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

130 THEORY OF PRODUCTION [CHAP. 6
6.5 Panel A of Table 6.6 is the same as Table 6.1. The TP Land (column 3 in panel B of this table) is derived
directly from panel A, by keeping labor fixed at one unit per time period and using alternative quantities
of land, ranging from 1/8 of a unit (acre) to 1 unit and assuming constant returns to scale. Explain (a)
how each value of the TP Land was obtained (start from the bottom of the table), (b) how the AP Land
values in column (4) of panel B were obtained and (c) how the MP Land values were obtained. (The
aim of this and the next four problems is to demonstrate the symmetry in the stages of production
for labor and land.)
Table 6.6
PANEL A: LABOR
PANEL B: LAND
(1) (2) (3) (4) (5) (1) (2) (3) (4) (5)
Land Labor TP Labor AP Labor MP Labor Land Labor TP Land AP Land MP Land
1 0 0 0 ...
1 1 3 3 3 1 1 3 3 ...
1
1 2 8 4 5
2
1 4 8 22
1
1 3 12 4 4
3
1 4 12 0
1 4 15 3 3 1
4
3
4
1 3 3 4
15 3
1 5 17 3 2 1
5
2
5
1 3 2 5
17 7
1 6 17 2 5 1
6
0
6
1 2 5 6
17 17
1 7 16 2 2 1
7
21
7
1 2 2 7
16 23
1 8 13 1 5 1
8
23
8
1 1 5 8
13 37
(a)
(b)
(c)
Starting from the bottom of panel A, we see that 8 units of labor on 1 unit of land produces 13 units of output;
therefore, using 1/8 of the quantity of labor and land should result in 1/8 of 13 units of output, because of
constant returns to scale. Thus, 1 unit of labor used on 1/8 unit of land produces 1/8 of13or15/8 units
of output [see the last row of column (3) in panel B]. The other figures of column (3) in panel B are obtained
by following the same procedure. Note that the TP Land [column (3) in panel B] is identical with the AP Labor
[column (4) in panel A].
From the TP Land we can derive the AP Land and the MP Land . The AP Land schedule [column (4)] is obtained by
dividing the TP Land [column (3)] by the corresponding quantities of land used [column (1)]. Starting at the
bottom of panel B, we divide the TP Land of 1 5 8 by 1 8 unit of land to obtain 13 as the corresponding AP Land
(1 5 8 4 1 8 ¼ 13
8 4 1 8 ¼ 13 8 8 1 ¼ 13). The other figures for the AP Land are obtained in a similar fashion. Note
that the AP Land [column (4) in panel B] is identical with the TP Labor [column (3) in panel A].
The MP Land is given by the change in the TP Land divided by the change in the quantity of land used. Starting at
the bottom of panel B, we see that when we change the amount of land used from 1 8 unit to 1 7 unit, the TP Land
changes from 1 5 8 to 22 7 units. Going from a TP Land of 1 5 8 to a TP Land of 2 2 7
represents a change of 37/56 unit of
output (2 2 7
1 5 8 ¼ 16 13 128 91
7 8
¼
56
¼ 37
56
). Going from 1/8to1/7 unit of land represents a change of 1/56 unit
of land ( 1 1
7 8 ¼ 8 7
56 ¼ 1 56 ). Dividing the change in the TP Land (37/56) by the corresponding change in the
quantity of land used (1/56), we get the MP Land of 37( 37
56 4 1
56 ¼ 37
56 56
1
¼ 37). This is recorded in the last
row of column (5) in panel B. The other figures for the MP Land recorded in column (5) of panel B are similarly
obtained.
6.6 (a) Plot, on the same set of axes, the information contained in panels A and B of Table 6.6. Let a movement
from left to right on the horizontal axis measure the increasing labor/land ratios given by moving
down columns (2) and (1) in panel A; the movement from right to left along the horizontal axis will then
measure the decreasing labor/land ratios given by moving up columns (2) and (1) in panel B. (b) What
can you say about the stages of production for labor and capital in the graph in part (a)?
(a)
Moving (in the usual way) from top to bottom in panel A of Table 6.6 corresponds to a movement from left to
right in Fig. 6-11, and we get the familiar TP Labor , the AP Labor , and the MP Labor (as in Fig. 6-2). On the other