ch11 - Chapter 11 Profit Maximization The Nature of Firms A...

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Chapter 11 Profit Maximization
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The Nature of Firms A firm is an association of individuals who have organized themselves for the purpose of turning inputs into outputs Different individuals will provide different types of inputs the nature of the contractual relationship between the providers of inputs to a firm may be quite complicated
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Contractual Relationships Some contracts between providers of inputs may be explicit may specify hours, work details, or compensation Other arrangements will be more implicit in nature decision-making authority or sharing of tasks
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Modeling Firms’ Behavior Most economists treat the firm as a single decision-making unit the decisions are made by a single dictatorial manager who rationally pursues some goal usually profit-maximization
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Profit Maximization A profit-maximizing 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 If firms are strictly profit maximizers, they will make decisions in a “marginal” way examine the marginal profit obtainable from producing one more unit or hiring one additional unit of capital or labor
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Output Choice 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 ( π ) are the difference between total revenue and total costs π ( q ) = R ( q ) – C ( q ) = p ( q ) q C ( q )
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Output Choice The necessary condition for the q that maximizes profits can be found by setting the derivative of π with respect to q equal to zero 0 ) ( ' = - = π = π dq dC dq dR q dq d dq dC dq dR = To maximize economic profits, the firm should choose the output for which marginal revenue is equal to marginal cost MC dq dC dq dR MR = = =
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Second-Order Conditions MR = MC is only a necessary condition for profit maximization For sufficiency, it is also required that 0 ) ( ' * * 2 2 < π = π = = q q q q dq q d dq d “marginal” profit must be decreasing at the optimal level of q
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Profit Maximization output 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 second-order condition prevents us 0 q 0
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Marginal Revenue If a firm can sell all it wishes without any effect on market price, marginal revenue equals price If it faces a downward-sloping demand curve, it can sell more output only by reducing the price dq dp q p dq q q p d dq dR q MR + = = = = ] ) ( [ ) ( revenue marginal If a firm faces a downward-sloping demand curve, marginal revenue is a function of output If price falls as a firm increases output, marginal revenue will be less than price
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Marginal Revenue Suppose that the demand curve for a sub sandwich is q = 100 – 10 p Solving for price, we get p = - q /10 + 10 This means that total revenue is R = pq = - q /10 + 10 q Marginal revenue will be given by
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Profit Maximization To determine the profit-maximizing output, we
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