Answer to Question #289611 in Macroeconomics for Muzayan

Question

Consider an economy with a different levels of aggregates as follows: c=0.8(1-t)Y t=0.25 I=900-50r G =800 L=0.25y-62.5r money supply: M=1000 price level :p=2 a) derive the IS and LM equation b) determine the equilibrium levels of income and interest rate c) calculate the government spending multiplier d)By how much income and interest change for a unit change in government spending? e) determine the amount of ''crowd out'' and interpret it

Answer 1

Solution:

a.). Derive IS and LM equation:

IS equation: AS = AD

Y = C + I + G

C = 0.8(1 – 0.25)Y = 0.6Y

Y = 0.6Y + 900 – 50r + 800

Y – 0.6Y = 1700 – 50r

0.4Y = 1700 – 50r

Y = 4250 – 125r

IS equation: Y = 4250 – 125r

 

LM equation: M^d = M^s

(M/P)^d = 0.25Y – 62.5r

1000/2 = 0.25Y – 62.5r

0.25Y – 62.5r  = 500

0.25Y = 500 + 62.5r

Y = 2000 + 250r

LM equation: Y = 2000 + 250r

 

b.). At equilibrium: IS = LM

4250 – 125r = 2000 + 250r

4250 – 2000 = 250r + 125r

2250 = 375r

r = 6

Interest rate = 6%

Equilibrium level of interest = 6%

Y = 4250 – 125(6) = 4250 – 750 = 3,500

Equilibrium level of income (Y) = 3,500

 

c.). Spending multiplier = $\frac{1}{(1 - MPC)} = \frac{1}{(1 - 0.8)} = \frac{1}{0.2} = 5$

Government spending multiplier = 5

 

d.). For a unit change in government spending, income and interest rate must change 5 times.

 

e.). The crowding-out effect is an economic theory that contends that rising public-sector spending reduces or even eliminates private-sector spending.

 Taxes = 0.25 x 3500 = 875

G = 800

Crowd Out = 875 – 800 = 75