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Unformatted text preview: Lecture 14: Profit Maximization Key Terms F i r m Profitmaximizing firm Inverse elasticity rule Average revenue curve Marginal revenue curve Shortrun supply curve Input demand function Substitution effect O u t p u t e f f e c t Cross price effect The Nature of Firms A firm is an association of individuals who have organized themselves for the purpose of turning inputs into outputs We as economists struggle to understand: Why are certain actions taken within the boundary of the firm while other actions are taken in the market? e.g.: Why hire someone in your firm to build an intermediate input rather than buy the intermediate input in the market? We will not worry about this here We just take the existence of firms as given. Profit Maximization Often, economists treat the firm as a single decisionmaking unit the decisions are made by a single dictatorial manager who rationally pursues some goal usually profitmaximization This is clearly a simplification and well make this simplification A profitmaximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits seeks to maximize the difference between total revenue and total economic costs Profit (a reminder) Total revenue for a firm is given by R ( q ) = p ( q ) q In the production of q , certain economic costs are incurred [ C(q) ] Economic profits ( ) are the difference between total revenue and total costs ( q ) = R ( q ) C ( q ) = p ( q ) q C ( q ) Output Choice The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the function with respect to q equal to zero d /dq = dR/dq dC/dq = 0 dR/dq = dC/dq To maximize economic profits, the firm should choose the output for which marginal revenue is equal to marginal cost MR = dR/dq = dC/dq = MC SecondOrder Conditions MR = MC is only a necessary condition for profit maximization For sufficiency, it is also required that ) ( ' * * 2 2 q q q q dq q d dq d marginal profit must be decreasing at the optimal level of q Profit Maximization Output per period Revenues, Costs R C q* Profits are maximized when the slope of the revenue function is equal to the slope of the cost function The secondorder condition prevents us from mistaking q as a maximum q How to solve for output choice? Up to now, we have solved for derived demand for inputs (assuming a fixed and arbitrary output) How does a firm actually determine its output? To solve for output choice, follow the following steps: 1) First solve for profit (total revenue minus total cost) as a function of q 2) Differentiate profit with respect to q and solve for the q that equates the derivative to zero 3) Make sure that the second derivative of profit is negative at the q you found in step 2.negative at the q you found in step 2....
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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.
 Spring '08
 Govel

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