How does the federal reserve change the money supply

Question

Assignment:

1. "An increase in the interest rate will cause reduction in investment, aggregate demand, and equilibrium output. Thus, an increase in the interest rate will cause a leftward shift in the IS curve."

Is this statement true, false or uncertain? Explain.

2. Assume that the money demand is given by

M^d = Y - 100i

How much should the supply of money be raised if the Federal Reserve wants to reduce the interest rate from 0.05 to 0.02 while keeping output unchanged? How does the Federal Reserve change the money supply?

3. Use the IS-LM model to analyze a simultaneous increase in taxes and a reduction in the interest rate.

(a) What is the effect of this policy mix on the IS curve? What is the effect on the LM curve?

(b) What are the effects of the policy mix on output?

(c) Do we know the effects of the policy mix on the level of investment if I = b₀ + b₁Y - b₂i? Do we know the effect if I = b₀ - b₂i Explain.

4. Let

Y = C + I + G

C = 100 + 0.4(Y-T)

T = 100

I = 100 + 0.1Y - 1000i

G = 100

i = 0.05

(a) Derive the equation for the IS curve.

(b) What is the value of the multiplier for autonomous demand?

(c) What is the equation for the LM curve.

(d) Find the equilibrium solution for aggregate output.

(e) Use a combination of fiscal policy (taxes T) and monetary policy to achieve Y = 520 and investment I = 172.