17_CostMinimization_Graphical_ToPost-1

17_CostMinimization_Graphical_ToPost-1 - A thing is worth...

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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 Cost-Minimization (Graphical) 2 Class 17 - Cost Minimization (Graphical) 3 Cobb-Douglas 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 - = < < 4 Cobb-Douglas 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 = Class 17 - Cost Minimization (Graphical) and do NOT have to sum to 1 5 Cobb-Douglas 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 = 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 pre-determined) 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 = + If =1, it is a perfect substitute utility function As 0, it becomes a Cobb-Douglas 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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17_CostMinimization_Graphical_ToPost-1 - A thing is worth...

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