Consider the following short$-$run IS$-$LM$$model with income taxation.$$The economy is described by equations $(1)$ through$(6)$:$$

$(1)$ C $=350+0\mathrm{.}8($Y $$ T$)$

$(2)$ I $=67520$ r

$(3)$ G $=400$

$(4)$ T $=500+0\mathrm{.}25$Y

$(5)$ Y $=$ C $+$ I $+$ G$$

$(6)$ M$/$P $=0\mathrm{.}5$Y $50$r

where the nominal money supply M $=2360$ and the price level is P$\_$bar $=2.($There are $25\%$ income taxes in this model$).$ Equation $(5)$ is the goods market equilibrium condition $($IS equation$),$ while equation $(6)$ is the money market equilibrium condition $($LM equation$).$ Suppose that government expenditures increase by $100$ units but that the Bank of Canada uses monetary policy to maintain the interest rate constant. Then this increase in government spending will cause

Question $22$ options:

an increase in equilibrium output but will leave the money supply unchanged.

the equilibrium output to remain the same, but the money supply to increase by $100$ units.

an increase in both the equilibrium output level and the money supply by $125$ units.

an increase in both equilibrium output and in the money supply by $250$ units.$$