Macroeconomics 13th Edition by William Baumol ,Alan Blinder

Exercise 8

(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 bank reserves (R) plus currency: 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 = $60 billion, how large will M be
c. What do you notice about the relationship between M and B