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

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?

• 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. – Stan Shunpike Apr 23 '15 at 1:54
• 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? – Stan Shunpike Apr 23 '15 at 1:57