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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.
Profit maximization of sellers: Firms sell where the most profit is generated, where marginal costs meet marginal revenue. Well defined property rights : These determine what may be sold, as well as what rights are conferred on the buyer.
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 necessary conditions are sufficient for optimality if the objective function of a maximization problem is a differentiable concave function, the inequality constraints are differentiable convex functions, the equality constraints are affine functions, and Slater's condition holds. [11]
That is that the MC company's profit-maximising output is less than the output associated with minimum average cost. Both an MC and PC company will operate at a point where demand or price equals average cost. For a PC company, this equilibrium condition occurs where the perfectly elastic demand curve equals minimum average cost.
In interdependent markets, It means firm's profit also depends on how other firms react, game theory must be used to derive a profit maximizing solution. Another significant factor for profit maximization is market fractionation. A company may sell goods in several regions or in several countries.
Specifically, the maximum profit can be rewritten as (,) = (()) where is the maximizing input corresponding to . Due to the optimality, the first order condition gives Due to the optimality, the first order condition gives
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 ...