Question

Consider the Aggregate Demand (AD)-Aggregate Supply (AS) model studied in class. The AD function is composed of the following elements:
? = ? + ??? ∙ (? − ?); ? = ? − ?; ? = ?; ?? = ?∗ − ?; ? = ? + ? ∙ ?
The AS is given by the function:
? = 4,
(a) Assume that the economy is in its very short-run equilibrium with the following values: ? = ? = 0; ? = ?∗ = 1; ??? = 0.5; ? = 8; ? = 4; ? = 1/3
Find the Budget Deficit.

(b) Suppose the government has two policies to reduce the budget deficit to zero:
 Reduce the level of government spending, or  Increase the level of lump-sum taxes.
(Note: The government can only use one of the two policies, and the rest of parameters remain constant).
Find the new levels of ? and ? that result in a budget balance in equilibrium, and the magnitude (a number, not a formula) of the fiscal multiplier under each policy.

Answer 1

(a) C = C + mpc(Y-T)

I = I - r

G=G

NX = P* - P

T = T +tY

P=4 (AS)

given: C=I=0, r=P*=1

mpc = 0.5, G=8,T=4,t=(1/3)

Y = C+I+G+NX from ISLM framework.

Y = 0 + 0.5(Y-4-(1/3)Y) - 1 + 8 + 1 - 4

or, Y = 0.5Y - 2 - (1/6)Y -1 + 8 + 1 -4

or, Y = (1/3)Y - 2 - 2 + 8 + 1 -4

or. Y(1-(1/3)) = -2 - 1 + 8 + 1 - 4

or, (2/3)Y = 2

or, Y = 3

G = 4

Thus budget deficit = Government Expenditure - government income

= G - T -tY

= 4 - 4 - (1/3)3 = 1 i.e there is a deficit of 1

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(b) # First method to reduce budget deficit is by reducing government spending by :

0 = G - T -tY

or, T+ tY = G

or, G = 4 + (1/3)3

or, G = 5. In our case government spending has to go down by (8 - 5 = 3)to make budget deficit 0

  # Second method to reduce budget deficit is by increasing lumpsum tax by:

0 = 4 - T - t.Y

or, 4 - (1/3)3 = T

or , T = 3. Lumpsum tax has to be increased by (4 - 3 = 1) for BD=0.

Multiplier in first case is : 1/(1-c(1-t))

= 1/(1-0.5(1-(1/3))

= 1/ (1-(1/3))

= 1/(2/3)

= 1.5 = Magnitude.

Multiplier in second case is: -c/(1-c(1-t))

= -0.5/(1-0.5(1-(1/3))

= -(1/3).

Thus , Magnitude is (1/3)