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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.
In a single-goods case, a positive economic profit happens when the firm's average cost is less than the price of the product or service at the profit-maximizing output. The economic profit is equal to the quantity of output multiplied by the difference between the average cost and the price.
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. = economic profit. Profit maximization means that the derivative of with respect to Q is set equal to 0:
These functions describe each firm's optimal (profit-maximizing) quantity of output given the price firms face in the market, , the marginal cost, , and output quantity of rival firms. The functions can be thought of as describing a firm's "Best Response" to the other firm's level of output.
The mathematical profit maximization conditions ("first order conditions") ensure the price elasticity of demand must be less than negative one, [2] [7] since no rational firm that attempts to maximize its profit would incur additional cost (a positive marginal cost) in order to reduce revenue (when MR < 0). [1]
The company maximises its profits and produces a quantity where the company's marginal revenue (MR) is equal to its marginal cost (MC). The company is able to collect a price based on the average revenue (AR) curve. The difference between the company's average revenue and average cost, multiplied by the quantity sold (Qs), gives the total profit.
Property P2 is not satisfied. Because the monopolist's profit-maximizing quantity is different from the socially-maximizing quantity, consumers have an incentive to demand more at the equilibrium price. However, at the market price, monopolists maximize their profits so they have no incentive to change their price.
The goal of maximizing profit is also what leads firms to enter markets where economic profit exists, with the main focus being to maximize production without significantly increasing its marginal cost per good.