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12. Profit Max

# 12. Profit Max - Profit Maximization Professor John Diamond...

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1 Profit Maximization Professor John Diamond ECON 370: Microeconomic Theory Lecture 12

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2 Economic Profit: Introduction A “multi - product” firm uses inputs j = 1…,m to make products i = 1,…n Output levels are y 1 ,…,y n Input levels are x ,…,x m Product prices are p ,…,p Input prices are w ,…,w
3 The Competitive Firm: Constants Perfectly competitive firm takes all output prices p 1 ,…,p n as given takes all input prices w 1 ,…,w m as given Note: perfectly competitive firm does not “compete” directly with its competitors gets all information through prices

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4 Economic Profit: Profit Formula Economic profit Can calculate for each production plan (x 1 ,…, x m ,y ,…, y n ) Equals revenues minus input costs Input costs must measure true opportunity costs m x w y p 1 1 1 1
5 Economic Profit: Flows Output and input levels are typically flows x 1 may be labor units used per day 2 may be capital services used per day y 3 may be cars produced per day Profit is typically also a flow dollars of profit earned per day

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6 Economic Profit and Value of a Firm To calculate value of a firm Let economic profits be Let r be the rate of interest Present-value of economic profit stream is Competitive firms act to maximize value PV r r 0 1 2 2 1 1 ( )
7 SR production function Maximizing SR Profit: Two Factor Case Firm is in SR situation ) ~ , ( 2 1 x f y 2 2 1 1 ~ w py 2 2 ~ 2 2 ~ FC Fixed cost is Profit function is F.O.C.: 1 1 1 11 0* y p w p MP w xx

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8 Short-Run Iso-Profit Lines: Introduction Iso-profit line All production plans providing profit level Equation is Or, so slope = w/p1 and intercept = 2 2 1 1 ~ x w py p y 2 2 1 1 ~ p x w / ) ~ ( 2 2
9 Short-Run Iso-Profit Lines: Graph y x 1 1 w Slopes p

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10 Short-Run Profit-Maximization The SR Profit Max Problem Choose production plan to maximize profits Given a production function SR: Choice variable is variable input x 1
11 Short-Run Profit-Maximization: Graph x 1 Technically inefficient plans y SR production function, technology set for 2 2 ~ x y f x x ( , ~ ) 1 2

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12 Short-Run Profit-Maximization: Graph x 1 p w Slopes 1 y y f x x ( , ~ ) 1 2
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12. Profit Max - Profit Maximization Professor John Diamond...

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