Suppose the Fed decides it needs to pursue an expansionary policy. Assume people hold no cash, the reserve requirement is 20%, and there are no excess reserves.
a. Show how the Fed would increase the money supply by $2M through changing the reserve requirement.
b. Show how the Fed would increase the money supply by $2M through open market operations
a. The simple formula that relates the monetary base (which is what is affected by open market operations) and the reserve requirements to the money supply is the following:
Money Supply = (1/RR)*(Monetary Base)
where RR are the reserve requirements (in this case, RR=0.2) and (1/RR) is the "money multiplier". Let's call M to the money supply and B to the monetary base.
M = (1/RR)*B
We want to take the money supply to M + 2 (you didn't supply a value for M in your question). Now, M + 2 can be rewritten as:
Contextualize expansionary policy.