How can the decision maker use profit changes as signposts pointing
toward the optimal output level? The answer is found by applying the maxim
of marginal analysis:Make a small change in the level of output if and only if this generates an increase
in profit. Keep moving, always in the direction of increased profits, and stop when
no further output change will help.Starting from a production level of 2.5 lots, the microchip firm should
increase output to 2.6 because marginal profit from the move ($30,000) is pos-
itive. Marginal profit continues to be positive up to 3.3 lots. Therefore, output
should be increased up to and including a final step going from 3.2 to 3.3 lots.
What about increasing output from 3.3 to 3.4 lots? Since the marginal profit
associated with a move to 3.4 is negative ($2,000), this action would decrease
profit. Having reached 3.3 lots, then, no further profit gains (positive marginal
profits) are possible. Note that the final output, 3.3, could have been reached
starting from a “high” output level such as 3.7 lots. As long as marginal profit
is negative, one should reduce output (i.e., reverse field) to increase profit.Marginal Analysis and Calculus
The key to pinpointing the firm’s optimal quantity (i.e., the exactoutput level at
which maximum profit is attained) is to compute marginal profit atany given level
of output rather than betweentwo nearby output levels. At a particular output, Q,
marginal profit is given by the slope of the tangentline to the profit graph atthat
output level. Figure 2.6 shows an enlarged profit graph with tangent lines drawn
at outputs of 3.1, and 3.3 lots. From viewing the tangents, we draw the following
simple conclusions. At 3.1 lots, the tangent is upward sloping. Obviously, marginal
profit is positive; that is, raising output by a small amount increases total profit.
Conversely, at 3.4 lots, the curve is downward sloping. Here marginal profit is neg-
ative, so a small reduction in output (not an increase) would increase total profit.
Finally, at 3.3 lots, the tangent is horizontal; that is, the tangent’s slope and mar-
ginal profit are zero. Maximum profit is attained at precisely this level of output.
Indeed, the condition that marginal profit is zero marks this point as the optimal
level of output. Remember: If Mwere positive or negative, total profit could be
raised by appropriately increasing or decreasing output. Only when Mis exactly
zero have all profit-augmenting opportunities been exhausted. In short, when the
profit function’s slope just becomes zero, we know we are at the precise peak of
the profit curve.^3 Thus, we have demonstrated a basic optimization rule:40 Chapter 2 Optimal Decisions Using Marginal Analysis(^3) In some cases, the M0 rule requires modification. For example, suppose demand and cost
conditions are such that M0 for all output quantities up to the firm’s current production
capacity. Clearly, the rule M0 does not apply. However, the marginal profit message is clear:
The firm should increase output up to capacity, raising profit all the while. (For further discussion,
see the appendix to this chapter and Problem 5 at the end of the chapter.)
c02OptimalDecisionsUsingMarginalAnalysis.qxd 8/17/11 5:17 PM Page 40