2. [Real Business Cycle]. Consider a simple RBC model as below: Household's Utility function is u(c,1)=bc +(1b)1 + BE {bc+7 +(1b)1+} where = 0.2 Budget restriction period-t is 't+1 C+E C++1 1+1+1 wl +E W+1+1 1+1+1 a. (5 points) Set up an appropriate Lagrangian form! b. (8 points) From point (a), construct the firs-order condition with respect to c, dan C++! c. (7 points) From point (b), show intertemporal consumption optimal condition (Euler equation)! d. (10 points) Explain clearly the effect of technological shock (4) on representative households' decision when: (i) covariant is zero, (ii) covariant is bigger than zero, and (iii) covariant is smaller than zero! provide brief economic interpretation. (Note: economic interpretation does not mean restating verbally the mathematics).