A representative household maximizes. where . BlogC1+i) j=0 Ct+j+kt+j (3) (4) Note that the second term of the right-hand side of the equation is expressed by not Kt+j-1 but Kt+j-2. In other words, the household receives returns from saving after two periods. 1. Define Lagrangian. (a) What are the variables that are optimized or control variables? (b) Derive the first-order condition(s). (c) Derive the Euler equation with respect to consumption.