Macroeconomics Exam Review 206

Macroeconomics Exam Review 206 - The function is the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The function is the composition of with and , ( x , y ) = ( ( x ) , ( y )) By the chain rule, the derivative of is [ x , y ] = [ 1 , z 2 ] ( [ x ] , [ x ] ) = ( z 1 , [ y ]) + ( [ x ] , z 2 ) = [ x ] [ y ]) + ( y ) [ x ] where z 1 = ( x ) and z 2 = ( y ). 4.25 For = 1, ( ) = is linear and therefore (Exercise 4.6) [ ] = 1 ( [ ]( ) = ). For = 2, let ( ) = so that ( ) = 2 = ( ) ( ). Using the product rule [ x ] = ( ) ( ) + ( ) ( ) = 2 Now assume it is true for − 1 and let ( ) = − 1 , so that ( x ) = ( ). By the product rule [ x ] = [ ] + ( )1 By assumption [...
View Full Document

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.

Ask a homework question - tutors are online