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 P_O potatoes. An increase in price moves her to the new budget constraint on which she purchases P_N potatoes, a quantity larger than P_O. 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.