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

174 COSTS OF PRODUCTION [CHAP. 7
(b)
Panel A of Fig. 7.25 shows the TP L and panel B shows the AP L and MP L from Table 7.15. Note that these
curves show only stage II of production for L and that MP L is plotted at the midpoints of L.
Fig. 7-25
7.26 For the Cobb-Douglas of Example 1, (a) derive the expansion path and (b) plot the expansion path,
assuming P L ¼ P K ¼ $1, and sketch on the same figure the isoquants for Q ¼ 10, Q ¼ 20, and Q ¼ 40.
(a)
The expansion path is the locus of producer equilibrium points resulting from increasing p expenditures while
holding factor prices constant. It is derived in Table 7.16 from Q ¼ 10L 1=2 K 1=2 ¼ 10
ffiffiffi pffiffiffiffi
L K by varying both
L and K proportionately.
Table 7.16
L K
p
10 ffiffiffi pffiffiffiffi
L K
0 0
p
10 ffiffi pffiffi
0 0
1 1
p
10 ffiffi pffiffi
1 1
2 2
p
10 ffiffi pffiffi
2 2
3 3
p
10 ffiffi pffiffi
3 3
4 4
p
10 ffiffi pffiffi
4 4
Q
0
10
20
30
40
(b)
Fig. 7-26 shows the expansion path and hypothetical isoquants for Q ¼ 10, Q ¼ 20, and Q ¼ 40. Note that the
expansion path is a straight line through the origin and the isoquants are equally spaced and have equal slope
along any ray or isocline from the origin.