Question 1: Monetary and Fiscal Policies Consider the Keynesian version of the I

Question

Question 1: Monetary and Fiscal Policies

Consider the Keynesian version of the IS-LM model, where policymakers truly believe in the benefits of having stabilization policies. Md/P = 6Y 8, 000i

M/P = 600, G = 100, C = 200 + 0.40(Y T), I = 100 + 0.10Y 200i, T = 400

(a) Derive the equation for the LM curve. (Hint: It will be convenient for later use to write this equation with i on the left side.)

(b) Derive the equation for the IS curve. (Hint: Recall S=I and then you want an equation with Y on the left hand side.)

(c) Solve for equilibrium real output and interest rate.

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

Explanation / Answer

a. LM curve is the equilibrium of money demand and money supply.

Md/P = Ms.

6Y - 8000i = 600

6Y - 600 = 8000i.

i = (Y - 100) *6/8000

i = Y/8000 - 1/80.

b. Y = C + I + G

Y = 200 + 0.4 * (Y - 400) + 100 + 0.1Y - 200i + 100.

Y - 0.4Y - 0.1Y = 200 - 160 + 100 + 100 - 200i

0.5Y = 240 -200i

Y = 480 - 400i.

c. At equilibrium, IS = LM.

Plugging the value of i from LM into IS equation,

Y = 480 - 400 * (Y/8000 - 1/80)

Y = 480 - 0.05Y + 5

Y + 0.05Y = 485

1.05Y = 485

Y = $461.90

I = 461.90/8000 - 1/80

i = 0.0577 - 0.0125

i = 0.0452 or 4.52%.

d. C = 224.76

I = 137.15

224.76 + 137.15 + 100 = $461.90.

Hence proved.

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