JNU SIS 2012 Question 21: IS-LM model

Consider the following form of the IS-LM model, where expected inflation is zero ($\pi^e = 0$) and net exports ($NX$) are also zero :

$C = c_0 + c_1(Y - T)$

$I = b_0 + b_1Y - b_2i$

$\frac{M^d}{P} = d_1 - d_2i$

$M^s = M$

where $C$ is the consumption, $Y$ is the income, $T$ represents taxes, $I$ is the investment, $i$ is the rate of interest, $M^d$ is the money demand, $P$ is the price level and $M^s$ is money supply. Let $G$ denote government spending. Then, the short-equilibrium (pair $(Y, i)$) that makes goods and money market to be in equilibrium at the same time is

Note that we define $m = \frac{1}{1 - b_1 - c_1}, b_1 + c_1 < 1$