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What is the difference between an inferior good and a Giffen good? Are the two following definitions for an inferior good equivalent?

Def 1: An inferior good is a good for which the demand decreases after a decrease of its price.

Def 2: An inferior good is a good for which the income effect leads to a decrease of demand after a relative decrease of its price.

A Giffen good (1) is when after a decrease in price of good (1) the demand for (1) decreases but the demand of some other good (2) increases.

Or is Def 1 just the definition of a Giffen good, which is a special type of inferior good ?

For a Giffen good the Income Effect is strong enough to outweigh the Substitution Effect... But isn't it also the case for all inferior goods? The change in their demand is going to be negative (we consume less after the decrese in price) and that change is equal to the sum of SE and IE, so we also get that Income Effect is strong enough to outweigh the Substitution Effect.

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  • $\begingroup$ As currently written, your "Def 1" defines a Giffen good, not an inferior good. Your "Def 2" is incorrect. A Giffen good is a special type of inferior good. $\endgroup$ – Matthew Gunn Nov 3 '18 at 16:12
  • $\begingroup$ So how do you define an inferior good? Your comment isn’t very helpful, for instance you don’t have to repeat that a Giffen good is a special type of inferior good. That’s my question. Why isn’t every inferior good not a Giffen good. What are particularities of Giffen goods that are absent in inferior goods? $\endgroup$ – John Nov 3 '18 at 16:21
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    $\begingroup$ Let $x_i(\mathbf{p}, w)$ denote the demand for good $i$ at price vector $\mathbf{p} = \begin{bmatrix} p_1 \\ \ldots \\p_k\end{bmatrix}$ and income $w$. A good is called inferior if you purchase less as your income increases: $\frac{\partial x_i(\mathbf{p}, w)}{\partial w} < 0$. A good is called normal if you purchase more as your income increases: $\frac{\partial x_i(\mathbf{p},w)}{\partial w} > 0$. A good is called a Giffen good if you purchase more as its own price $p_i$ increases. $\frac{\partial x_i(\mathbf{p},w)}{\partial p_i} > 0$. For a Giffen good, demand is upward sloping. $\endgroup$ – Matthew Gunn Nov 3 '18 at 23:58
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It's not always the case that the income effect will outweigh the substitution effect. The ones that outweigh the substitution effect are the Giffen goods. The ones that don't are just plain inferior goods.

Example: Suppose you are on a low nutrious diet because you earn less and can't afford other items. Now your income increases the demand for your current good decreases. These low nutritional products are your inferior goods.

Now, take the case where the price increases for the low nutrious dietary items, but your demand will decrease like any other usual good but will not increase.

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