9781118041581

Marginal Analysis 41

Maximum profit is attained at the output level at which marginal profit is zero

(M0).

A practical method for calculating marginal profit at any level of output is

afforded by the simple rules of differential calculus. (For a thorough review, read

the appendix to this chapter.) Consider once again the firm’s profit equation:

[2.6]

Marginal profit (the slope of the corresponding profit graph) is found by taking

the derivative of this equation with respect to Q. The result is

[2.7]

With this formula in hand, we can find the marginal profit at any output level

simply by substituting the specified quantity into the equation. For example,

Md/dQ 132 40Q.

 100 132Q20Q^2

FIGURE 2.6

A Close-Up View of

Profit

Maximum profit occurs

at an output where

marginal profit is zero,

that is, the slope of the

tangent line is zero.

119

118

117

116

Profit (Thousands of Dollars)

3.0 3.1 3.2 3.3 3.4 3.5

Quantity (Lots)

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