Answer to Question #211654 in Macroeconomics for NARTEY SAMUEL

Question

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 – 62.5.i

M / P = 500

a. What is the value of the simple multiplier (with taxes)

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?

Answer 1

(a)

Y = C + I + G

Y = 0.8(1-t)Y + I +G

Y = 0.8(1-0.25)Y + I + G

Y = 0.8(0.75)Y + I + G

Y = 0.6Y + I + G

0.4Y = I + G

Y = (1/0.4) (I + G)

Y = 2.5 (I + G)

Here, Multiplier = 1/0.4

Multiplier = 2.5

.

(b)

Y = C + I + G

Y = 0.8(1-t)Y + 900 - 50i + G

Y = 0.8(1-0.25)Y +900 - 50i +G

Y = 0.8(0.75)Y + 900 - 50i + G

Y = 0.6Y + 900 - 50i + G

0.4Y = 900 - 50i + G

Y = 2250 - 125i + 2.5G..................(1)

.

Money market equilibrium condition

L = M/P

0.25Y - 62.5i = 500

-62.5i = 500 - 0.25Y

Multiply both sides by 2

-125i = 1000 - 0.5Y ..................(2)

For equilibrium in both the markets

Put (2) in (1)

Y = 2250 +1000 - 0.5Y + 2.5 G

1.5Y = 3250 + 2.5G

Differentiate w.r.t G

1.5 dY/dG = 2.5

dY/dG = 2.5 / 1.5

dY/dG = 5/3

dY/dG = 1.67

An increase in G by 1 unit will increase the equilibrium income (Y) by 1.67 units.

.

(c)

Put (1) in (2)

-125i = 1000 - 0.5Y

-125i = 1000 - 0.5(2250 - 125i + 2.5G)

-125i = 1000 - 1125 + 62.5i - 1.25G

-125i - 62.5i = -125 -1.25G

-187.5i = -125 - 1.25G

187.5i = 125 + 1.25G

Differentiate w.r.t G

187.5 di/dG = 1.25

di/dG = 1.25/187.5

di/dG = 0.0067

So, a one-unit increase in G will increase the equilibrium interest rate (i) by 0.0067 or 0.67%