# Utility Maximization and Giffen Goods

In the context of the usual utility maximization problem involving n (>2) goods, prove that not all goods can be Giffen and that a Giffen good must have at least one gross complement.

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First some background. Recall that when there are at least two goods, the demand of one may increase and the price of the other falls. This is a Giffen good. For example, if a consumer buys as much of a luxury good as they can afford, and satisfy their remaining needs with an ordinary good. They would prefer to use only the luxury good, but are constrained by their budget to use some of the ordinary good as well. If the price of the ordinary good falls, they can ...

#### Solution Summary

In the context of the usual utility maximization problem involving n (>2) goods, prove that not all goods can be Giffen and that a Giffen good must have at least one gross complement.