Question

Suppose the goods-market of the economy of Macronium is described by the following equations

Consumption: C = 400 + 0.80 Yd
where Yd refers to disposable (post-tax) income.

Government collects lump-sum taxes at the amount 250 units, i.e. Taxes T = 250

Investment demand is given by Investment: I = 250 -500r

Government purchases has two components:
1- Lump Sum government purchases at G' = 50
2- A proportional component g: 10% of the output, i.e. gY= 0.10Y

Hence, total government purchases are:

Government Purchases: G = G' + gY = G' + 0.10Y =50+0.10Y
You can interpret this formulation as that government purchases increase in good times

and decrease in bad times.

Also, the money-market of the economy of Macronium is described by the following equations:

Money Demand: L(r,y) = 0.5Y - 2500r Money Supply: Ms =$4800
Price Level : P=$2

a)Solve for equilibrium interest rate and income level.

b)Calculate consumption, investment, government purchases, private saving, public saving & national saving under this equilibrium.

c)Suppose that the government of Macronium reduces lump-sum government purchases by 10 (from 50 to 40). Calculate the effect of this change on the equilibrium output and real interest rate.

d)Suppose that Fed wants to get the economy back to the equilibrium output level you calculated in part d, and to achieve this goal, it plans to change the money supply. How much change in nominal money supply should the Fed make (also in what direction) and what is the new real interest rate after Fed’s intervention?

Answer 1

A) y=C+I+G( IS equation,as there is no exports and imports given)

Y=400 + 0.80 (Y-250) +250-500r+50+0.1Y

Y=500+0.9Y-500r

Y=5000-5000r(is equation)

Ms/p=L(r,y){lm equation}

4800/2=0.5y-2500r

r=0.0002y-0.96

Y=5000-5000(0.0002Y-0.96)

Y=5000-1y+4800=9800-1Y

Y=9800/2=4900

r=0.0002*4900-0.96=0.02=2%

B) C=400+0.8(4900-250)=4120

I=250-500*0.02=240

G=50+0.1*4900=540

PS=Y-C-T=4900-4120-250=530

Public saving=T-G=250-540=-290

National saving = private + public saving=530-290=240

C)after reduction of g=40+0.1Y

Is equation: Y=4900-5000r

Y=4900-5000(0.0002Y-0.96)

Y=9700-1y

Y=9700/2=4850

r=0.0002*4850-0.96=0.01=1%

D)AD equation after G reduction:

Y=4900-5000(0.0002Y-M/2500P)

Y=4900-1Y+2M/P

Y=2450+M/P

Y=4900,p=2

4900=2450+M/2

2450*2=M

M=4900

r=0.0002*4900-4900/2*2500=0.98-0.98=0=0%