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Starting from the initial consumption bundle, first the substitution effect is calculated, then the income effect. Why not the other way around?

My guess would be, because with increasing utility the shape of the utility level curve might change, the substitute effect would differ not just proportionally, while there is no such problem with income effect. However, I don't see why the initial utility level curve is preferred to the new one.

One could argue, that the initial utility curve is unrepresentative, because it doesn't represent the current situation.

Nick The Dick
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  • Hi! It seems to me that in case of Slutsky (or Hicks) decomposition, what you actually calculate are three consumption bundles. The pre price change choice $(A)$, the post price change choice $(C)$, and the income compensated choice given the new price $(B)$. Once you have these three bundles, you can freely calculate the income $(x_1^C - x_1^B)$ and substitution $(x_1^B - x_1^A)$ effects in the order you want? Do I misunderstand your question? – Giskard Dec 17 '21 at 17:01
  • Hey! I was talking about taking point B as the choice with the old price and the income adjusted (reduced if prices rise) so as to be on the new indifference curve. But as you put it this way, income compensated sounds to have a better meaning – Nick The Dick Dec 18 '21 at 07:43
  • Okay, but is anything stopping you from calculating $x_1^B - x_1^A$ before calculating $x_1^C - x_1^B$? – Giskard Dec 18 '21 at 09:28

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That's actually just a convention. While these two methods to partition the total effect lead to different results for any discrete price change, they coincide in the limit of an infinitesimal price change.

VARulle
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  • Are you writing about Slutsky decomposition here? If yes, what two methods? I seem to have lost the thread. – Giskard Dec 17 '21 at 15:25
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    @Giskard, I was actually referring to this problem https://economics.stackexchange.com/questions/417/ambiguous-definition-of-substitution-and-income-effect – VARulle Dec 20 '21 at 08:43