The firm and its objectives
The proposition is that no firm can be earning maximum profits unless its marginal cost and its marginal revenue are (at least approximately) equal, i.e., unless an additional unit of output will bring in as much money as it costs to produce, so that its marginal profitability is zero.
It is easy to show why this must be so. Suppose a firm is producing 200,000 units of some item, x, and that at that output level, the marginal revenue from x production is $1.10 whereas its marginal cost is only 96 cents. Additional units of x will, therefore, each bring the firm some 14 cents = $1.10 — 0.96 more than they cost, and so the firm cannot be maximizing its profits by sticking to its 200,000 production level. Similarly, if the marginal cost of x exceeds its marginal revenue, the firm cannot be maximizing its profits, for it is neglecting to take advantage of its opportunity to save money—by reducing its output it would reduce its income, but it would reduce its costs by an even greater amount.
We can also derive the marginal-cost-equals-marginal-revenue proposition with the aid of Figure 1.
At any output, OQ, total revenue is represented by the area OQPR under the marginal revenue curve (see Rule 9 of Chapter 3). Similarly, total cost is represented by the area OQKC immediately below the marginal cost curve. Total profit, which is the difference between total revenue and total cost is, therefore, represented by the difference between the two areas—that is, total profits are given by the lightly shaded area TKP minus the small, heavily shaded area, RTC. Now, it is clear that from point Q a move to the right will increase the size of the profit area TKP. In fact, only at output OQm will this area have reached its maximum size—profits will encompass the entire area TKMP. But at output OQm marginal cost equals marginal revenue—indeed, it is the crossing of the marginal cost and marginal revenue curves at that point which prevents further moves to the right
