(1) Briefly explain in words how the money multiplier is supposed to work (i.e., how, under normal financial circumstances, a Fed purchase of Treasury securities is said to result in a multiplied expansion of the quantity of money in circulation).
(2) This question is designed to help you work through, step-by-step, the formulas and relations underlying the "money multiplier" as discussed in class (and to illustrate its shortcomings as well). Your numerical answers should be "neat"-whole numbers or simple decimals (no ugly decimal answers). Here are all of the relevant definitions and formulas:
1) total currency = (currency in circulation) + (vault cash)
2) cu = (currency in circulation)/D(D = total deposits)
3) total reserves of banks = (vault cash) + (reserve deposits)
4) ε = (total reserves)/D
5) M = (1 + cu)D
6) MB = (currency in circulation) + (total reserves)
7) MB = (cu + ε)D
8) mm = [(1 + cu)/(ε + cu)] (mm = money multiplier)
9) M = (mm)MB
Suppose there is 200 worth of total currency, and 10% of it sits in the vaults of banks.
(a) How much currency is in circulation?
Suppose the "currency/deposit ratio" cu = 0.1.
(b) How large is the total amount of deposits in banks (D)?
(c) Given your answers above, how large is the money supply M?
Suppose the total of bank reserve deposits at the Fed is 196.
(d) How large are the total reserves of banks?
(e) Given the answers to (a) and (d), what is the value of the monetary base MB? (f) Given the answers to (b) and (d), what is the "reserve/deposit ratio" ε?
(g) Given the answer to (e) and prior information, what is the value of mm?
Now, suppose that, faced with a financial crisis that begins with a "credit crunch" and leads to a depressed level of GDP, the Fed attempts stimulus and launches a significant expansion of its balance sheet (known as "quantitative easing"), buying 396 worth of securities from banks, but the banks (weighed down with "toxic" assets and perceiving high risk involved with lending) simply hold all of the Feds payments as added reserves and do not alter their lending behavior.
(d') Repeat part (d) above, and find the new total reserves of banks.
(e') Repeat part (e) above, and find the new value of MB.
(f') Repeat part (f) above, and find the new value of ε.
(g') Repeat part (g) above, and find the new value of mm.
(h) Given these results, how large is M now, after the Feds action and the banks reaction? (Here, use eq. (9)). Comparing (c) and (h), explain why the ?M is what it is here.
(i) Sometimes, economic commentators (perhaps influenced by the legacy of Monetarism) argue that a large increase in MB will inevitably create significant price inflation (because the Fed is said to be "printing money"). Based on the numerical example here, is the claim of "inevitability" persuasive? Why or why not?
(3) Within the IS-LM model:
(a) If output is falling, what happens to the real demand for money (L)? Why?
(b) If there is, as in (a) or for any other reason, an excess supply of money, what happens in the bond market, to the price of bonds? Why? What does this do to the interest rate? Why?
(c) If the interest rate declines, what happens to overall aggregate expenditure on output? Why? [remember, output was falling in part (a) where this sequence began]
(4) There has been a lot of discussion recently about central bank policy and "negative interest rates." In answering the questions below, refer to the following article from the NY Times: https://nyti.ms/1U22Gtm.
(a) What are some of the reasons that a central bank would want to pursue a negative interest rate policy?
(b) What "special case" of the IS-LM model does a negative interest rate policy try to address? (Hint: in this "special case," what is unique about the implied equilibrium interest rate?)
(c) Why have economists traditionally assumed that negative interest rates are not possible? For bonus points, explain why economists assumed wrong.