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Slutsky identity is given by: ∆x/∆p = (∆x/∆p)|substitution effect + (∆x/∆p)|income effect Now we know ∆m= x*∆p => ∆p=∆m/x Therefore, ∆x/∆p = (∆x/∆p)|substitution effect + (x*(∆x/∆m))|income effect But in HAL Varian's book there's minus sign in front of income effect. I am not being able to figure out how the minus sign came there. I think of income effect as total effect minus substitution effect.

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    $\begingroup$ Perhaps your definition of income effect is wrong. Could you please include the definition in your question? $\endgroup$
    – Giskard
    Nov 14, 2017 at 8:28
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    $\begingroup$ Have you looked at the Wikipedia entry for Slutsky equation? By the way, please use Mathjax to format your equations. Currently they are very hard to decipher. $\endgroup$
    – Herr K.
    Nov 16, 2017 at 4:32

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Intuitively, if the price of a particular good in a basket rises, then the individual can no longer afford to buy the same overall basket of goods

If there were no substitution effect, then this would be likely to result in amounts of each of the goods being bought being reduced, even those whose price had not changed, since the overall effect would be similar to a real reduction in income. Since the impact is negative, the equation needs a negative sign for this income effect

In general there will be a negative income effect on all goods and a positive substitution effect on all goods apart from the one whose price has increased. Which is dominant for a particular good may depend on the particular situation

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  • $\begingroup$ If we consider only the good whose price has changed then the substitution effect will always be negative. What about income effect? $\endgroup$ Nov 16, 2017 at 3:55
  • $\begingroup$ In order to analyse substitution effect we change the income so the initial bundle is just affordable at New prices. That change in income is given by ∆m= x1*∆p. Am I right? $\endgroup$ Nov 16, 2017 at 4:02

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