1. Consider the situation of an individual with income in the current period of $3,000. Next period the individual faces unemployment risk, so that income will be $3,000 if still employed, but it can also be 0 if the individual becomes unemployed. The probability of becoming unemployed is 13%. Assume that there are two securities, one which guarantees the payment only if employed and the other which guarantees the payment only if unemployed in the next period. Two securities can be traded with a risk-free bond which yields 4% rate of return for sure. The preference of the individual is U(C1,C2u,C2e)=lnC1+0.9{plnC2u+(1p)lnC2e} in which p is the probability of unemployment. Construct the utility maximization problem and find out how much the total saving is. (Hint: total saving = sum of all securities purchased)