A student is shown four envelopes. Envelope A contains $2,000; envelopes B, C and D contain uncertain amounts of money but with the following probabilities: Envelope B -- $5,000 with a 10 percent probability, $2,000 with an 88 percent probability, and $100 with a two percent probability. Envelope C -- $2,000 with a 12 percent probability and $100 with an 88 percent probability. Envelope D -- $5,000 with a 10 percent probability and $100 with a 90 percent probability.
(a) What is the Expected Monetary Value (EMV) of envelope B?
(b) You are told that of the four envelopes, the student assigns the highest expected utility to envelope A.
TRUE or FALSE:
(i) The student’s preference for envelope A over envelope B is consistent with the student being Risk Averse.
(ii) The student’s preference for envelope A over envelope B is consistent with the student being Risk Neutral.
(c) Assuming the marginal utility of money is greater than zero, show mathematically that if envelope A has a higher expected utility than envelope B, then it must also be true that envelope C has a higher expected utility than envelope D.