The firm and its objectives

The profit- and sales-maximizing outputs are, respectively, OQ_P and OQ,. Now if, for example, the minimum required profit level is OP\, then the sales-maximizing output OQ, will provide plenty of profit, and that is the amount it will pay the sales maximizer to produce.

His selling price will then be set at Q,R,/OQ,. But if the producer’s required profit level is OP₂, output OQ,, which yields insufficient profit, clearly will not do. Instead, his output will be reduced to level OQ_C, which is just compatible with his profit constraint.

It will be argued presently that in fact only equilibrium points in which the constraint is effective (OQ_C rather than OQ,) can normally be expected to occur when other decisions of the firm are taken into account.

The profit-maximizing output, OQ_P, will usually be smaller than the one which yields either type of sales maximum, OQ, or OQ_C. This can be proved with the aid of the standard rule that at the, point of maximum profit marginal cost must equal marginal revenue. For marginal cost is normally a positive number (we can’t usually produce more of a good for nothing).