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Marginal Revenue and Marginal Cost 45

Marginal Cost

Marginal cost (MC)is the additional cost of producing an extra unit of output.

The algebraic definition is

The computation of MC is particularly easy for the microchip manufacturer’s

cost function in Equation 2.4. From the cost equation, C  100 38Q, it is

apparent that producing an extra lot (increasing Q by a unit) will increase cost

by $38 thousand. Thus, marginal cost is simply $38 thousand per lot. Note that

regardless of how large or small the level of output, marginal cost is always con-

stant. The cost function in Equation 2.4 has a constant slope and thus also an

unchanging marginal cost. (We can directly confirm the MC result by taking

the derivative of the cost equation.)

Profit Maximization Revisited

In view of the fact that R C, it should not be surprising that

[2.9]

In other words, marginal profit is simply the difference between marginal rev-

enue and marginal cost.

The logic of this relationship is simple enough. Suppose the firm produces

and sells an extra unit. Then its change in profit is simply the extra revenue it

earns from the extra unit net of its additional cost of production. But the extra

revenue is MR and the extra cost is MC, so MMR MC.

Thus far, we have emphasized the role of marginal profit in characterizing

the firm’s optimal decision. In particular, profits are maximized when marginal

profit equals zero. Thus, using the fact that MMR MC, an equivalent

statement is MR MC 0. This leads to the following basic rule:

The firm’s profit-maximizing level of output occurs when the additional revenue

from selling an extra unit just equals the extra cost of producing it, that is, when

MR MC.

There are a number of ways to check the logic of the MR MC decision

rule. Figure 2.8 provides a graphic confirmation. Part (a) reproduces the

microchip manufacturer’s revenue and cost functions (from Equations 2.3 and

2.4) in a single graph. The graph of profit also is shown in Figure 2.8a and,

MMRMC.

¢C/¢Q[C 1 C 0 ]/[Q 1 Q 0 ].

Marginalcost[Change in Cost]/[Change in Output]

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