Question

The following equations describe an economy. (Think of C , I , G , etc., as being measured in Billions and I as a percentage; a 5 percent interest rate implies I = 5.)
C= 0.8(1 - t )Y
T=0.25
I=900-50i
-G=800
L = 0.25Y-62.5i
-M/-P= 500
a. What is the value of aG which corresponds to the simple multiplier (with taxes) of Chapter 10 ?
b. By how much does an increase in government spending of ∆G increase the level of Income in this model, which includes the money market?
c. By how much does a change in government spending of ∆G affect the equilibrium Interest rate?
d. Explain the difference between your answers to parts a and b.

Answer 1

$Given;\\ C=0.8(1−t)Y\\T=0.25\\I=900−50i\\\bar{G}=800\\L=0.25Y−62.5i\\\frac{\bar{M}}{\bar{P}}=500\\i=5$

$a) aG=\frac{1}{1−c(1−t)}\\ therefore;\\ aG=\frac{1}{1−0.8(1−0.25)}\\ =\frac{1}{1−0.8(0.75)}\\ =\frac{1}{1−0.6}\\ =\frac{1}{0.4}\\ =2.5$

b) To calculate increase in the level of Income in this model, which includes the money market we need to calculate fiscal policy multiplier. So,

$\frac{∆Y}{∆G}=γ\\ =\frac{aG}{1+\frac{b}{h}KaG}\\ =\frac{2.5}{1+\frac{50}{62.5}×0.25×2.5}\\ =\frac{2.5}{1+\frac{50}{62.5}×0.625}\\ =\frac{2.5}{1+(50×0.01)}\\ =\frac{2.5}{1+0.5}\\ =\frac{2.5}{1.5}\\ =1.667$

Change in level of income= 1.667

c) Effect of change in government spending on interest rate:- 

$\frac{∆i}{∆G}=γ×\frac{k}{h}\\ =1.667×\frac{0.25}{62.5}\\ =1.667×0.004 \\=0.0067$

Change in interest rate= 0.0067

d)

in (a) it is te value of expenditure that is suitable with taxation while in (b) it is the impact of the change in expenditure to the income.