Answer to Question #228157 in Macroeconomics for Kevin

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=50+.8YD
I=70
G= 200
TR=100
t=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 = .9 rather than .8?
e. Can you explain why the multiplier is 1 when t=1?

Answer 1

In a closed economy, the equilibrium level of income is attained at Y =Aggregate demand where AD= Consumption + Investment + Government Expenditure.

Budget Surplus = Government Revenue minus Government expenditure where Government Revenue= Tax and Government expenditure = Transfers and G 

a.

Given, C=50+.8YD

I=70

G= 200

TR=100

t=20

Equilibrium Condition : Y = AD

where AD = C+I +G

=> AD = 50+0.8Y_D +70 + 200

=> AD =50+0.8( Y - 0.2Y + 100) +70 + 200   [ Since Y_D = Y - TAX + TRANSFERS ]

=> AD = 50+0.8Y−0.16+80+70+200

50+0.8Y-0.16+80+70+200

=> AD= 400+0.64Y

400+0.64Y

 

Now, Set Y = AD

We get, Y = 400+0.64Y

=> Y-0.64Y

Y-0.64Y= 400

=> 0.36Y =400

0.36Y =400

=> $Y = \frac{1}{ 0.36}$

×400

Y = 10.36×400

=> Y = 1111.1

Y = 1111.1

Here, =Multiplier $αG = \frac{1}{ 0.36}$

=2.7

b.

Budget Surplus = Revenue - Government expenditure

Budget Surplus = Revenue - Government expenditure

=> Budget Surplus = Tax - Transfers - Government Expenditure

Budget Surplus = Tax - Transfers - Government Expenditure

=> Budegt Surplus = 0.2Y -100-200

Budegt Surplus = 0.2Y -100-200

=>Budget Surplus = (0.2×1111.1) -100-200

Budget Surplus = (0.2×1111.1) -100-200

=>Budegt Surplus= 222.2 -300

Budegt Surplus= 222.2 -300

=>Budget Surplus = -77.8

Budget Surplus = -77.8

Here, a negative value means it is a deficit.

c.

Now, Given t= 0.25

We know, Equilibrium Condition : Y = AD

where AD = C+I +G

=> AD = 50+0.8Y_D +70 + 200

=> AD =50+0.8( Y - 0.25Y + 100) +70 + 200   [ Since Y_D = Y - TAX + TRANSFERS ]

=> AD = 50+0.8Y−0.2+80+70+200

50+0.8Y-0.2+80+70+200

=> AD= 400+0.6Y

400+0.6Y

 

Now, Set Y = AD

We get, Y = 400+0.6Y

Y = 400+0.6Y

=> Y-0.6Y

Y-0.6Y= 400

=> 0.4Y =400

0.4Y =400

$=> Y =\frac{ 1}{ 0.4} \times 400$

Y = 1000

Here, =Multiplier αG = 1

0.4$αG = \frac{1}{ 0.4}=2.5$