Answer to Question #231667 in Macroeconomics for Gogeta

Question

Consumption is given by C = 100+0.8YD and I = 50. The fiscal policy is summarized by G=200, TR = 62.5 and t = 0.25.
a). what is the equilibrium level of income?
b). what is the value of the new multiplier? Why is this less than the multiplier in the earlier problem?
c). what is the value of the budget surplus(BS) when I = 50 ?
d). What is BS when investment increases to 100?
e). Assuming that the full employment level of income Y* = 1200, what is the full employment BS* when I=50?

Answer 1

a)

$Y=100+0.8(1-t)Y+62.5+200+62.5\\Y(1-0.8(1-0.25)=425$

$Y=\frac{425}{1-(0.8)(0.75)}=\frac{400}{1-0.6}$

$\frac{400}{0.4}=1,000$

Therefore equilibrium income = 1000

b)

Value of multiplier $=\frac{1}{1-c(1-t)}$

$=\frac{1}{1-0.8(0.75)}$

$=\frac{1}{1-0.6}=\frac{1}{0.4}=2.5$

This is less than earlier due to taxes, when taxes are introduced, multiplier is less

C)

Equilibrium level of income is given by:-

$Y=C+I+G\\=100+0.8YD+50+200\\YD=(Y+TR-t.Y)\\\therefore Y=100+0.8(Y+62.5-0.25Y)+50+200\\\implies Y=350+0.8Y+50-0.2Y\\Y=400+0.6Y\\Y-0.6Y=400\\Y=1000$

total Tax. $t.Y=0.25\times1000=250$

Budget surplus

$=(T-G)=250-200\\=50$

d)

Budget surplus at I=100

$Y=C+I+G\\=100+0.8YD+100+200\\YD=(Y+TR-t.Y)\\\therefore Y=100+0.8(Y+62.5-0.25Y)+100+200\\\implies Y=400+0.8Y+50-0.2Y\\Y=450+0.6Y\\Y-0.6Y=450\\Y=1125$

e)

Total tax

$=t.Y=0.25\times1125=281.25-200\\=81.25$

When Y=1200

$T=0.25\times1200\\=300$

Budget surplus=300-200=100