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

CHAP. 6] THEORY OF PRODUCTION 139
market. Therefore, it pays for the firm to substitute labor for capital until it reaches point N. The opposite is true at
point P.
As an alternative to maximizing output for a given TO, the firm might want to minimize the cost of producing
a specified level of output. This corresponds to finding the lowest isocost (TO) necessary to reach the specified
isoquant (level of output).
6.18 Assume that (1) the firm has isoquants I, II, and III of Problem 6.12, (2) P K and P L are $1 and $2,
respectively, and they remain constant, and (3) the TO of the firm rises from $12 to $16 and then to
$20 per time period. Derive the firm’s expansion path.
With isocost 1, the producer is in equilibrium at point R on isoquant I; with isocost 2, the producer is in equilibrium
at point N on isoquant II; with isocost 3, the producer is in equilibrium at point S on isoquant III. The line
joining equilibrium points R, N, and S is the expansion path of this firm. Notice that in this case as output rises, the
slope of the expansion path (the DK/DL ratio) falls. Isocosts 1, 2, and 3 are parallel because P K and P L remain
constant. Since the absolute slope of all three isocosts is equal to 2, the MRTS LK at equilibrium points R, N, and
S, is also equal to 2. That is, at equilibrium points R, N, and S,
Thus, expansion path ORNS is an isocline.
MRTS LK ¼ MP L =MP K ¼ P L =P K ¼ 2
Fig. 6-19
FACTOR SUBSTITUTION
6.19 Starting from equilibrium position M in Fig. 6-6, find the new equilibrium point if P L falls to $0.50
(while P K and TO remain unchanged at $1 and $10, respectively).
When P L falls to $0.50 (while P K and TO remain unchanged) the isocost rotates counterclockwise from isocost
2 to isocost 4 (see Fig. 6-20). With this new isocost, the producer is in equilibrium at point W where isocost 4 is
tangent to isoquant III. Thus when P L falls from $1 to $0.50 (ceteris paribus), the quality of labor purchased by this
producer increases from 5 to 9 units per time period. This total effect is the combined result of an output effect and a
substitution effect. These are analogous to the income and substitution effects of demand theory (Chapter 4). The
output effect results because when P L falls, the producer could produce a greater output (isoquant III as opposed to
isoquant II) with a given TO. This means that the producer could produce the output level indicated by isoquant II
with a smaller TO, after P L has fallen.