Consider a two-period model where a household chooses consumption Ct and Ct+1, and savings St, given the endowment Yt and Yt+1 and interest rate r to maximize following lifetime utility U=u(Ct)+u(C_t+1) with u(C)=-(1/a)exp(-aC), (0,1), a>0

1. Show that the utility function u(C) features a positive marginal utility and a diminishing marginal utility.
2. Write down the household problem for finding the optimal C_t andC_t+1. Derive the first-order conditions.
3. Then solve for C_t as a function of Y_t, Y_t+1, r (and, of course, the parameters). Using the result and the lifetime budget constraint, verify that C_t=C_t+1 if(1+r)=1.