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Profit maximization using the total revenue and total cost curves of a perfect competitor. To obtain the profit maximizing output quantity, we start by recognizing that profit is equal to total revenue minus total cost (). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph.
C. Robert Taylor points out that the accuracy of Hotelling's lemma is dependent on the firm maximizing profits, meaning that it is producing profit maximizing output and cost minimizing input . If a firm is not producing at these optima, then Hotelling's lemma would not hold. [2]
Mathematically, the markup rule can be derived for a firm with price-setting power by maximizing the following expression for profit: = () where Q = quantity sold, P(Q) = inverse demand function, and thereby the price at which Q can be sold given the existing demand C(Q) = total cost of producing Q.
Notice that at the profit-maximizing quantity where =, we must have = which is why we set the above equations equal to zero. Now that we have two equations describing the states at which each firm is producing at the profit-maximizing quantity, we can simply solve this system of equations to obtain each firm's optimal level of output, q 1 , q 2 ...
An accountant measures the firm's accounting profit as the firm's total revenue minus only the firm's explicit costs. An economist includes all costs, both explicit and implicit costs, when analyzing a firm. Therefore, economic profit is smaller than accounting profit. [3] Normal profit is often viewed in conjunction with economic profit ...
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The profit maximization issue can also be approached from the input side. That is, what is the profit maximizing usage of the variable input? To maximize profits the firm should increase usage "up to the point where the input’s marginal revenue product equals its marginal costs". So, mathematically the profit maximizing rule is MRP L = MC L. [10]