Consider a two period model in which an individual has lifetime utility, u(c1, c2) =v(c1) +v(c2). with the period expected utility functionv(c) strictly increasing and strictly concave.

(a) Suppose that period 1 income ism1= 10 with period 2 income m2= 0 and that the individual may save out of period 1 income (at interest rate 0) for second period consumption. Write down the first order condition that identifiesc', the optimal level of consumption in period 1 and use it to show that optimal consumption is constant over time.