Party A and party B are trying to split $100. Based on their beliefs, if they go to an arbitrator, there is a 50% chance that the arbitrator will allocate $10 to party A and $90 to party B, and another 50% chance that the arbitrator will allocate $90 to party A and $10 to party B. Both parties have a utility function of U(x) = 10x , where x is income allocation.

(1) (2 points) What is party A's expected income allocation from arbitration? What is party B's expected income allocation from arbitration?

(2) (2 points) What is party A's expected utility from arbitration? What is party B's expected utility from arbitration?

(3) (4 points) Now, instead of going to an arbitrator, party A and party B are trying to come to an agreement on their own. What is the range of income allocation that party A would agree to? What is the range of income allocation that party B would agree to?

(4) (2 points) What is the contract zone?

(5) (10 points) What is the contract zone if both parties believe that the arbitrator will allocate

$30 to party A and $70 to party B with a probability of 0.5 and $70 to party A and $30 to party B with a probability of 0.5? Is the contract zone bigger or smaller now? Why?