The Certainty Equivalent of a Gamble Is Defined to Be

question 2

Essay

The certainty equivalent of a gamble is defined to be the amount of money which, if you were promised it with certainty, would be indifferent to the gamble.
a.If an expected utility maximizer has a von Neuman-Morgenstern utility function U(W)= W^1/2 (where W is wealth)and if the probability of events 1 and 2 are both 1/2, write a formula for the certainty equivalent of a gamble that gives you x if event 1 happens and y if event 2 happens.
b.Generalize your formula in part (a)to the case where the probability of event 1 is p and the probability of event 2 is 1 - p.
c.Generalize the formula in part (a)to the case where U(W)= W ^a for a > 0.

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Definitions:

Profit Margins

An indicator of a company's financial health, calculated as the difference between revenue and expenses in relation to revenue.

Employee Benefits

Compensation in forms other than cash.

Nonunion Operations

Workplaces or businesses that do not have their employees represented by a labor union or similar worker's association.

Turnover

The rate at which employees leave a company and are replaced by new employees over a given period.