The mathematical method of MR=MC profit maximization principle proves that if π is profit, Q is the output of the manufacturer, TR is the total income of the manufacturer, and TC is the total cost of the manufacturer, then π(Q) = TR(Q)? 6? 1 TC(Q). The necessary condition for profit maximization is that the first derivative of π to q is zero, and the first derivative of TR to q is the marginal revenue MR, that is, the marginal cost MC. Therefore, when MR=MC, that is, the marginal revenue equals the marginal cost, the profit is maximized.

Profit maximization requires that the second derivative of π is negative, that is to say, profit maximization requires that the slope of marginal cost function is greater than that of marginal revenue function. Generally, in different market structures, the slope of marginal cost function is positive, while in a perfectly competitive market, the slope of marginal revenue function is zero, and in an imperfect competitive market, it is negative.