Guy reveals the following piece of information regarding his preferences for ris

Question

Guy reveals the following piece of information regarding his preferences for risky prospects with prizes of $20, $12, and $0. He is indifferent between (0,1, 0: 20, 12, 0) and (0.7, 0, 0.3: 20, 12, 0)

[(a)]* Explain in words the meaning of this preference statement

[(b)]* Assuming that Guy satisfies the expecte utility assumptions, find a utility function that represents Guy's preferences for prospects with these three prizes

[(c)]* Is Guy risk-adverse, risk-neutral, or risk-inclined?

[(d)]* Compute Guy's expected utlity for the following prospects:
Prospect A (0.6, 0, 0.4: 20,12, 0)
Prospect B (0.4,0.2, 0.4: 20, 12, 0)

Prospect C (0, 1, 0: 20, 12 ,0)
Prospect D (0.3, 0.4, 0.3: 20, 12, 0)
Prosepct E (0.5, 0.2, 0.3: 20, 12, 0)

[(e)]* What is Guy's preference ordering for these prospects?

Explanation / Answer

(0,1, 0: 20, 12, 0) and (0.7, 0, 0.3: 20, 12, 0) means that he is indifferent between 1) $12 with probablility 1( i.e certain ) and $20 with 0.7 probability and 0 with 0.3 probability

U() = 0.5*1*$20 + 0.5*(0.7*$20 + 0.3*0)

The guy is risk averse as he prefers lesser denomination of the lottery with certainty rather than preferring the higher denomination.

U(a) = 0.6*20 + 0.4*0 = 12

U(b) = 0.4*20 + 0.2*12 + 0.4*0 = 10.4

U(c) = 1*$12 = 12

U(d) = 0.3*20 + 0.4*12 + 0.3*0 = 10.8

U(e) = 0.5*20 + 0.3*12 + 0.2*0 = 13.6

preference order of these prospects

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