Recall the two-period consumption - leisure model (chapter 5). Suppose that the representative consumer's lifetime utility (two -period) function is given by V(c 1,1- n'l ) +[3V(c2 ,1- n2 ), where ct is consumption in period t, nt is labor in period t, and thus 1- nt is leisure in period t. The period-1 resource constraint of the economy is c'l + k2 - (1- 5 ) kl = f(k1,n'l ) , and the period-2 resource constraint is c2 + k3 + (1- 6 )k2 = f (k2 ,n2 ) . Note here that the production function depends on both capital and labor, the rest of the timing of events and notations are as in chapter '18. a. Combine the period-1 resource constraint and period-2 resource constraint into a lifetime resource constraint for the economy. (Hint: If you need to recall how to combine period-by-period constraints into a lifetime constraint, refer back to chapter 3.) b. Using the lifetime resource constraint you derived in part a, set up a lifetime Lagrangian for the Social Planner's p roblem in this two-period economy and characterize the economically efcient choices of consumption and labor (leisure) in each of the two periods that is, derive the rst-order conditions of the Social Planner's problem that describes the economical] y efcient choices of c 1, c2, n'l , and n2 and combine them into appropriate optimality conditions. (Hint: You should obtain two consumption - leisure optimality conditions and one consumption - savings condition here. Note that you won't be able to solve for these objects, though, because you are not given a utility functio n