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# ch19lec - ECON 306 Chapter 19 Profit Maximization RUST CHO...

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ECON 306 Chapter 19: Profit Maximization RUST, CHO, DIAZ

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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: ±² ±³ ´ ±² ±³ ´ 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 ±² ±³ ´ . 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 ( ) , ( 0 factor of price factor of MP of value x x x f w x x pMP w p ± w w ± ± ² ± ± ³ ´ . 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. x The solution is characterized by a tangency condition (see Fig. 19.1): the slope of the production function should equal the slope of the isoprofit line: , , line isoprofit of

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