Question $5(16$ points$)$

Consider the basic Neoclassical model discussed in class:

$C_t=C^d(Y_t-G_t,Y_{t+1}-G_{t+1},r_t)$

$N_t=N^s(w_t,{}_t)$

$N_t=N^d(w_t,A_t,K_t)$

$I_t=I^d(r_t,A_{t+1},K_t)$

$Y_t=A_t{K}_t^{}{N}_t^{1-}$

$Y_t=C_t+I_t+G_t$

$M_t=P_t{M}^d(r_t+{}_{t+1}^e,Y_t)$

$r_t=i_t-{}_{t+1}^e$

where $\{Y_t,C_t,I_t,N_t,r_t,w_t,P_t,i_t\}$ are endogenous and $\{A_t,A_{t+1},G_t,G_{t+1},{}_t,M_t,{}_{t+1}^e,K_t\}$ are exogenous. Graphically analyze the effects of:

$($a$)$ An increase in $G_{t+1}.$

$($b$)$ An increase in $A_{t+1}.$

In each case, clearly describe how each of the eight endogenous variables changes.