ECON102S08Note1

# ECON102S08Note1 - Econ 102 Macroeconomic Theory Session...

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Econ 102 Macroeconomic Theory Session Note-1 TA (Section: 1P): Daisuke Miyakawa April 1st. 2008 1. Key Properties of Cobb-Douglas production function I Suppose we have the following Cobb-Douglas production function: F ( K;L ) = AK L 1 where 0 1 and A is TFP (Technology parameter) I The production function has several basic properties: (i) This production function exhibits Constant Retunes to Scale property (i.e., F ( ±K;±L ) = ±F ( K;L ) where ± is a constant). F ( ±K;±L ) = A ( ±K ) ( ±L ) 1 = ± 1 K L 1 = ±AK L 1 = ±F ( K;L ) (ii) This production function exhibits Diminishing Marginal Productivity property with respect to K and L . @F ( K;L ) @K = 1 L 1 ) @ 2 F ( K;L ) @K 2 = (+) z}|{ ( 1) | {z } ( ) (+) z }| { AK 2 L 1 < 0 @F ( K;L ) @L = (1 ) AK L ) @ 2 F ( K;L ) @L 2 = (+) z }| { (1 )( ) | {z } ( ) (+) z }| { AK L 1 < 0 (iii) is the share of the capital (i.e., total rental payment divided by output). Recall that the real rental price of capital

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## This note was uploaded on 12/11/2009 for the course ECON 180364203 taught by Professor Edwardmcdevitt during the Spring '09 term at UCLA.

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ECON102S08Note1 - Econ 102 Macroeconomic Theory Session...

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