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

CHAP. 7] COSTS OF PRODUCTION 173
Fig. 7-24
Points along the expansion path correspond to the points of optimal adjustment. So STC equals LTC and
the STC curve is tangent to the LTC curve. Points off the expansion path correspond to points of suboptimal
adjustment. So STC exceeds LTC and the STC curve is above the LTC curve. Thus, STC is never less than
LTC and the STC curve is never below the LTC curve. (Note that from the expansion path we can also
derive directly the LAC schedule and show the relationship between LAC and SAC. Try to do that.)
THE COBB-DOUGLAS PRODUCTION FUNCTION
7.25 Assuming that K is constant at K ¼ 1 for the Cobb-Douglas production function of Example 1,
(a) derive the TP L ,AP L ,MP L and (b) plot the TP L ,AP L , and MP L .
p
(a) TP L ¼ 10L 1=2 1 1=2 ¼ 10L 1=2 ¼ 10 ffiffiffi
L
Table 7.15
L TP L AP L MP L
0 0 ... ...
1 10.00 10.00 10.00
2 14.14 7.07 4.14
3 17.32 5.77 3.18
4 20.00 5.00 2.68