Answer to Question #296758 in Macroeconomics for Tesema

Question

Given the following information for a hypothetical economy (all are in billion dollars)

Money demand = 10Y-0.2r

Money supply = 1000

C = 80 + 0.1 Ya

G = T = 20

I=20-0.3r

A. Derive the IS equation

B Derive the LM equation

C. Find the equilibrium interest rate

D. Find the equilibrium income level

E. Show your results graphically

Answer 1

Solution:

A.). IS equation: Y = C + G + I

C = 80 + 0.1Yd = 80 + 0.1(Y – T) = 80 + 0.1(Y – 20) = 80 + 0.1Y – 2

Y = 80 + 0.1Y – 2 + 20 + 20 – 0.3r

Y – 0.1Y = 118 – 0.3r

0.9Y = 118 – 0.3r

Y = 131.11 – 0.33r

IS equation: Y = 131.11 – 0.33r

 

B.). Derive the LM equation:

Md = Ms

10Y – 0.2r = 1000

Y = 100 + 0.02r

LM equation: Y = 100 + 0.02r

 

C.). At equilibrium: IS = LM

131.11 – 0.33r = 100 + 0.02r

131.11 – 100 = 0.02r + 0.33r

31.11 = 0.35r

r = 88.89

The equilibrium interest rate = 88.89

 

D.). Equilibrium income level:

Y = 131.11 – 0.33r

Y = 131.11 – 0.33(88.89) = 131.11 – 29.33 = 101.78

Y = 101.78

Equilibrium income level = 101.78

 

E.). The graph is as follows: