Answer to Question #226688 in Macroeconomics for fatima

Question

Now we look at the role taxes play in determining equilibrium income. Suppose we have an

economy of the type in Sections 10-4 and 10-5, described by the following functions:

C 5 50 1 .8YD

−

I

5 70

−−

G

5 200

−−

TR

5 100

t

5 .20

a.

Calculate the equilibrium level of income and the multiplier in this model.

b.

Calculate also the budget surplus, BS.

c.

Suppose that t increases to .25. What is the new equilibrium income? The new multiplier?

d. Calculate the change in the budget surplus. Would you expect the change in the surplus

to be more or less if c 5 .9 rather than .8?

e. Can you explain why the multiplier is 1 when t 5 1? 

Answer 1

(a)

Equilibrium level of income.

$Y=C+I+G-t$

$Y=550+1.8Y+570+5200-5.20$

$Y=2251.94$

$Multiplier=\frac {1}{5.20}=0.2$

(b)

Budget surplus = Total income by government- Total expenditure by government.

$=(5100+570+5.20)-5200$

$=5675.2-5200=475.2$

(c)

$t=5.25$

$Y=2257.14-5.25=2251.89$

New multiplier $=\frac {1}{5.25}=0.19$

(d)

New budget surplus$=(5100+570+5.25)-5200=475.25$

Change in budget surplus $=475.25-475.20=0.05$

Change in surplus will be more if C 5.9

(e)

Multiplier is 1 when t=5.1 because the higher the value of t, the lower the multiplier and vice versa.