Question $1.$ The money supply $M$ is determined by the Central Bank, and the money demand

$L$ is positively related to the general price level $p(t)$ and the real output level $Y.$

Inflation is the positive change in the general price level, dp$/$dt$,$ and therefore, is

closely associated with the excess money supply. The model can be written as

follows

$L=p(t)Y,>0$

$\frac{dp}{(d)t}=j(M-L),j>0$

where $$ and $j$ are positive constants.

$($a$)$ What is the time path of price $p(t)?$

$($Hint: Write the model as a differential equation in the form of $y^{}+ay=b)$

$($b$)$ What is the intertemporal equilibrium of price

$($Hint: The level at which the model reaches equilibrium is asked. The reaches

intertemporal equilibrium $p^{**}$ when the price level is fixed $($no longer changes$),$

$\{$:$\frac{dp}{(d)t}=0.)$

$($c$)$ Fiyat Obtain and interpret the solution of the time path you created for the price.

$($Hint: Solve the equation you found in part$($a$),$ put the $p^{**}$ term in the appropriate

place in the solution, and interpret the solution according to the departure from

equilibrium.$)$