Suppose, in the graphs to the right, we examine some consumer's choice of potatoes (P) and all other goods (O). On the original budget constraint she consumes PO potatoes. An increase in price moves her to the new budget constraint on which she purchases PN potatoes, a quantity larger than PO. This is very strange because this means that her demand curve for potatoes is actually upward sloping. We ruled out upward sloping demand early on but let's consider this possibility now.

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