A representative household maximizes where E ) 3 [log(C++ j 0Ct+j_1) Xht+j], j=0 Ct+j + Kt+j = Wt+jht+j+rt+jKt+j1+It+j T. 1. Discuss economic intuitions behind the term with 0. 2. Define Lagrangian. 3. What are the variables that are optimized or control variables? 4. Derive the first-order condition(s). 5. Derive 6. Discuss (a) the labor supply condition; and (b) the Euler equation with respect to consumption. (a) how the past consumption influences today's consumption; (b) how the real interest rate influences today's consumption. (c) how the real wage influences labor supply. (1) (2)