Answer to Question #239269 in Macroeconomics for jaaaaaaa

Question

(C, I, G, etc., are being measured in billions and i as a percentage)

C = 0.8(1 − t)Y t = 0.25

I = 900 − 50i   = 800

L = 0.25Y − 62.5i

= 500

 

1. What is the equilibrium interest rate? (Hint: Start by writing the equations for the IS curve and LM curves with the given data points). (0.5 Mark)

2. What is the equilibrium level of income in this model? (0.5 Mark)

 

3. What is the value of αG which is the simple multiplier with proportional income tax? (1 Mark)

 

4. By how much does an increase in autonomous government spending of DG =300 increase the level of equilibrium income in this model, which includes the money market? (Hint: Start by writing the IS and LM equations in functional forms). (1 Mark)

 

5. What is the value of the ultimate fiscal multiplier in the aforesaid case? (1 Mark)

 

6.  By how much does an increase in autonomous government spending of DG = 300 affect the equilibrium interest rate? (1 Mark)

Answer 1

1.

$IS\\Y=C+I+G=0.8(1-0.25)Y+900-50i+800\\=1700+0.6Y-50i\\Y-0.6Y=1700-50i\\Y=4250-125i$

$LM\\L=\frac{M}{P}\\0.25Y-62.5i=500\\0.25Y=500+62.5i\\Y=2000+250i$

$Is=LM\\4250-125i=2000-250i\\2250=375i\\\space \\1.\\i=6\\2.\space \\Y=4250-125(6)=2000-250(6)\\Y=3500$

$3.\\aG=\frac{1}{1-c(1-t)}\\\frac{1}{1-0.8(1-0.25}\\\frac{1}{1-0.6}\\=2.5$

4.

$IS\\Y=C+I+G=0.8(1-0.25)Y+900-50i+800+300\\=2000+0.6Y-50i\\Y-0.6Y=2000-50i\\Y=5000-125i$

$Y=5000-125(6)=2000-250(6)\\Y=3500\\=3800$

It will increase by 300

5.

$3.\\aG=\frac{1}{1-c(1-t)}\\\frac{1}{1-0.8(1-0.25}\\\frac{1}{1-0.6}\\=2.5$

6.

It remains constant