An individual lives for two periods with certainty, and for a third period with probability 50 percent. He finds out at the end of period one (after he has done his consumption) whether he will die at the end of period two or at the end of period three. He has earnings of one unit in the first period, and no labor income thereafter. His instantaneous utility function is \( u(c_t) = \ln(c_t) \). He can borrow or lend at an interest rate of zero, and has a time discount rate of zero.