Macroeconomics Exam Review 158

Macroeconomics Exam Review 158 - 3.176 Let be the...

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Unformatted text preview: 3.176 Let be the production function. If is homothetic, there exists (Exercise 3.175) a linearly homogeneous function and strictly increasing function such that = . ( w , ) = min x { w x : ( x ) } = min x { w x : ( ( x )) } = min x { w x : ( x ) 1 ( ) } = 1 ( ) ( w , 1) by Exercise 3.166. 3.177 Let : be positive, strictly increasing, homothetic and quasiconcave. By Exercise 3.175, there exists a linearly homogeneous function : and strictly increasing function ( ) such that = . = 1 is positive, quasiconcave (Exercise 3.148) and homogeneous of degree one. By Proposition 3.12, is concave and therefore = is concavifiable. 3.178 Since ( ) is a supporting hyperplane to at x , then ( x ) = and either ( x )...
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This note was uploaded on 01/16/2012 for the course ECO 2024 taught by Professor Dr.dumond during the Fall '10 term at FSU.

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