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

Md/P = 0.25Y – 62.5i

Ms/P = 500

Derive the equations that describes the IS and LM curves?     

What is the equilibrium level of income and interest rate?  

Answer 1

$a.\\ Y=C+I+G=0.8(1-t)Y+900-50R+800=0.6Y+900-50R+800=0.8Y+1700.8-50R\\ Y-0.6Y=1700-50R\\ 0.4Y=1700-50R\\ Y=4250-125R$

$0.25Y-62.5R=500 0.25Y-500=62.5R\\ R=0.004Y-8\\ \\ LM=0.004Y-8$

$b. \\Y=4250-125(0.004Y-8)\\ Y=4250-0.5Y+1000\\ Y+0.5Y=5250\\ 1.5Y=5250\\ Y=3500\\ R=0.004\times 3500-8=6$