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:

Psychoanalytic Approach

A theory and method of psychological treatment developed by Sigmund Freud that emphasizes unconscious processes and childhood experiences in understanding and treating psychopathology.

Medical Degree

A qualification awarded to students who have successfully completed a course of study in medicine, qualifying them to work as a physician or surgeon.

Free Association

A psychoanalytic technique where patients are encouraged to verbalize any thoughts that come to mind without censorship.

Spontaneously Express

The act of showing emotions, thoughts, or actions naturally and without premeditation.