(More difficult) The money supply (M) is the sum of bank deposits (D) plus currency in the hands of the public (call that C). Suppose the required reserve ratio is 20 percent and the Fed provides $50 billion in bank reserves (R = $50 billion).

a. First assume that people hold no currency (C = 0). How large will the money supply (M) be? If the Fed increases bank reserves to R = $60 billion, how large will M be then?

b. Next, assume that people hold 20 cents worth of currency for each dollar of bank deposits; that is, C = 0.2D. Define the monetary base (B) as the sum of reserves (R) plus currency (C): B = R + C. If the Fed now creates $50 billion worth of monetary base, how large will M be? (Hint: You will need a little bit of algebra to figure this out. Remember that the $50 billion monetary base is divided between two purposes: bank reserves and currency.) Now, if the Fed increases the monetary base to B 5 $60 billion, how large will M be?

c. What do you notice about the relationship between M and B?