Answer to Question #212148 in Macroeconomics for sam

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

           L = 0.25Y – 62.5.i

           M / P = 500

Show that a given change in the money stock has a larger effect on output the less interest sensitive is the demand for money.

Answer 1

If the demand for money is extremely sensitive to interest rates, then the rate of increase in interest rates is small, the demand for money will decrease, and the money market will return to equilibrium.

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

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