Even without a formal assessment process, it often is possible to learn something about an individual’s utility function just through the preferences revealed by choice behavior. Two persons, A and B, 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 agree that the probability of rain tomorrow is 0.10,what can you say about their utility functions?
b. If they both agree that the probability of rain tomorrow is 0.30,what can you say 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.