I've done something similar to this before, but my knowledge on it is a bit rusty. I've managed to come up with some answers on the first half of the problem, but I forget how the second half is solved. The question is listed word-for-word.

A closed economy is described by the following simple IS-LM system:

$\displaystyle C=a+b(1-t)Y-\ell R$ (consumption)

$\displaystyle I=\overline{I}$ (investment)

$\displaystyle G=\overline{G}$ (government spending)

$\displaystyle L=kY-hR$ (money demand)

$\displaystyle M=\overline{M}$ (money supply)

where $\displaystyle R$ and $\displaystyle Y$ are the interest and real GDP, respectively, and $\displaystyle a>0$, $\displaystyle 0<b<1$, $\displaystyle 0<t<1$, $\displaystyle k>0$, and $\displaystyle h>0$ are known constants (exogenous parameters).

a)Find an expression for the linear IS curve and an expression for the linear LM curve.

My answers

IS Curve: $\displaystyle Y=C+I+G=a+b(1-t)Y-\ell R+\overline{I}+\overline{G}$

LM Curve: $\displaystyle M/P=L(R,Y)\Rightarrow M^d=P\times L(R,Y)=P(kY-hR)$, where $\displaystyle P$ represents the price level.

b)Find solutions for $\displaystyle R$ and $\displaystyle Y$.

(I don't have any answers for these yet)

If someone could help me out with the second half of the question, that'd be great. Also, if I've done anything wrong with the first half, please point it out.