Slutsky theorem -mathematical presentation, Microeconomics

Slutsky Theorem - Mathematical Presentation:

We already know from the first order conditions of utility Maximisation that,  

2037_Slutsky Theorem -Mathematical Presentation.png

where Dij is the co-factor of the ith row and jth column of the determinant |D|. For income effect we know dp1=dp2=0, therefore we have from equation (h),  

432_Slutsky Theorem -Mathematical Presentation1.png

Now for own price effect we have dM=dp2=0. So from equation (h) we get,  

522_Slutsky Theorem -Mathematical Presentation2.png

Lastly, to find out own substitution effect we consider utility is constant in terms of income so, -dM+x1dp1+x2dp2=0 and dp2=0. We have from equation  

1507_Slutsky Theorem -Mathematical Presentation3.png

Posted Date: 10/26/2012 3:16:37 AM | Location : United States

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