In the risk-trading example in Section 1, you had a risky
income that was $160,000 with good luck (probability 0.5) and $40,000 with bad
luck (probability 0.5). When your neighbor had a sure income of $100,000, we
derived a scheme in which you could eliminate all of your risk while raising
his expected utility slightly. Assume that the utility of each of you is still
the square root of the respective income. Now, however, let the probability of
good luck be 0.6. Consider a contract that leaves you with exactly $100,000
when you have bad luck. Let x be the payment that you make to your neighbor
when you have good luck.
(a) What is the minimum value of x (to the nearest penny)
such that your neighbor slightly prefers to enter into this kind of contract
rather than no contract at all?
(b) What is the maximum value of x (to the nearest penny)
for which this kind of contract gives you a slightly higher expected utility
than no contract at all?