LECTURE 15
THE SUNDEVIL MINE PRODUCTION FUNCTION
(CONTINUED)
Look again at Table 131, from which we created Figures 141 and 142.
Also, have Figure 151 and 152 in front of you while you read through this
lecture.
Figures 151 and 152 are smooth,
typical
, shortrun Total Product
(TP), Marginal Product (MP), and Average Product (AP) curves that apply to
any and all firms operating with at least one fixed input.
In our case the fixed
input is Land (the mine shaft that we have decided to lease and reopen).
Look carefully at Figures 141 and 142 and compare them to the two graphs
depicted on Figure 151.
Essentially they are identical.
The actual graphs
look different, but the key features of each set of graphs are identical.
In both Figures 14 and Figure 15, as we apply more and more units of the
variable input (doses of labor and capital for our mine) to some fixed input
(our leased land & mine shaft) TP increases; at first at an
increasing
rate (the
TP curve is
concave upward
.
Then the TP curve reaches an
inflection point
(the first vertical dashed line in Figure 151) at which point the TP curve
increases at a
decreasing
rate (the TP curve is
concave downward
).
The TP
curve continues to increase at a decreasing rate until it reaches a
maximum
at the second vertical dashed line, where the slope of the TP curve, which
has been decreasing since the first vertical dashed line, becomes zero, (the
horizontal dashed line at the maximum point of the TP curve).
After this point
TP begins to decrease.
The relationship between total physical product (TP) and the number of units
of the variable inputs employed each period (Doses of N & K) is an
empirical
relationship for any firm, including our mining company.
We alter the physical
units of labor and capital that we apply to the mine shaft each week and we
record the different levels of output, in ounces of gold, that we obtain.
The Marginal Product (MP) and Average Product (AP) curves in Figure 142
and the bottom portion of Figure 151 are
derived
from the TP function.
AP = (TP) / (Doses of N&K)
Equation 151
Where AP is
average product per dose of labor and capital, measured in
ounces per week; TP is total product, measured in ounces per week; and
Doses of N&K is the number of doses of the variable inputs employed each
week.
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View Full DocumentMP = (
∆
TP) / (
∆
1
Equation 15
2
Where MP is
marginal product per dose of labor and capital, measured in
ounces per week, and is defined as the change in TP brought about by a one
unit change in the number of doses employed.
Both in the top and bottom portions of Figure 151, note there are three
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 Spring '07
 nancy
 AP, Economics of production, total fixed cost, vertical dashed line

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