1. Economic Efficiency in the Two-Period Consumption-Leisure Model (from Chapter 18). Recall the twp-period consumption-leisure model (from chapter 5). Suppose the representative individual's lifetime utility (two-period) function is given by u(c1,1n1)+u(c2,1n2). The period- 1 resource constraint of the economy is c1+k2(1)k1=f(k1,n1), and the period-2 resource constraint is c2+k3(1)k2=f(k2,n2). Note here that the production function depends on both capital and labor; the rest of the timing of events and notation are as in chapter 18. (a) Combine the period-1 and period-2 resource constraints into a lifetime resource constraint for the economy. (b) Using the lifetime resource constraint you derived in (a), set up a lifetime Lagrangian for the Social Planner's problem in this two-period economy and characterize the economically-efficient choices of consumption and labor (leisure) in each of the two periods - i.e., derive the FOCs of the Social Planner's problem that describe the economically-efficient choices of c1,c2,n1, and n2, and combine them into appropriate optimality conditions. (Hint: you should obtain two consumption-leisure optimality conditions, and one consumption-savings optimality condition here.)