Varian_Chapter19_Profit_Maximization

Varian_Chapter19_Profit_Maximization - Chapter Nineteen...

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Chapter Nineteen Profit-Maximization
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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.
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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.
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Economic Profit ± The economic profit generated by the production plan (x 1 ,…,x m ,y 1 ,…,y n ) is Π = Π= + + py p y w x w x nn m m 11 LL .
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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.
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Economic Profit ± How do we value a firm? ± Suppose the firm’s stream of periodic economic profits is Π 0 , Π 1 , Π 2 , … and r is the rate of interest. ± Then the present-value of the firm’s economic profit stream is PV r r =+ + + + + Π Π Π 0 12 2 1 1 () L
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Economic Profit ± A competitive firm seeks to maximize its present-value. ± How?
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Economic Profit ± Suppose the firm is in a short-run circumstance in which ± Its short-run production function is yf x x = (, ~ ). 12 xx 22 ~ .
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Economic Profit ± Suppose the firm is in a short-run circumstance in which ± Its short-run production function is ± The firm’s fixed cost is and its profit function is yf x x = (, ~ ). 12 Π = py w x 11 2 2 ~ . xx 22 ~ . FC = ~
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Short-Run Iso-Profit Lines ± A $ Π iso-profit line contains all the production plans that provide a profit level $ Π . ± A $ Π iso-profit line’s equation is Π≡ py w x 11 2 2 ~ .
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Short-Run Iso-Profit Lines ± A $ Π iso-profit line contains all the production plans that yield a profit level of $ Π . ± The equation of a $ Π iso-profit line is ± I.e. Π≡ py w x 11 2 2 ~ . y w p x wx p =+ + 1 1 22 Π ~ .
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Short-Run Iso-Profit Lines y w p x wx p =+ + 1 1 22 Π ~ has a slope of + w p 1 and a vertical intercept of Π + p ~ .
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Short-Run Iso-Profit Lines Π Π Π Π ′′ Π Π ′′′ I n c r e a s i g p ro f t y x 1 Slopes w p =+ 1
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Short-Run Profit-Maximization ± The firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the firm’s constraint on choices of production plans. ± Q: What is this constraint?
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Short-Run Profit-Maximization ± The firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the firm’s constraint on choices of production plans. ± Q: What is this constraint? ± A: The production function.
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Short-Run Profit-Maximization x 1 Technically inefficient plans y The short-run production function and technology set for xx 22 ~ .
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Varian_Chapter19_Profit_Maximization - Chapter Nineteen...

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