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

CHAP. 6] THEORY OF PRODUCTION 141
6.21 Find the elasticity of substitution of L for K for the factor price change of Problems 6.19 and 6.20.
The degree of substitutability of L for K depends on the curvature of the isoquant and is measured by the coefficient
of elasticity of technical substitutions. In Fig. 6-21, K/L at point M is 1 (the slope of ray OM), and K/L at
point Z is 0.5 (the slope of ray OZ). Thus, D(K/L) from M to Z is 0.5. The MRTS LK at point M equals 10/10 or 1 (the
absolute slope of isocost 2). The MRTS LK at point Z equals 3.5/7 or 0.5 (the absolute slope of isocost 4 0 ). Thus
DMRTS LK from M to Z is 0.5. Substituting these values into the formula for the coefficient of elasticity of technical
substitution, we get
(e subt.) LK ¼
D K K
L L
¼ 0:5=1
D(MRTS LK Þ=MRTS LK 0:5=1 ¼ 1
6.22 If, starting from the equilibrium position of Problem 6.17, P L falls to $1 while P K and TO remain
unchanged, (a) separate geometrically the output effect from the substitution effect resulting
from the change in P L and (b) find the coefficient of elasticity of technical substitution for the
change in P L .
(a)
Fig. 6-22
When P L falls from $2 to $1, we move from equilibrium point N on isocost 2 and isoquant II to equilibrium
point Z on isocost 4 and isoquant IV. This firm would produce the old output level (i.e., the output level indicated
by isoquant II) at the new input prices (the slope of isocost 4) with $5 less of TO. This gives the new