Every worker lives for three periods and is born with zero assets. They are endowed with one unit of time in each period to be divided between labor and leisure. Workers have time- separable preferences over consumption and leisure, {ct, }-1, and a subjective time discount factor B. A young worker's optimization problem is written a follows: 3 max [ Bt-1al( Ct, It) (1) subject to: Ct + at+1 = Wt (1 - t) (1 - 1;) (2) C+1 + at+2 = We+1(1 - 7:+1)(1 - 4+1)+ Ri+10:+1 (3) Ct+2 = B *e+ Rt+20:+2 (4) e = Wt(1 - h) + we+1(1 - 4+1) (5) 2 where e denote the worker's average lifetime labor earnings and B is the replacement rate of a simple social security program (in the U.S. the average B is about 0.35). Assume the following utility function for the rest of the problem set: u(c, l) = 0In(c) + (1 - 0) In(1) 1. Write out all of the first-order conditions. 2. Solve for the following set of endogenous variables as a function of ONLY exogenous variables: {C1, C2, C3, a2, a3, l1, 12}