where we set & to be one (full depreciation). 1. S5Setthe maximization problem and Lagrangean equation. 2. Derive the intertemporal decision rule. Explain its economic meaning. 3. Derive the intratemporal decision rule. Explain its economic meaning. 4, Find the optimal comsumption. (You may need to \"guess and verify\". Dynamic Stochastic General Equilibrium Consider an economy populated by many identical households who maximize their life time utility: 00 Uo = Eo > S' In(ct - xit), (1) where c and nr are the consumption and labor at period f =, and / e (0, 1) is the discounting factor. In x is the natural log function, and its first derivative is 1/x. Also, the production takes place using capital and labor inputs (kr and n) to the following technology at time t: yt = atkin;-, (2) where yr and at denote the output and productivity (TFP). The productivity follows i.i.d. lognormal distribution: or - LN(-0.50', q'). Note that E[x*] = exp(ku + ko*/2) where x - LN (u, o'). The capital accumulation is kt+1 = it + (1 - 8)kt where we set & to be one (full depreciation). 1. Set the maximization problem and Lagrangean equation