New Insights into the Theory of Giffen Goods pp 161-171
Lotteries and the Law of Demand
In economies with nonconvexities consumers can increase their expected utility by consuming lotteries. Lotteries are probability distributions over bundles in the consumption set. Standard revealed preference logic can be applied to choices in lottery space, however the implications are not readily interpretable. In this paper, we formulate the law of demand for lottery economies in terms of commodity price changes and changes in demand for commodities. The finding is that the standard expression of the compensated law of demand necessarily holds in expectation only.
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