Build The IS-LM Model

Assume that we have the following data:

C=100+0.50Y 

Ip=100-20r 

Mt=0.10Y 

Ms=100-10r 

M=80

a. Build the IS-LM function

Suppose the government spending, and the net export(NExpo) is o, then the model will be:

IS Model:

Y = Aggregate demand = Consumer and household consumption expenditures + Investment + Government spending + NExpo

Y = (100 + 0.5Y) + (100 - 20r) = 200 +0.5Y -20r

0.5Y = 200 - 20r

Y = 400 - 40r (The IS Equation)

The LM Model:

Money demand (speculative, transaction demand) is equal to the Money supply.

Money demand = Money supply

100 - 10r + 0.1Y = 80

0.1Y = 10r - 20

Y = 100r - 200 (The LM Equation)

The IS & LM intersection

400 - 40r = 100r - 200

140r = 600

r = 4.29

Y = 100r - 200

Y = (100 * 4.29) - 200

Y = 429 - 200

Y = 229

The intersection is (229, 4.29), which means the equilibrium interest rate 4.29% and the eqiilibrium output 229.

b. If we assume an increase in Investments by 100 units, please calculate again the IS-LM functions.

Assume an increase in Investments by 100 units, then....

The original IS Equation = Y = 400 - 40r

The new IS Equation = Y = 400 - 40r +100 = 500 - 40r

Y = 500 - 40r 

For every given data, the IS Equation will shift rightward (+100), and cause the equilibrium to have a larger aggregate output and larger interest rate which will also increase the supply of goods. 

c. The intersection of IS-LM functions defines four areas. Please analyze the behavior of the markets for goods and money for each area. 

Normally, there are four areas on the graph, separate by the equilibrium point of the intersection of the LM Equation line and the IS Equation line.

Region AB represents the pressure on the interest rate to fall down since it's higher than the theoretical equilibrium interest rate. As the interest rate goes down, the IS or LM curve respectively moving by their causes.

Region CD represents the pressure on the interest rate to increase since it's lower than the theoretical equilibrium interest rate. As the interest rate goes up, the IS or LM curve respectively moving by their causes.

Region BC represents the pressure on the output and supply to fall down since it's higher or lower than the theoretical equilibrium output and demand. 

Region AD represents the pressure on the output and supply to increase since it's lower than the theoretical equilibrium output and demand. 

Reference

Wright, R. E., & Quadrini, V. (2009).Money and Banking. Flat World Knowledge Inc.