Consider two identical fishermen with utility functions U(x)= x/2, where x is the number of fish caught. Assume that the probability of either fisherman catching a fish is .05 and that it is impossible for either of them to catch more than one fish. If the two fishermen decided to divide whatever catch was taken, the expected utility of each fisherman would be:
A)0.1.
B)less than 0.025.
C)greater than 0.025 and less than 0.1.
D)more than 0.1.

Question

Quizplus · Accepted Answer

Since the probability of either fisherman catching a fish is 0.05, the expected number of fish caught between the two of them is 0.05. 
If they decide to divide the catch equally, each fisherman will have an expected catch of 0.025 (half of 0.05). 
Using their utility function U(x)= x/2, the expected utility of each fisherman with a catch of 0.025 is 0.0125. 
Therefore, the expected utility of each fisherman if they divide the catch equally is greater than 0.025 (which is the utility they would get if they caught 1 fish alone) and less than 0.1 (which would be the utility they would get if they caught all 10 fish alone). Hence, the answer is C.

Consider Two Identical Fishermen with Utility Functions U(x)= X/2, Where