1.Suppose M1 is given by currency plus deposits: , and the base is given by curr
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Question
1.Suppose M1 is given by currency plus deposits: , and the base is given by currency plus reserves: . Recall that the base and the money supply are connected by the multiplier, m, such that . Suppose further that banks must keep a fraction, rr, of their deposits on hand , and the public holds a fraction, k, of their deposits as cash so . Solve for the multiplier in terms of just r and k.
2.Refer to the above. Recessions historically have been (and sometimes still are) accompanied by runs on banks. What complications are presented for monetary policy in this situation? What happens if the central bank does nothing?
3.Refer to #1. Suppose banks can voluntarily hold excess reserves (hold more reserves than their reserve requirement). Let reserves be the sum of required reserves (N) and excess reserves (E), , where , and . Rederive the multiplier in terms of just k, rr, and e.
4.Refer to the above again. If banks decide to hold excess reserves what should happen to the multiplier?
5.Go to the FRED website I have used in class. It is located at: https://research.stlouisfed.org/fred2/
Find data on the M1 money stock and the monetary base from the year 2000 to the present. Make sure both are in monthly or quarterly (whatever you choose) frequency. Divide M1 by the monetary base.*(What is this series?) Print out the graph.
Now find data on excess reserves from 2000 to the present. Print that graph out as well. Explain the relationship between the two graphs you produced.
*-This step can be done with the in-website tools or with Excel. To use FRED, follow these instructions: https://fredqa.stlouisfed.org/2014/03/27/fred-graph-how-to-creating-custom-transformation-formulas/
To use Excel, click “Download data” in the top left corner, then in the first row of data, click the cell immediately to the right, and type “=B14/C14”. Then with D14 selected, double click the black box in the corner to fill down.
6.What is a hyperinflation? How do hyperinflations begin? What does Cagan say about ending a hyperinflation? What are some good ways of doing so?
7.Suppose we expect an inflation rate of 2% for the next year. If a lender requires a 3% real return on a one year loan, what interest rate should he charge?
8.Refer to above. Suppose we get an unexpected 1% of additional inflation over the year. Who is made worse off by this? Who is made better off? What does this imply about inflation’s ability to arbitrarily redistribute wealth?
9.Refer to above. Given your answer in 10, how do you believe credit and financial markets will respond in the presence of uncertainty about inflation? If the Fed wants to keep these markets stable, how should it behave?
10.What are the four types of unemployment and give an example of each.
11.What factors influence frictional unemployment? Can we ever completely get rid of it? What factors influence structural unemployment?
12.Suppose we pursued a policy that made it more difficult for firms to fire their workers (e.g. mandatory severance packages, long notice time, burdensome paperwork, or prior government approval). What do you imagine will happen to the natural unemployment rate? Why? (Hint: use the formula we derived for the natural rate of unemployment).
Explanation / Answer
Q1. M1 = C + D
Monetary base = C + R
Currency in hand (C) = k*D
Required reserves = r
Reserves (R) = r*D
We know that,
Monetary base * Multiplier = M1
(C+R)*m = C + D
m = (C+D)/(C+R)
m = (k*D + D)/(k*D + r*D)
m = (k + 1)/(k + r)
Thus, multiplier in terms of k and r is m = (k + 1)/(k + r)
Q7. Expected inflation rate = 2%
Real interest rate = 3%
Calculate nominal interest rate –
Nominal interest rate = Real interest rate + Expected inflation rate
= 3% + 2%
= 5%
Thus, if a lender requires a 3% real return on a one year loan then he should charge 5% as interest rate.
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