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

120 THEORY OF PRODUCTION [CHAP. 6
EXAMPLE 2. In Fig. 6-1, the AP L at point A on the TP curve is equal to the slope of OA. This is equal to 3 and is recorded
as point A 0 in panel B. Similarly, the AP L at point B on the TP curve is equal to the slope of dashed line OB. This equals 4 and
is recorded as point B 0 in panel B. At point C, the AP L is again 4. This is the highest AP L . Past point C, the AP L declines but
remains positive as long as the TP is positive.
The MP L between the origin and point A on the TP curve is equal to the slope of OA. This slope is equal to 3 and is
recorded halfway between 0 and 1, or at 1 2 , in panel B. Similarly, the MP L between A and B is equal to the slope of AB. This is
equal to 5 and is recorded at 1 2 , in panel B. The MP L between B and C is equal to the slope of BC. This is 4 and is equal to the
highest AP L (the slope of OB and OC). Between E and F, the TP remains unchanged; therefore, the MP L is zero. Past point F,
the TP begins to decline and the MP L becomes negative.
EXAMPLE 3. The MP L curve reaches a maximum before the AP L curve (see Fig. 6-1). Also, as long as the AP L is rising,
the MP L is above it; when the AP L is falling, the MP L is below it; when AP L is maximum, the MP L is equal to the AP L . This is
as it should be: for the AP L to rise, the addition to TP (the MP L ) must be greater than the previous AP L ; for the AP L to fall,
the addition to TP (the MP L ) must be less than the previous average; for the AP L to remain unchanged, the addition to TP
(the MP L ) must be equal to the previous average. The law of diminishing returns starts operating at point J in panel B of
Fig. 6-1, or when the MP L begins to decline. This occurs because “too much” labor is used to work one acre of land. If even
more workers were used on one acre of land, these workers would start getting in each other’s way until eventually the MP L
becomes zero and then turns negative.
6.3 STAGES OF PRODUCTION
We can use the relationship between the AP L and MP L curves to define three stages of production for labor.
Stage I goes from the origin to the point where the AP L is maximum. Stage II goes from the point where the AP L
is maximum to the point where the MP L is zero. Stage III covers the range over which the MP L is negative. The
producer will not operate in stage III, even with free labor, because it would be possible to increase total output
by using less labor on one acre of land. Similarly, the producer will not operate in stage I because, as shown in
Problems 6.5–6.9, stage I for labor corresponds to stage III for land (the MP Land is negative). This leaves stage
II as the only stage of production for the rational producer.
EXAMPLE 4. Fig. 6-2, with some modifications, is the same as Fig. 6-1 and shows the three stages of production for
labor. Note that in stage II, the AP L and the MP L are both positive but declining. Thus, the rational producer operates in
the range of diminishing returns within stage II. (The symmetry in the stages of production of labor and land will be examined
in Problems 6.5 to 6.9.)
Fig. 6-2