Maximization of Profits, Again

We can now give another rule for the maximization of profits. The new rule is really just the same rule as we saw before, only now we state it in terms of price and costs. It is the equimarginal principle in yet another form.

The question is: "I want to maximize profits. How much output should I sell, at the given price?"

The answer is: increase output until

p=MC

The point is illustrated by the following table, which extends the marginal cost table in an earlier page to show the price and the profits for the example firm.

Table 4

Output Average
Cost Marginal
Cost price profit

0 0 100 0

9.45
945 137.57 100 -35503.65

52.91

1780 101.12 100 -1993.60

59.88

2505 91.82 100 20490.90

68.97

3120 89.74 100 32011.20

81.30

3625 91.03 100 32516.25

99.01

4020 94.53 100 21989.40

126.58

4305 99.88 100 516.60

175.44

4480 107.14 100 -31987.20

285.71

4545 116.61 100 -75492.45

769.23

Output	Average Cost	Marginal Cost	price	profit
0	0	100	0
9.45
945	137.57	100	-35503.65
52.91
1780	101.12	100	-1993.60
59.88
2505	91.82	100	20490.90
68.97
3120	89.74	100	32011.20
81.30
3625	91.03	100	32516.25
99.01
4020	94.53	100	21989.40
126.58
4305	99.88	100	516.60
175.44
4480	107.14	100	-31987.20
285.71
4545	116.61	100	-75492.45
769.23

Notice how profits are greatest (at 32516.25) when the marginal cost is almost exactly equal to the price of $100. This occurs at an output of 3625, with marginal cost at 99.01. The profit-maximizing output would be very slightly more than 3625.