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Ellsberg paradox and expected utility theory

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Important Note: Please try to use mathematical notation as much as you can to demonstrate your answer, but don't forget to carefully define each step you make.

Question

(a) What is expected utility theory?
(b) On what assumptions is the theory based, and how plausible are these assumptions?
(c) Explain the Ellsberg paradox?
(d) Do such paradoxes imply we should abandon the theory?

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Solution Summary

Assumptions of expected utility theory and challenges to it.

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Expected utility theory is a means of analyzing choices under uncertainty. Utility is a quantitative measure of the value of an outcome to a decision-makers. All decision makers want to maximize their relative utility, and will choose the outcomes that do so. However, this is not straight-forward with outcomes are not guaranteed. While normally a decision maker can choose the least expensive bundle to maximize his utility, under uncertainty he must choose the most desirable alternative. Since his final utility comes from the outcome of the alternative's different possible values, we build a model based not on the value of the goods themselves but on the values of these different alternatives. A decision maker may then choose a less desirable outcome with a higher probability of occurring. There are three steps to finding expected utility:
1. Assign numerical weights to various outcomes.
2. Linearly weight outcomes according to their probability.
3. Choose whatever gamble has the highest linearly weight outcome.

We use the equation U x P to ...

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