profit - Econ 301 - Microeconomic Theory 2 Lecture Note...

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Econ 301 - Microeconomic Theory 2 Lecture Note Profit Maximization (additional notes) Department of Economics University of Waterloo Fall 2011
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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.
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Profit Maximization If firms are strictly profit maximizers, they will make decisions in a “marginal” way examine the marginal profit obtainable from producing one more unit of hiring one additional laborer.
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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 choosing the level of q that maximizes profits can be found by setting the derivative of the π function with respect to q equal to zero 0 ) ( ' = - = π = π dq dC dq dR q dq d dq dC dq dR =
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Output Choice 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 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 second-order condition prevents us from mistaking q 0 as a maximum q 0
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Marginal Revenue If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the good’s price dq dp q p dq q q p d dq dR q MR + = = = = ] ) ( [ ) ( revenue marginal
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Marginal Revenue If a firm faces a downward-sloping demand curve, marginal revenue will be 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 2 /10 + 10 q Marginal revenue will be given by MR = dR / dq = - q /5 + 10
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Profit Maximization To determine the profit-maximizing output, we must know the firm’s costs If subs can be produced at a constant average and marginal cost of $4, then MR = MC - q /5 + 10 = 4 q = 30
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Marginal Revenue and Elasticity The concept of marginal revenue is directly related to the elasticity of the demand curve facing the firm The price elasticity of demand is equal to the percentage change in quantity that results from a one percent change in price q p dp dq p dp q dq e p q = = / / ,
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profit - Econ 301 - Microeconomic Theory 2 Lecture Note...

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