Important Macroeconomics question!?

Question

Assume that a hypothetical economy with an MPC of .8 is experiencing severe recession. By how much would government spending have to increase to shift the aggregate demand curve rightward by $25 billion? How large a tax cut would be needed to achieve the same increase in aggregate deman? Why the difference? Determine one possible combination of government spending increases and tax decreases that would accomplish the same goal.

Answer 1

MPC=0.8

ΔY/ΔG=1/(1-MPC)

ΔY=+25

ΔG=25*(1-0.8)=25*0.2= $+5 billion

ΔY/ΔT = -MPC/(1-MPC)

ΔT= 25*(1-0.8) / -0.8 = $-6.25 billion (tax-cut)

Difference due to different multiplier effects.

Combination:

ΔG= $+4 billion

ΔY= 4/0.2= $+20 billion

Left 25-20= $+5 billion

So Δy= $+5 billion

5/ΔT= -0.8/(1-0.8)

ΔT=5*0.2 / -0.8 = -1.25

So possible combination is:

ΔT= $-1.25 billion and  ÃŽÂ”G= $+4 billion

Answer 2

To answer this you need to know that:

AD=Y=C+I+G+CA

C= c0+ c1(Y-T).

Now it should be easy, just a matter of algebra!

c0 is autonomous consumption, which you can assume to equal zero. c1 is the MPC. Y= output, I= investment, G= govt spending and CA= current account. You can assume that CA=0.