ch19lec - ECON 306 Chapter 19: Profit Maximization RUST,...

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Unformatted text preview: ECON 306 Chapter 19: Profit Maximization RUST, CHO, DIAZ Profits x Economic Profits revenues minus costs. x Need to include all factors of production used by the firm. x Each factor should be valued at its market price. x What if the firm owns the input? opportunity costs . x Denote the price of output i by i p , and the price of input j by j w . x General case with n outputs and m inputs: Cost 1 Revenue 1 S m j j j n i i i x w y p . x Our particular case, one output and two inputs: 2 2 1 1 2 1 ) , ( x w x w x x f p y S . x Measured in flow terms. Competitive model we will assume that firms take price of its product and prices of inputs as given. Short-Run Profit Maximization x In the short run some inputs are fixed. x The firm chooses the optimal level of variable inputs. x Assuming input 2 is fixed in the short run, the maximization problem is 2 2 1 1 2 1 1 ) , ( max x w x w x x pf x x The first-order condition (FOC) for maximization is: , 1 1 1 2 * 1 1 1 1 ) 2 , 1 ( ) , ( factor of price factor of MP of value x x x f w x x pMP w p w w . x Therefore, the value of the marginal product of a factor should equal its price. x Graphic derivation of the optimality condition. From the profit equation 2 2 1 1 x w x w py S get the isoprofit lines : 2 2 1 1 x x y p w p w p S . x The profit-maximization problem is then to find the point on the production function that has the highest associated isoprofit line....
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This note was uploaded on 10/25/2011 for the course ECON 326 taught by Professor Hulten during the Spring '08 term at Maryland.

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ch19lec - ECON 306 Chapter 19: Profit Maximization RUST,...

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