Help to solve Macroeconomical problem!!!?

Question

Consider the following economy:

C =150 +0.6Yd; I=0.4Y-5000i; G=110; T=100; i=0.004; Y=N*N; BC = 150 - 0.1Yd;

Where Y represents the production, BC is the Trade Balance and N represents millions of workers.

a) Calculate the employment correspondent to the equilibrium level of aggregate demand and the trade balance.

b) Calculate the changes in public revenues and public expenses in order to reduce unemplyment by 1 million and in order to keep the equilibrium of the trade balance.

Consider now the monetary market of this economy:

M=1212,5; P=1; Lt=0.5Y; Ls=0(i>0.007) or =962.5-13750*i (i<=0.007)

The income level correspondent to total utilization of available resources is 1681 m.u..

c) Calculate the necessary changes on the quantity of money in order to achieve that goal. Represent graphically.

Answer 1

AE=C+I+G+BC

Yd=Y-T=Y-100

Y=N²

N=√Y

Equilibrium condition AE=Y

AE=150+0.6(Y-100) +0.4Y-5000*i+110+150-0.1(Y-100)

AE=Y

Y=360-5000*i+0.9Y

a)

i=0.004

Y=360-5000*0.004+0.9Y

Y=340+0.9Y

0.1Y=340

Y=340/0.1=3400

N=√3400≈58.3095

BC=150-0.1(Y-T)=150-0.1(3400-100) =150-330= - 180

b)

N=58.3095+1=59.3095

Y=N²=59.3095²≈3517.619

i=0.004

BC=150-0.1(3400-100)=150-330= -180

-180=150 - 0.1 (Y-T)

0.1(Y-T)=330

Y-T=3300

T=Y-3300

Y=3517.619

T= 3517.619-3300=217.619

Yd=Y-T= 3517.619 - 217.619 = 3300

3517.619 =150+0.6*3300 + 0.4*3517.619 - 5000*0.004+G-180

G=180.571

Required changes:

ΔG=180.571-110 = + 70.571

ΔT=217.619-100 = + 117.619

ΔG%=180.571/110=1.641= +64.1%

ΔT%=217.619=2.1762= +117.62%

ΔY%=3517.619/3400=1.0346= +3.46%

Share of government in economy=180.57/3517.619=0.0513= 5.13%

Where are you planning to gather such tax increase?

It should more than double.

Increase in tax revenue due to GDP growth = +3.46%

Remaining increase in taxes=2.1762/1.0346=2.10= +110% (!!!)

Imagine consequences on budget deficit.

c)

Y=1681

Ld=Ls+Lt

M/P=Ld

P=1 and we will assume that prices are sticky in short-run so P is constant

Ld=M

Y=C+I+G+BC

1681=C+I+G+BC

Yd=Y-T=Y-100= 1681-100=1581

1681=150+0.6*1581+0.4*1681 -5000i+110+150-0.1*1581

191.9=5000i

i=191.9/5000=0.03838

M=Ld

Lt=1681/2=840.5

Ld=Lt+Ls

i&lt;0.007 so Ls=962.5-13750i

Ld=840.5+962.5-13750*0.03838

Ld=1275.275

Ld=M

M=1275.275

Current M=1212.5 so required change should be:

ΔM=1275.275-1212.5= +62.775