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My professor said, in practice, Marshallian demand follows the law of demand (ie that increase in price decreases demand). But he said in theory, the Marshallian case is ambiguous and it does not follow the law of demand.

MY QUESTION:

Why isn't the Law of Demand true for Marshallian demand?

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Marshallian demand is also called uncompensated demand. That is a price changes and you see what changes in what the household buys. This consists of two effects.

  1. The good itself is more expensive
  2. The household is poorer because they can no longer afford their old consumption bundle.

The effect of (1) is always to make you consume less of the good. The effect of (2) is what is ambiguous. An inferior good is one where as you get richer (poorer) you consume less (more) of it. For an inferior good forces (1) and (2) oppose. You consume more of the good because you are poorer and less because it is more expensive. A good (check out Giffen goods) could be so powerfully inferior that the effect of (2) is bigger than the effect of (1). No one seems to be able to find evidence that they exist, but they certainly are possible. Often potatoes in Ireland are used as an example, though they were not.

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    $\begingroup$ economics.stackexchange.com/questions/131/what-are-giffen-goods had a "good" discussion, including the more convincing Jensen and Miller paper. $\endgroup$
    – dismalscience
    Apr 23, 2015 at 1:09
  • $\begingroup$ Thx for answering. Let me see if I understand. So in the Slutsky equation, the $$\frac{\partial x^H}{\partial p}$$ is negative. And so is the $$\frac{\partial x}{\partial I}x$$ in the case of an inferior good. But because that term is subtracted it is positive and if sufficiently large, will make $$\frac{\partial x}{\partial p}$$ positive violating the law of demand. Hence, Marshallian demand doesn't always follow the law of demand. $\endgroup$
    – Stan Shunpike
    Apr 23, 2015 at 1:54
  • $\begingroup$ Also, let me clarify: if we rewrite the Slutsky equation so as to have the Hicksian term by itself on one side, then $$\frac{\partial x}{\partial I}x$$ is the Hick's transfer (aka compensation) that moves us back to being able to consume the original bundle prior to the price increase. Is that all correct? $\endgroup$
    – Stan Shunpike
    Apr 23, 2015 at 1:57

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