes 2 units of labor
for 3 units of capital to produce the same level of output. Substituting the values from this problem into
the formula, we get the coefficient of elasticity of substitution of labor for capital between points N and
T, as follows:
D K
K 7 2 7
L L 6 1 12
(e subt:) LK ¼
¼ ¼ ¼ 7 ffi 1:17
D(MRTS LK ) 1 1 6
MRTS LK 2 2
To separate the substitution from the output effect for an increase in the price of a factor, we proceed in a
manner analogous to that followed to separate the substitution from the income effect of a rise in the price of
a commodity [see Problem 4.34(a)].
6.23 On one set of axes, draw three isoquants showing zero (e subst.) LK and constant returns to scale. On
another set of axes, draw three isoquants showing infinite (e subst.) LK and constant returns to scale.
In Fig. 6-23, the isoquants of panel A show zero (e subst.) LK and constant returns to scale. Production takes
place with a K/L ¼ 1, regardless of relative factor prices. Thus, if relative factor prices change, D(K/L) ¼ 0,
and the (e subst.) LK ¼ 0. The firm will use 2K and 2L to produce 100 units of output (point D). If the firm used
2K and more than 2L, say, 4L (point F), output would still be 100 units. Thus, the MP L ¼ 0. Similarly, if the
firm used 4K and 2L (point E), output would again be 100 units. Thus, the MP k ¼ 0. If the firm doubles all
inputs (point G), output doubles. Thus we have constant returns to scale. Production takes place along ray OC.
Fig. 6-23
The isoquants of panel B show infinite (e subst.) LK and constant returns to scale. Since the slope of the
isoquants (MRTS LK ) remains unchanged, DMRTS LK ¼ 0 and (e subst.) LK ¼ 1. In addition, since output increases
proportionately to the increase in both inputs, we have constant returns to scale.
The usual isoquane is convex to the origin and has an (e subst.) LK between zero and infinity (depending on the
location and the curvature of the isoquant). In drawing continuous isoquants which are convex to the origin, we are
implicitly assuming that inputs are available in continuously variable quantities.