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Slutsky Theorem - Mathematical Presentation:
We already know from the first order conditions of utility Maximisation that,
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),
Now for own price effect we have dM=dp2=0. So from equation (h) we get,
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
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