V19 - 2010 W. W. Norton & Company, Inc. 19...

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Unformatted text preview: 2010 W. W. Norton & Company, Inc. 19 Profit-Maximization 2010 W. W. Norton & Company, Inc. 2 Outline Economic profit Short-run profit maximization Comparative statics Long-run profit maximization Profit maximization and returns to scale Revealed profit maximization 2010 W. W. Norton & Company, Inc. 3 Economic Profit A firm uses inputs j = 1,m to make products i = 1,n. Output levels are y 1 ,,y n . Input levels are x 1 ,,x m . Product prices are p 1 ,,p n . Input prices are w 1 ,,w m. 2010 W. W. Norton & Company, Inc. 4 The Competitive Firm The competitive firm takes all output prices p 1 ,,p n and all input prices w 1 , ,w m as given constants. 2010 W. W. Norton & Company, Inc. 5 Economic Profit The economic profit generated by the production plan (x 1 ,,x m ,y 1 ,,y n ) is . 1 1 1 1 m m n n x w x w y p y p -- + + = 2010 W. W. Norton & Company, Inc. 6 Economic Profit Output and input levels are typically flows. E.g. x 1 might be the number of labor units used per hour. And y 3 might be the number of cars produced per hour. Consequently, profit is typically a flow also; e.g. the number of dollars of profit earned per hour. 2010 W. W. Norton & Company, Inc. 7 Economic Profit How do we value a firm? Suppose the firms stream of periodic economic profits is , 1 , 2 , and r is the rate of interest. Then the present-value of the firms economic profit stream is PV r r = + + + + + 1 2 2 1 1 ( ) 2010 W. W. Norton & Company, Inc. 8 Economic Profit A competitive firm seeks to maximize its present-value. How? 2010 W. W. Norton & Company, Inc. 9 Economic Profit Suppose the firm is in a short-run circumstance in which Its short-run production function is y f x x = ( , ~ ). 1 2 x x 2 2 ~ . 2010 W. W. Norton & Company, Inc. 10 Economic Profit Suppose the firm is in a short-run circumstance in which Its short-run production function is The firms fixed cost is and its profit function is y f x x = ( , ~ ). 1 2 = - - py w x w x 1 1 2 2 ~ . x x 2 2 ~ . FC w x = 2 2 ~ 2010 W. W. Norton & Company, Inc. 11 Short-Run Iso-Profit Lines A $ iso-profit line contains all the production plans that provide a profit level $ . A $ iso-profit lines equation is - - py w x w x 1 1 2 2 ~ . 2010 W. W. Norton & Company, Inc. 12 Short-Run Iso-Profit Lines A $ iso-profit line contains all the production plans that yield a profit level of $ . The equation of a $ iso-profit line is I.e. - - py w x w x 1 1 2 2 ~ . y w p x w x p = + + 1 1 2 2 ~ . 2010 W. W. Norton & Company, Inc....
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V19 - 2010 W. W. Norton & Company, Inc. 19...

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