MORE PROBLEMS AND APPLICATIONS

Question 5.16

1. In the Cagan model, if the money supply is expected to grow at some constant rate μ (so that Emt+s = mt + sμ), then Equation A9 can be shown to imply that pt = mt + γμ.

  1. Interpret this result.

  2. What happens to the price level pt when the money supply mt changes, holding the money growth rate μ constant?

  3. What happens to the price level pt when the money growth rate μ changes, holding the current money supply mt constant?

  4. If a central bank is about to reduce the rate of money growth μ but wants to hold the price level pt constant, what should it do with mt? Can you see any practical problems that might arise in following such a policy?

  5. How do your previous answers change in the special case where money demand does not depend on the expected rate of inflation (so that γ = 0)?

1 Milton Friedman and Anna J. Schwartz, A Monetary History of the United States, 1867–1960 (Princeton, NJ: Princeton University Press, 1963); Milton Friedman and Anna J. Schwartz, Monetary Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest Rates, 1867–1975 (Chicago: University of Chicago Press, 1982).

2 Stanley Fischer, “Seigniorage and the Case for a National Money,” Journal of Political Economy 90 (April 1982): 295–313.

3 Mathematical note: This equation relating the real interest rate, nominal interest rate, and inflation rate is only an approximation. The exact formula is (1 + r) = (1 + i)/(1 + π). The approximation in the text is reasonably accurate as long as r, i, and π are relatively small (say, less than 20 percent per year).

4 Robert B. Barsky, “The Fisher Effect and the Forecastability and Persistence of Inflation,” Journal of Monetary Economics 19 (January 1987): 3–24.

5 See, for example, Chapter 2 of Alan Blinder, Hard Heads, Soft Hearts: Tough-Minded Economics for a Just Society (Reading, MA: Addison Wesley, 1987).

6 Robert J. Shiller, “Why Do People Dislike Inflation?” in Reducing Inflation: Motivation and Strategy, edited by Christina D. Romer and David H. Romer (Chicago: University of Chicago Press, 1997), 13–65.

7 The movie made about forty years later hid much of the allegory by changing Dorothy’s slippers from silver to ruby. For more on this topic, see Henry M. Littlefield, “The Wizard of Oz: Parable on Populism,” American Quarterly 16 (Spring 1964): 47–58; and Hugh Rockoff, “The Wizard of Oz as a Monetary Allegory,” Journal of Political Economy 98 (August 1990): 739–760. It should be noted that there is no direct evidence that Baum intended his work as a monetary allegory, so some people believe that the parallels are the work of economic historians’ overactive imaginations.

8 For an examination of this benefit of inflation, see George A. Akerlof, William T. Dickens, and George L. Perry, “The Macroeconomics of Low Inflation,” Brookings Papers on Economic Activity 1996, no. 1: 1–76. Another argument for positive inflation is that it allows for the possibility of negative real interest rates. This issue is discussed in Chapter 12 in an FYI box on The Liquidity Trap.

9 For more on these issues, see Thomas J. Sargent, “The End of Four Big Inflations,” in Inflation, edited by Robert Hall (Chicago: University of Chicago Press, 1983), 41–98; and Rudiger Dornbusch and Stanley Fischer, “Stopping Hyperinflations: Past and Present,” Weltwirtschaftliches Archiv 122 (April 1986): 1–47.

10 The data on newspaper prices are from Michael Mussa, “Sticky Individual Prices and the Dynamics of the General Price Level,” Carnegie-Rochester Conference on Public Policy 15 (Autumn 1981): 261–296.

11 This model is derived from Phillip Cagan, “The Monetary Dynamics of Hyperinflation,” in Studies in the Quantity Theory of Money, edited by Milton Friedman (Chicago: University of Chicago Press, 1956): 25–117.

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