in this problem we are going to use the money

Question

In this problem, we are going to use the money market to model two real world events:

i) a portfolio shock to money demand and ii) a shock to the money multiplier.

Suppose you have the following information:

Original money demand function:

M^d = P X [ 200 + .5 Y - 200 i]

where P = 1 (P remains constant in this problem), Y = 1600, M^s = 600, MB = 400 MM=1.5

a) Solve for the nominal interest rate ( i ) that clears the money market.

b) points for correct and completely labeled diagram) In the space below, draw a money demand / money supply diagram depicting these initial conditions.

c) We now experience a portfolio shock to money demand so that the new money demand function is:

M^d = P X [ 400 + .5 Y - 200 i]

Solve for the new market clearing interest rate, assuming there is no change in the money supply and label as point B on your diagram.

d) Assuming the Fed wanted to keep interest rates constant, what would they need to do exactly? Please explain and show as point C, the conditions after the Fed did what they need to do to keep interest rates steady and their initial level as in part a).

e) Re-draw a money demand and money supply diagram showing the initial conditions and label as point A.

f) Instead of a portfolio shock to money demand, we now experience a shock to the money multiplier. In particular, the money multiplier (MM) falls and is now = .8 (it was 1.5 before the shock). Assuming the Fed does nothing, what is the new money market clearing interest rate? Label this as point B on your diagram.

g) Now we assume that the Fed is pro-active and responds to the money multiplier shock immediately to keep interest rates at their initial level. What would the Fed have to do exactly in terms of open market operations (show work) and label this as point C on your diagram.