Answer to Question #253585 in Macroeconomics for Kelly

Question

Okahao island is a hypothetical small, closed economy in the northern part of Namibia. Autonomous

consumption in Okahao dollars is N$400.00, government spending is N$200.00 and Tax = 0.1Y. The investment function is I = 300 – 10r and the money demand function is [m/p]^d  = Y - 50r. Money supply is N$2500.00 and price level is N$5.00.

 

1. Derive the equations for the IS curve and the LM curve. 

2.Find the equilibrium interest rate. 

3. Compute the equilibrium level of income.

4. Use the IS-LM model to graphically depict the equilibrium interest rate and level of income calculated in (2) and (3) above. Show both intercepts.

5. Suppose that the government decides to double both the taxes and government spending. Calculate the new rate of interest and the level of investment. 

6. Does your answer in (5) above depend on the marginal propensity to consume? 

Answer 1

Solution:

1.). IS curve: Y = C + I + G

C = 400 + Yd

Yd = Y – 0.1Y

Y = 400 + (Y – 0.1Y) + 300 – 10r + 200

Y = 400 + 0.9Y + 300 – 10r + 200

Y – 0.9Y = 400 + 300 + 200 – 10r

0.1Y = 900 – 10r

Y = 9000 – 10r

IS Curve: Y = 9000 – 10r

 

LM curve: (M/P)^d = (M/P)^s = M/P

Y – 50r = 2500/5

5Y – 250r = 2500

5Y = 2500 + 250r

Y = 500 + 50r

LM Curve: Y = 500 + 50r

2.). Equilibrium interest rate:

At equilibrium: IS = LM

9000 – 100r = 500 + 50r

9000 – 500 = 50r + 150r

8500 = 150r

r = 56.67

The equilibrium interest rate = 56.67

 

3.). The equilibrium level of income:

Y = 9000 – 100r = 9000 – 100(56.67) = 9000 – 5667 = 3333

The equilibrium level of income = 3333

 

4.). The IS-LM model is depicted as below:

5.). New taxes = (0.1Y $\times$ 2) = 0.2Y

G = (200 $\times$ 2) = 400

New IS curve: Y = C + I + G

C = 400 + Yd

Yd = Y – 0.2Y

Y = 400 + (Y – 0.2Y) + 300 – 10r + 400

Y = 400 + 0.8Y + 300 – 10r + 400

Y – 0.8Y = 400 + 300 + 400 – 10r

0.2Y = 1100 – 10r

Y = 5500 – 50r

New IS Curve: Y = 5500 – 50r

At equilibrium: IS = LM

5500 – 50r = 500 + 50r

5500 – 500 = 50r + 50r

5000 = 100r

r = 50

The equilibrium interest rate = 50

The equilibrium level of income:

Y = 5500 – 50r = 5500 – 50(50) = 5500 – 2500 = 3000

The new equilibrium level of income = 3000

The new level of investment = 300 – 10r = 300 – 10(50) = 300 – 500 = -200