Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand

Abstract

We formalize the Marshallian idea that when the proportion of income spent on any commodity is small then the income effects are small. If n is the number of goods, we show, under certain assumptions on preferences and prices, that the order of magnitude of the norm of the income derivative of demand is 1/√n. As a corollary we get that for the case of a single price change the percentage error in approximating the Hicksian Deadweight Loss by its Marshallian counterpart goes to zero at least at the rate 1/√n and that demand is downward sloping for n large enough.

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