Question

Let’s consider an alternative version of the social planner’s problem in which the planner also chooses Mt, in addition to Ct,Ct+1, and Kt+1. subject to max U = u(Ct) + v(Mt ) + βu(Ct+1) Ct ,Ct+1 ,Kt+1 ,Mt Pt Ct +Kt+1 −(1−δ)Kt +Gt =AtF(Kt) Ct+1 − (1 − δ)Kt+1 + Gt+1 = At+1F (Kt+1) (a) What is the optimality condition with respect to Mt? (b) Does the planner’s optimal allocation of money coincide with the allocation of money at the equilibrium of the Neoclassical model? (c) Is there a nominal interest rate at which the planner’s solution coincides with the equilibrium allocation?

          Let’s consider an alternative version of the social planner’s problem in which the planner also chooses Mt, in addition to Ct,Ct+1, and Kt+1.
subject to
max U = u(Ct) + v(Mt ) + βu(Ct+1) Ct ,Ct+1 ,Kt+1 ,Mt Pt
Ct +Kt+1 −(1−δ)Kt +Gt =AtF(Kt) Ct+1 − (1 − δ)Kt+1 + Gt+1 = At+1F (Kt+1)
(a)  What is the optimality condition with respect to Mt?
(b)  Does the planner’s optimal allocation of money coincide with the allocation of
money at the equilibrium of the Neoclassical model?
(c)  Is there a nominal interest rate at which the planner’s solution coincides with the equilibrium allocation?

Added by Madison B.

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