Question

Even without a formal assessment process,it often is possible to learn something about an individual's utility function through the preferences revealed by choice behavior.Two persons A and B and make the following bet:A wins $40 if it rains tomorrow and B wins $10 if it does not rain tomorrow.

a)If they both agee that the probability of rain tomorrow is 0.10 .what can you tell about their utility functions?

b)If they both agree that the probability of rain tomorrow is 0.30 .what can you tell about their utility functions?

c)Given no information about their probabilities,is it possible that their utility functions could be identical?

d)If they both agree that the probability of rain tomorrow is 0.20 .Could both individuals be risk averse?Is it possible that their utility functions could be identical?Explain

a)If both

Answer 1

a. If both the probability of rain tomorrow is 0.10, the expected gain for A = 0.1*40 =$4 and for B=0.9*10 =$9. The rationale is that B is going to make more money than A .. B is risk averse and make more gain.

b. Here, the gain for A =0.3*40 = $12 and B =0.7*10 =$7. Here also B is more risk averse, but makes a lower gain. A takes higher risk and makes higher gain

c.Here, the gain for A =0.2*40 =$8 and for B =0.8*10 =$8 Since both are equally poised. Since the expected retrun of both are same, we can say both are equally risk averse.