Question

Consider the economy with the following data

𝐶 = 200 + 0.25(𝑌 − 𝑇)

𝐼 = 150 + 0.25𝑌 − 1000𝑟

𝐺 = 250

𝑇 = 200

(𝑀⁄𝑃)

= 2𝑌 − 100𝑟

𝑀 = 3200,

𝑃 = 2

a. Mathematically derive the IS-curve

b. Mathematically derive the LM-curve

c. Solve for the equilibrium income (Y) and interest rate (r)

d. Calculate the value of consumption (C) at the equilibrium level

e. Analyze effect that a monetary expansion will have on the equilibrium values for Output, Interest Rate, Consumption and Investment in the model.

Answer 1

Solution:

a.). IS-Curve:

IS = Y

Y = C + I + G

Y = 200 + 0.25(Y – T) + 150 + 0.25Y – 1000r + 250

Y = 200 + 0.25(Y – 200) + 150 + 0.25Y – 1000r + 250

Y = 200 + 0.25Y – 50 + 150 + 0.25Y – 1000r + 250

Y – 0.25Y – 0.25Y = 200 + 150 + 250 - 50 – 1000r

0.5Y = 550 – 1000r

Y = 1100 – 2000r

IS Curve: Y = 1100 – 2000r

 

b.). LM Curve:

(M/P)^d = (M/P)^s = M/P

M/P = 3,200/2 = 1,600

2Y – 100r = 1,600

2Y = 1,600 + 100r

Y = 800 + 50r

LM Curve: Y = 800 + 50r

 

c.). At equilibrium: IS Curve = LM curve

1100 – 2000r = 800 + 50r

1100 – 800 = 50r + 2000r

300 = 2050r

r = 0.146

Interest rate = 0.146

 

Equilibrium income (Y): Y = 1100 – 2000r

Y = 1100 – 2000(0.146) = 1100 – 292 = 808

Equilibrium income = 808

 

d.). Consumption: C = 200 + 0.25(Y – T) = 200 + 0.25(808 – 200)

C = 200 + 202 – 50

C = 452

Consumption = 452

 

e.). Monetary policy refers to controlling the money supply. When the money supply expands, interest rates fall, which boosts consumption and investment. Increases in consumption and investment raise aggregate demand, which raises real GDP to its equilibrium level and vice versa.