Marginal Revenue and Marginal Cost 47except for scale, is identical to Figure 2.5. (Note that, for any level of output,
the firm’s profit is measured as the vertical distance between the revenue and
cost curves.) The firm’s break-even outputs occur at the two crossings of the
revenue and cost curves. At these outputs, revenue just matches cost, so profit
is zero. Positive profits are earned for quantities between these two output lev-
els. Of course, the firm incurs losses for very high or very low levels of pro-
duction, outside the break-even output levels. From the figure, we observe the
profit peak at an output of Q 3.3 lots.
Using the MR MC rule, how can we confirm that the output level Q
3.3 is profit maximizing? A simple answer is provided by appealing to the rev-
enue and cost curves in Figure 2.8a. Suppose for the moment that the firm
produces a lower quantity, say, Q 2 lots. At this output, the revenue curve is
steeper than the cost line; thus, MR MC. Hence, the firm could increase its
profit by producing extra units of output. On the graph, the move to a greater
output widens the profit gap. The reverse argument holds for a proposed
higher quantity, such as 4 lots. In this case, revenue rises less steeply than cost:
MR MC. Therefore, a reduction in output results in a greater cost saved than
revenue sacrificed. Again profit increases. Combining these arguments, we con-
clude that profit always can be increased so long as a small change in output
results in differentchanges in revenue and cost. Only at Q 3.3 is it true that
revenue and cost increase at exactly the same rate. At this quantity, the slopes
of the revenue and cost functions are equal; the revenue tangent is parallel to
the cost line. But this simply says that marginal revenue equals marginal cost.
At this optimal output, the gap between revenue and cost is neither widening
nor narrowing. Maximum profit is attained.
It is important to remember that the M0 and MR MC rules are
exactly equivalent. Both rules pinpoint the sameprofit-maximizing level of out-
put. Figure 2.8b shows this clearly. At Q 3.3 lots, where the profit function
reaches a peak (and the profit tangent is horizontal) in part (a), we note that
the MR line exactly intersects the MC line in part (b). This provides visual con-
firmation that profit is maximized at the output level at which marginal rev-
enue just equals marginal cost.
The MR MC rule often is the shortest path to finding the firm’s opti-
mal output. Instead of finding the marginal profit function and setting it
equal to zero, we simply take the marginal revenue and marginal cost func-
tions and set them equal to each other. In the microchip manufacturer’s
problem, we know that MR 170 40Q and MC 38. Setting MR MC
implies that 170 40Q 38. Solving for Q, we find that Q 3.3 lots. Of
course, this is precisely the same result we obtained by setting marginal profit
equal to zero.Once again let us consider the price equation P 340 .8Q and the cost equation
C 120 100Q. Apply the MR MC rule to find the firm’s optimal output. From the
inverse demand curve, find its optimal price.CHECK
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