1 N onseparable utility A representative household enjoys utility from consumption and disutility from labor supply. He/she maximizes DC! E: Z 5j(03+j(1 Nt+j)\")1_ga (1) j=0 subject to the budget constraint: Ct+j + Bt+j = wi+th+j + +jBt+j1: (2) where Ct, wt, n, and N: represent consumption, the real wage, the rate of return (> 1), and labor supply in period t, respectively, and Bf represents riskless bond holdings at the end of period t. 1. Define Lagrangian. 2. What are the variables that are optimized or control variables? 3. Derive the rst-order condition(s) with respect to the above control variables in period t. 4. Derive the labor supply equation for N; using 03 and wt