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

124 THEORY OF PRODUCTION [CHAP. 6
6.8 PRODUCER EQUILIBRIUM
A producer is in equilibrium when he or she maximizes output for the given total outlay. Another-way of
saying this is that a producer is in equilibrium when the highest isoquant is reached, given the particular isocost.
This occurs where an isoquant is tangent to the isocost. At the point of tangency, the absolute slope of the isoquant
is equal to the absolute slope of the isocost. That is, at equilibrium, MRTS LK ¼ P L /P K . (This is completely
analogous to the concept of consumer equilibrium discussed in Chapter 4.) Since MRTS LK ¼ MP L /MP K ,
at equilibrium,
MP L
MP K
¼ P L
P K
or
MP L
P L
¼ MP K
P K
This means that at equilibrium the MP of the last dollar spent on labor is the same as the MP of the last dollar
spent on capital. The same would be true for other factors, if the firm had more than two factors of production.
(Again, this is completely analogous to the concept of consumer equilibrium.)
EXAMPLE 10. By bringing together on the same set of axes the firm’s isoquants (Fig. 6-3) and its isocost (Fig. 6-5), we
can determine the point of producer equilibrium. This is given by point M in Fig. 6-6. The firm cannot reach isoquant III with
its isocost. If the firm produced along isoquant I, it would not be maximizing output. Isoquant II is the highest isoquant the
firm can reach with its isocost. Thus, in order to reach equilibrium, the firm should spend $5 of its TO to purchase 5K and its
remaining $5 to purchase 5L. At the equilibrium point (M),
MRTS LK ¼ MP L
MP K
¼ P L
P K
¼ 1
6.9 EXPANSION PATH
Fig. 6-6
If the firm changes its total outlay while the prices of labor and capital remain constant, the firm’s isocost
shifts parallel to itself—up if TO is increased and down if TO is decreased. These different isocosts will be
tangent to different isoquants, thus defining different equilibrium points for the producer. By joining these
points of producer equilibrium, we get the firm’s expansion path. This is analogous to the income-consumption
curve discussed in Chapter 4.
EXAMPLE 11. If the firm’s isoquants are those of Fig. 6-3, if P L ¼ P K ¼ $1 and remains unchanged, and if the firm’s TO
rises from $6 to $10 and then to $14 per time period, we can derive the firm’s expansion path (see Fig. 6-7). Isocosts 1, 2, and
3 are parallel to each other because P L /P K remains unchanged (at the value of 1). When TO ¼ $6, the producer reaches