Question Consider households problem. Households live for two periods and have preferences u(c) =-e-KC, where K>0. Discount factor is denoted by B. Initially, households own their assets aj. Then, households are working at an investment bank that pays $100,000 to consume cy and save a2. This job has generous raises, so their salary increases with the rate of interest. That is, their salary is $100,000x(1+r) in the second period and they consume c2. (a) Find the optimal allocation of {C1,C2,a2}. The next two questions consider a different problem. The basic setting is the same as above. However, the exact amount of their salary is uncertain in the second period depending upon their health status. More concretely, if they are in good health status H, they work more and get an additional salary $10,000. So, their salary in the second period becomes $100,000x(1 + r) +$10,000. On the other hand, if they are in bad health status, they work less and lose $10,000. The probability of good health status is . Let c and c denote consumption in the second period when they are in good health status and bad health status, respectively. Assume that B(1+r) = 1 for the rest of the problem. Answer following questions. (b) Set up the household problem and derive the optimal conditions. (c) Are i) consumption in the first period, ii) saving in the first period, iii) consumption when households are good health status and iv) consumption when households are bad health status lower or higher than the case without uncertainty (i.e. (a))