answer for cdef please

where e(u)=0+bu,>1 Production now satisfies y=kss(uke)eh1se. Take the first order condition with respect to u in the household problem. You can do this by modifying the Lagrangian above. How does u depend on q and the marginal product of capital equipment y/ke ? (Hint: the first order condition is static; you don't need to worry about multiple periods.) Provide intuition on the effects of an endogenous utilization rate on the transmission mechanism in the economy. Growth model with investment-specific productivity shocks. Consider the social planner formulation of the following stochastic growth model: V(ks,ke,q)c+is+iekskeclogq=c,h,is,iemaxlogc+(1)log(1h)+Eq[V(ke,ks,q)]s.t.=ksskeeh1se=(1s)ks+is=(1e)ke+qie0,is0,ie0=qlogq1+,N(0,q2) where c is consumption, h is labor supply, is is investment in structures and ie is investment in equipment. Here, the primes ' denote next-period value and the subscripts 1 denote past values. The non-negativity constraint on each type of investment means that machines cannot be removed once they are installed. System (1) is a recursive formulation. One can also write the problem as an infinite (b) Characterize the equilibrium of the economy. The equilibrium conditions involve a resource constraint, labor leisure tradeoff, and two (intertemporal) Euler equations. (Hint: take first order conditions with respect to ct,ht,ks,t+1 and ke,t+1 and rearrange. You can follow the logic of the real business model closely but now note that there are two types of investment). (c) Carefully interpret the equilibrium conditions, in particular the intertemporal condition with respect to investment in capital equipment. (d) Suppose there is a positive realization to t. Describe the transmission of the shock into the economy. Compare the transmission to that of a total factor productivity shock in the standard real business cycle model. (e) Write the steady-state conditions of the model. (Take the equilibrium conditions and remove the time indices. You can simplify by using the rate of time preference r=(1)/. The steady state can be written as a function of c,ke,ks and h alone, where output satisfies y=ksskeeh1se.) (f) Suppose equipment can be utilized at rate u. The law of motion for equipment is ke=(1e(u))ke+qie where e(u)=0+bu,>1 Production now satisfies y=kss(uke)eh1se. Take the first order condition with respect to u in the household problem. You can do this by modifying the Lagrangian above. How does u depend on q and the marginal product of capital equipment y/ke ? (Hint: the first order condition is static; you don't need to worry about multiple periods.) Provide intuition on the effects of an endogenous utilization rate on the transmission mechanism in the economy. Growth model with investment-specific productivity shocks. Consider the social planner formulation of the following stochastic growth model: V(ks,ke,q)c+is+iekskeclogq=c,h,is,iemaxlogc+(1)log(1h)+Eq[V(ke,ks,q)]s.t.=ksskeeh1se=(1s)ks+is=(1e)ke+qie0,is0,ie0=qlogq1+,N(0,q2) where c is consumption, h is labor supply, is is investment in structures and ie is investment in equipment. Here, the primes ' denote next-period value and the subscripts 1 denote past values. The non-negativity constraint on each type of investment means that machines cannot be removed once they are installed. System (1) is a recursive formulation. One can also write the problem as an infinite (b) Characterize the equilibrium of the economy. The equilibrium conditions involve a resource constraint, labor leisure tradeoff, and two (intertemporal) Euler equations. (Hint: take first order conditions with respect to ct,ht,ks,t+1 and ke,t+1 and rearrange. You can follow the logic of the real business model closely but now note that there are two types of investment). (c) Carefully interpret the equilibrium conditions, in particular the intertemporal condition with respect to investment in capital equipment. (d) Suppose there is a positive realization to t. Describe the transmission of the shock into the economy. Compare the transmission to that of a total factor productivity shock in the standard real business cycle model. (e) Write the steady-state conditions of the model. (Take the equilibrium conditions and remove the time indices. You can simplify by using the rate of time preference r=(1)/. The steady state can be written as a function of c,ke,ks and h alone, where output satisfies y=ksskeeh1se.) (f) Suppose equipment can be utilized at rate u. The law of motion for equipment is ke=(1e(u))ke+qie