Question $5($not for submission, only for Practice$)$

Suppose the economy currently is in recession, with output lower than the potential level by $$400$ billion, and the government decides to use expansionary fiscal policy to close the recessionary gap. The people's marginal propensity to consume $($MPC$)$ is estimated to be $0\mathrm{.}75.$

a$)$ Suppose the fiscal policy to fight recession is specifically to increase government spending, and suppose there will be no crowding$-$out effect from such a policy. Should the increase of government spending be $$100$ billion, more than $$100$ billion, or less than $$100$ billion? Explain and show calculations.

b$)$ How would you modify your answer above if there is crowding$-$out effect? Explain.

c$)$ Alternatively, suppose the expansionary fiscal policy adopted is to cut the taxes by $$100$ billion $($with no change to government spending$).$ In the short$-$run with no change of the price level, how much is the initial effect of the tax cut on aggregate demand $($i$.$e$.$ before there is multiplier effect$)?$ And how much is the total effect on the aggregate demand $($i$.$e$.$ after the multiplier effect$)?$ Show calculations.

d$)$ Suppose the government spending increase $($as the only policy measure$)$ required to end the recession is $$120$ billion. How much tax cut $($as the only policy measure$)$ is needed to end the recession? Show calculations.

e$)$ In addition to increase in government spending and decrease of taxes, in the tool box of the government to fight recession is also the expansionary monetary policy. Will the long$-$run equilibrium restored by these three policy measures respectively be the same in terms of total output $($Y$),$ consumption $($C$),$ investment $($I$),$ and government purchases $($G$)?$ Explain.