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Choice Under Uncertainty

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(a) Explain what it means that a consumer has preferences over lotteries (in particular, define lotteries).

(b) Explain what it means that the preference relation has a utility function representation, and define the notion of a von Neumann-Morgenstern utility function.

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The solution explains what it means that a consumer has preferences over lotteries. It also defines lotteries.

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Please refer to the attachment.

(a) Explain what it means that a consumer has preferences over lotteries (in particular, define lotteries).

If a consumer has preferences over lotteries to a certain amount of income, the person is called risk-inclined.
A lottery is a game that offers two or more different outcomes with uncertainty. Each outcome in a lottery has a specific probability.

Let's define the expected value to be the weighted average of the possible outcomes (Xi), where the weights are the probabilities (Pr) of occurrence assigned to each outcome. That is,
EV = ∑PriXi

Expected utility is calculated in the same way as expected value, except that the utility associated with a payoff [U(X)] is ...

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