GATE 2026 Question 51: IS-LM model

Consider the following IS-LM model where, $C_0$ is autonomous consumption, $c$ is marginal propensity to consumption, $T_0$ is the autonomous tax, $t$ is the tax rate on income $Y$, $b$ is the interest sensitivity of investment to real interest rate $r$, $M^S$ is exogenously determined nominal money supply, $P$ is the aggregate price level, $l_1$ is the income sensitivity of money demand to income, $l_2$ is the interest sensitivity of money demand

Consumption function: $C=C_0+cY^d$; $0<c<1$

Disposable Income: $Y^d=Y-T$

Tax function: $T=T_0+tY$; $0<t<1$

Investment function: $I=I_0-br$; $b>0$

LM equation: $\dfrac{M^S}{P}=l_1Y-l_2r$; $l_1>0,l_2>0$

Closed economy without government: $Y=C+I$

Which one of the following options gives the investment multiplier $\left(\dfrac{\partial Y}{\partial I_0}\right)$?