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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.
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.
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