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Unformatted text preview: “A thing is worth what it can do for you, not what you choose to pay for it.” –J ohn Ruskin ECON 410 CostMinimization (Graphical) 2 Class 17  Cost Minimization (Graphical) 3 CobbDouglas Utility Function One of the most commonly used functions in economics. When used as a utility function, it represents monotonic, convex, continuous, complete, transitive preferences. It has the property that at low levels of each good, they are complementary. At high levels of each good, they are more substitutable. Class 17  Cost Minimization (Graphical) 1 1 2 1 2 , ) ,0 1 ( x U x x x α α α = < < 4 CobbDouglas Production Function One of the most commonly used functions in economics. When used as a production function, it represents production processes with the possibility of inaction, free disposal, and a range of convexity/returns to scale properties depending on the parameter values. , ) ( f L K L aK α β = Class 17  Cost Minimization (Graphical) and do NOT have to sum to 1 5 CobbDouglas Production Function One of the most commonly used functions in economics. When used as a production function, it represents production processes with the possibility of inaction, free disposal, and a range of convexity/returns to scale properties depending on the parameter values. If +<1, the production set is strictly convex If +>1, the production set is not convex , ) ( f L K L aK α β = Class 17  Cost Minimization (Graphical) 6 Perfect Complements: Perfect Complements are goods that a consumer is interested in consuming only in fixed proportions. Class 17  Cost Minimization (Graphical) 1 2 1 2 , ) mi , ( n( ) x ax x bx U = 7 Leontief Production Function A Leontief Production Function, or a fixed proportions production function, represents a production process in which the factors of production are used in fixed (technologically predetermined) proportions. , ) min( , ( ) L a f K K bL = Class 17  Cost Minimization (Graphical) 8 Perfect Substitutes: Perfect S ubstitutes are goods that a consumer is indifferent as to which to consume. She only cares about the total amount consumed. Class 17  Cost Minimization (Graphical) 1 2 1 2 , ) ( x x U ax x b = + 9 Linear Production Function A Linear Production Function represents a production process in which the factors of production are perfect substitutes. , ) ( K L b f aK L = + Class 17  Cost Minimization (Graphical) 10 Constant Elasticity (CES) Utility Function A chameleon function that can “mimic” other utility functions. Class 17  Cost Minimization (Graphical) 1 1 2 1 1 2 2 , ) [ ] ( x x x U x ρ ρ ρ α α = + If =1, it is a perfect substitute utility function As 0, it becomes a CobbDouglas utility function As , it becomes a perfect complement utility function 11 Constant Elasticity (CES) Production Function A chameleon function that can “mimic” other production functions....
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This note was uploaded on 01/05/2012 for the course ECON 410 taught by Professor Codrin during the Fall '07 term at UNC.
 Fall '07
 Codrin
 Utility

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