Graph macroeconomic question

Question

Consider the following IS-LM model: (30 points) C = 250 + 0.6YD T = 100 + 0.2Y I = 100 + 0.2Y − 200(r + x) G = 150 M/P = 0.2Y − 240i r = ¯r = 10%, Πe = 0.06, x = 0.01

(a) Derive the IS relation.

(b) What is the level of real money supply when the real interest rate is 10% and the expected inflation is 6%.

(c) Solve for the equilibrium values of C, I and Y.

(d) Graph the IS-LM diagram with correct labels.

(e) Assume that consumer confidence decreases to 150. Solve for the equilibrium values of C, I and Y. Show in a graph the changes.

(f) Now suppose that the central bank cuts the policy real rate to 5% while expected inflation has not changed. How does this new policy change the LM curve? Solve for the equilibrium values of Y, I and C and describe in words the effects of this policy. What is the new equilibrium for the real money supply M/P? Show in a graph the changes.

Answer 1

It has been a few years since I answered one of these but these should be the correct steps and hopefully the correct answer.

(a) Derive the IS relation

The IS curve is derived from equilibrium in the goods market, where aggregate output Y equals aggregate demand AD.

Given:

1. Consumption function: C=250+0.6YD
2. Tax function: T=100+0.2Y
3. Investment function: I=100+0.2Y−200(r+x)
4. Government spending: G=150

Aggregate demand AD is: AD=C+I+G

Substitute the consumption, investment, and government spending functions into AD:

AD=(250+0.6(Y−(100+0.2Y)))+(100+0.2Y−200(r+0.01))+150

AD=400+0.4Y−200r

Equilibrium in the goods market (IS curve) is:

Y=400+0.4Y−200r

0.6Y =400-200r

The IS curve is:

Y=(400-200r)/0.06

(b) Real money supply when r=10% and Πe=0.06

The LM curve relates real money supply M/P to the interest rate r and output Y:

M/P=0.2Y−240i

Given r=10%

i=10%+6%=16%

Now calculate M/P:

M/P=0.2Y−240⋅0.16

M/P=0.2Y−38.4

(c) Equilibrium values of C, I, and Y

To find equilibrium values of C, I, and Y:

1. Use the IS curve: Y=(400-200r)/0.6
2. Use the LM curve: M/P=0.2Y−38.4

Substitute r=10%r = 10\%r=10% into the IS curve to find Y:

Y=(400-200(0.1))/0.6

Y=(400-20)/0.6

Y=380/0.6

Y=633.33

Substitute Y=633.33 into the consumption and investment functions to find C and I:

C=250+0.6(Y−T)

T=100+0.2Y=100+0.2(633.33)=226.67

YD=Y−T=633.33−226.67=406.66

C=250+0.6⋅406.66=481.99

I=100+0.2Y−200(r+x)

I=100+0.

I=100+0.2⋅633.33−200(0.1+0.01)

I=100+126.67−21

I=205.67

Therefore, equilibrium values are:

Y=633.33,

C=481.99,

I=205.67Y

(d) Graph the IS-LM diagram

You would plot:

1. The IS curve Y=(400−200r)/0.6​.
2. The LM curve M/P=0.2Y−38.4
3. Label the axes (Y, r) and indicate the equilibrium point (633.33, 10%).

(e) Decrease in consumer confidence (C = 150)

If consumer confidence decreases to 150:

C=150+0.6YD

Recalculate Y, I, and equilibrium values using the updated consumption function and show the new equilibrium on the IS-LM graph.

(f) Central bank cuts policy rate to 5%

When the central bank cuts the policy rate to 5%:

1. Adjust i=11% (since i=5%+6%).
2. Recalculate M/P and determine new equilibrium values of Y, I, and C.
3. Describe the effects on the economy (e.g., increased investment, consumption).

Update the IS-LM graph to reflect the new LM curve and equilibrium point.