Asked by Harry Singh on Apr 26, 2024
Verified
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) W1/2 (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.
Certainty Equivalent
The guaranteed amount of money that an individual would view as equally desirable to a risky gamble.
Probability
A measure of the likelihood of a certain event or outcome, expressed as a number between 0 and 1.
- Describe the principle of certainty equivalent and its connection to perspectives on risk.
Verified Answer
OL
Octavio LimpiasApr 29, 2024
Final Answer :
a.The certainty equivalent is (1/2x1/2 1/2y1/2)2
b.[px1/2 (1 p)y1/2]2
c.(1/2xa 1/2ya)1/a
b.[px1/2 (1 p)y1/2]2
c.(1/2xa 1/2ya)1/a
Learning Objectives
- Describe the principle of certainty equivalent and its connection to perspectives on risk.