Suppose there are two states with probability and 1 . Consider the following utility functions for consumption (c1,c2) in the two states.

2.Suppose there are two states with probability π and 1 − π. Consider the following utility functions for consumption (c1,c2) in the two states.

Ua(c1, c2) =πlog (c1) + (1 - π) √c2Ub(c1, c2) =π log (c1) + (1 - π)log(c2) Uc(c1,c2) =π^2 log (c1) + (1 - π) log(c2)Ud(c1,c2) = π√c1 +(1−π)√c2 

If Rob, the consumer, satisfies the expected utility hypothesis, then neither the utility function nor the function could represent his preferences.

1. (A)  Ub, Uc
2. (B)  Ua, Uc
3. (C)  Ua, Ub
4. (D)  Ud, Ub
5. (E)  None of the above.

3. Consider three assets A, B and C whose payoffs in the in the two states ω1 and ω2 are shown below. Only two of these three assets are traded in a certain market.

          A         B        C

ω1    78      87        66                

ω2     39      35        33

Markets are not complete if asset ____and asset___  are traded.

1. (A)  A,B
2. (B)  A,C
3. (C)  B,C
4. (D)  Markets are incomplete for more than one of the above combinations
5. (E)  Not enough information is supplied to conclude any of the above.