Question

# C = 100 + 0.75YD I = 225 + 0.15Y - 600i G = 450 T...

C = 100 + 0.75YD
I = 225 + 0.15Y - 600i

G = 450
T = 100

a. Derive the IS relation.
b. The central bank sets an interest rate of 75% (i = 0.75). How is that decision represented in the equations?
c. What is the level of real money supply when the interest rate is 75%? Use the expression:

?? = 3 ? − 9 9 0 0 ?

d. Solve for the equilibrium values of C and I, and verify the value you obtained for Y by adding C, I, and G.

e. Now suppose that the central bank cuts the interest rate to 5% (i=0.05). How does this change the LM curve? Solve for Y, I, and C, and describe in words the effects of an expansionary monetary policy. What is the new equilibrium value of M/P supply?

f. Return to the initial situation in which the interest rate set by the central bank is 75%. Now suppose that government spending increases to G = 600. Summarize the effects of an expansionary fiscal policy on Y, I, and C. What is the effect of the expansionary fiscal policy on the real money supply?

(a)

YD = Y - T = Y - 100

In goods market equilibrium, Y = C + I + G

Y = 100 + 0.75(Y - 100) + 225 + 0.15Y - 600i + 450

Y = 775 + 0.75Y - 75 + 0.15Y - 600i

(1 - 0.75 - 0.15)Y = 700 - 600i

0.1Y = 700 - 600i

Y = 7000 - 6000i..........(1) (Equation of IS curve)

(b)

When i = 0.75,

I = 225 + 0.15Y - (600 x 0.75) = 225 + 0.15Y - 450 = 0.15Y - 225

Y = 7000 - (6000 x 0.75) = 7000 - 4500 = 2500

(c)

When i = 0.75, Y = 2500. So

MP = 3Y - 9900i = (3 x 2500) - (9900 x 0.75) = 7500 - 7425 = 75

(d)

When i = 0.75, Y = 2500. So

C = 100 + 0.75 x (2500 - 100) = 100 + 0.75 x 2400 = 100 + 1800 = 1900

I = 225 + (0.15 x 2500) - (600 x 0.75) = 225 + 375 - 450 = 150

Therefore, Y = 1900 + 150 + 450 = 2500 (Value of Y derived in part b)