Question

The following equations describe an economy. (Think of C, I, G, etc as being measured in billions and I as a percentage; a 5 percent interest rate implies i = 5.)

C = 0.8(1 – t)Y

t = 0.25

I = 900 – 50i

G = 800

M^d/P = 0.25Y – 62.5i

M^s/P = 500

 

a)     Derive the equations that describes the IS and LM curves?                          

b) What is the equilibrium level of income and interest rate?   

Answer 1

a) the equation that describes the IS curve

Y=C+I+G=0.8(1-t)Y+900-50R+800=0.6Y+900-50R+800=0.8Y+1700.8-50R

Y-0.6Y=1700-50R

0.4Y=1700-50R

Y=4250-125R

the equation that describes the LM curve

0.25Y-62.5R=500

0.25Y-500=62.5R

R=0.004Y-8

b)

IS=4250-125R

LM=0.004Y-8

Y=4250-125(0.004Y-8)

Y=4250-0.5Y+1000

Y+0.5Y=5250

1.5Y=5250

Y=3500

R=0.004*3500-8=6