LECTURE 17
PROFIT MAXIMIZATION:
MARGINAL COST & MARGINAL REVENUE
Figure 163 and Figure 164 demonstrated, along with Table 151 from which
the figures were derived, that the profit maximizing level of output is that level
of output where the slope of the total revenue curve, marginal revenue (MR)
is equal to the slope of the total cost curve, marginal cost (MC).
Remember,
this is where the vertical distance between the TR curve and the TC curve, or
profit, is the greatest.
Figure 171 shows the MC and MR curves from Figure 162.
Note that on
Figure 162, the MC curve crosses the MR curve at a level of output of 7
ounces per week.
FOR ANY TYPE OF FIRM, THE PROFIT MAXIMIZING LEVEL OF OUTPUT
FOR THE FIRM IS WHERE MARGINAL COST IS EQUAL TO MARGINAL
REVENUE.
1
Look at the different possible levels of output.
Ounces 1 through 6, inclusive,
all bring in more revenue to the firm (MR) than they each cost to produce
(MC).
We should produce these units as we make a profit on each.
Note that
if we produce ounces 8 through 12, inclusive, each ounce produced costs us
more to produce than it brings in as revenue to the firm.
We should not
produce these units as we take a loss on each.
When MC = MR we make the
most profit.
Figure 172 puts it all together.
Note that MC = MR at or near 7 ounces of
gold produced per week.
When the price of gold is $600 per ounce, MR is
$600.
TR is P X Q, or $600 X 7 = $4,200 per week.
The MC of the 7th ounce
of gold is $590.
We should produce the 7th ounce of gold.
We make $10
profit on it.
At 7 ounces of gold produced per week, ATC is $428.57 per
week.
(This number, as all numbers, is from our empirically derived Table 15
1.)
TC = $428.57 X 7 = $3,000 per week.
2
1
Since MC can initially start out above MR, and cut MR when MC is falling, and then cut MR again later
when MC is rising, to be perfectly precise, the rule is
the profit maximizing level of output for the firm is where
rising marginal cost is equal to marginal revenue.
2
Remember, if ATC is defined as TC / Q, then if we have Q and ATC, as we do in this graph, then TC = ATC
x Q.
Note carefully the relationship between this graph and Table 151.
The ATC of 1 oz = $810.
The AVC
and MC of 1 oz = $240.
The ATC of 7 oz = $428.57.
The AVC of 7 oz = $347.14.
The vertical distance
between ATC and AVC at any level of output is AFC.
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Graphically, TR is the area of the rectangle with a height of $600 and a length
of 7 ounces.
TC is the area of the rectangle with a height of $428.57 and a
length of 7 ounces.
Note the profit rectangle:
E
Eis the area of the rectangle with a height of
$171.43 ($600  $428.57 = $117.43) and a length of 7 ounces.
($171.43 / ounce) x (7 ounces per week) = $1,200 per week.
3
Examine Figure 173.
Figure 173 depicts the MC and ATC curves for our
Sun Devil Gold Mine, derived in earlier lectures.
There is one difference.
At
a price of $600 per ounce, the profit maximizing level of output for our mining
operation is still 7 ounces per week.
However, the ATC curve has been
moved up, and now it would appear that we are making $0 of profit each
week.
The minimum point of the ATC curve is tangent to the MR curve.
Total
cost appears to be equal to total revenue.
This implies that profit is zero.
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 Spring '07
 nancy
 Economics

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