The firm and its objectives
(further output increases) from adding still more to the total profit area. Thus, we have once again established that at the point of maximum profits, marginal costs and marginal revenues must be equal.
Before leaving the discussion of this proposition, it is well to distinguish explicitly between it and its invalid converse. It is not generally true that any output level at which marginal cost and marginal revenue happen to be equal (i.e., where marginal profit is zero) will be a profit-maximizing level. There may be several levels of production at which marginal cost and marginal revenue are equal, and some of these output quantities may be far from advantageous for the firm. In Figure 1 this condition is satisfied at output OQt as well as at OQm. But at OQt the firm obtains only the net loss (negative profit) represented by heavily shaded area RTC. A move in either direction from point Qt will help the firm either by reducing its costs more than it cuts its revenues (a move to the left) or by adding to its revenues more than to its costs. Output OQt is thus a point of minimum profits even though it meets the marginal profit-maximization condition, «marginal revenue equals marginal cost.»
This peculiar result is explained by recalling that the condition, «marginal profitability equals zero,» implies only that neither a small increase nor a small decrease in quantity will add to profits. In other words, it means that we are at an output at which the total profit curve (not shown) is level—going neither uphill nor downhill. But while the top of a hill (the maximum profit output) is such a level spot, plateaus and valleys (minimum profit outputs) also have the same characteristic—they are level. That is, they are points of zero marginal profit, where marginal cost equals marginal revenue.
We conclude that while at a profit-maximizing output marginal cost must equal marginal revenue, the converse is not correct—it is not true that at an output at which marginal cost equals marginal revenue the firm can be sure of maximizing its profits.
