Front Page Titles (by Subject) 6.3.: Inflation and the Taxation of Money Balances - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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6.3.: Inflation and the Taxation of Money Balances - James M. Buchanan, The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution) 
The Collected Works of James M. Buchanan, Vol. 9 The Power to Tax: Analytical Foundations of a Fiscal Constitution, Foreword by Geoffrey Brennan (Indianapolis: Liberty Fund, 2000).
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Inflation and the Taxation of Money Balances
Comparison of money and the land analogy. In some ways, money is similar to the land in our simple example, but in other ways it is profoundly different. It is similar in the sense that the time profile of supply determines the “price” in each period: all future releases onto the market will be taken into account in determining current prices. To the extent that individuals’ expectations about those future releases are in error, individuals will bear capital losses and government can increase its revenue acquisitions from sale above the “maximum revenue yield,” L*Q*. In much the same way, the demand for money depends on expectations about the future quantity of money that government may release. If those expectations are wrong, the government might obtain revenue significantly in excess of the maximum revenue yield when expectations about the future course of the money supply are completely accurate.
It will be useful to try to conceptualize the problem so as to make it as closely analogous as possible to the simpler land example introduced above. We can depict, in Figure 6.3, a “demand curve” for real money balances, Dm. Care must be taken, however, in defining the units to be measured, along both the abscissa and the ordinate. Along the abscissa, we measure the quantity of real money balances, but it is useful to define these in units of initial period dollars, M0. Along the ordinate, we want to measure the “prices,” or current capitalized costs, that individuals face in holding differing quantities of real balances, so measured, in perpetuity.
In this conceptualization, the demand curve for real money balances in Figure 6.3 becomes analogous to that for land in Figure 6.2. But there is an extremely important distinction between land and money that emerges here. As noted earlier, with land the supply or stock is measured in units of physical quantity directly (in acres, square miles, or square feet). The number of such physical units expected to be in productive use determines the prices that persons are prepared to pay for rights to permanent usage. The monopoly supplier can determine this price, or value, by changing the physical quantity offered for sale.
Money is dramatically different in this respect. It matters not at all whether money is denominated in dollars, dimes, or cents. The quantity of the nominal units of money, the parameter over which government may be allowed to exercise direct control, does not determine directly the value persons place on any given stock. The monopoly issuer of nominal money can determine the value that persons place on any given regime offering monetary services only by varying the rate of inflation—the rate of increase in the stock of nominal units. In a stationary or no-growth economy, the zero-inflation regime would yield to government an initial-period capital value, defined in units of initial-period money, M0, precisely equal to the number of units created in that period. The price per unit placed on this money stock, and hence on the permanent “rights” to the quantity of real money balances indicated by the appropriate point along the demand curve, would be, quite simply, $1. In this noninflationary regime, therefore, the capitalized value of the monopoly franchise to government is measured either by the area 0JCS or by the distance 0J in Figure 6.3.
In an inflationary regime, however, measurement of the capitalized value of a unit of real money balances becomes considerably more complex. In order to maintain a unit of real money balances in perpetuity, a person must reckon on suffering a current capitalized “cost” that is larger than the number of initial-period dollars held in the form of monetary assets. Hence, the “price” for a unit of real money balances, defined in M0, must exceed $1. Obversely, the value of the monopoly franchise to government must be larger per unit of real money balances under regimes with positive than with zero rates of inflation.
The “price” of a unit of real money balances, defined as a dollar’s worth of M0, to be maintained in perpetuity may be computed more precisely as follows:
In a regime with a preannounced and permanent positive inflation rate, i, invariant as among periods, there must be an increment in resource requirements in each period. To get a current capitalized value, these increments must, of course, be appropriately discounted. The aggregate cost of these increments in present-value terms is given by
The revenue-maximizing government will select that rate, i*, which given the demand for money, Dm, will maximize
With linear demand curves, the revenue-maximizing solution will be determined at that quantity of real money balances where marginal revenue equals marginal cost (in this case, zero), indicated by H in Figure 6.3. Note that the quantity of real money balances in this solution will always be precisely one-half that quantity which would be dictated by an “optimum” regime, where the negative rate of inflation must offset the positive real rate of interest.7
Quite apart from considerations relating to revenue-maximizing government, the formulation here is helpful in any assessment of the genuine opportunity costs of any regime of permanent and continuing inflation. By utilizing the formula M0 (1 + i/r), and by selecting values for i and for r, we can define the capitalized costs for a unit of real money balances under differing regimes. Consider, for example, an i of 10 percent, with an r of 2 percent, chosen as plausibly descriptive for the United States in 1980. In this case, the capitalized cost of a dollar’s worth of real balances, defined in the M0numéraire, is $6. This says, quite simply but dramatically, that the cost of maintaining a unit of resource value in the form of monetary assets in a continuing regime described by these parameters is six times the cost of maintaining a unit in a noninflationary regime. Even if the positive rate of inflation only matches the real rate of interest, the cost of maintaining real money balances doubles over that incurred in the zero-inflationary setting.
The foregoing analysis is applicable only to those settings where the government is presumed able to select one from among a set of alternative permanent inflationary regimes with rates of inflation stable through time, a selection that both individuals and the government treat as binding. In our land example, we noted that the government monopolist could guarantee against further exploitation by destroying a part of the total stock. Even in the absence of this sort of demonstrated protection, however, additional releases of land for sale, beyond the revenue-maximizing quantity offered in the initial period, would drive the incremental gains to government toward zero. Money is also quite different from land in this respect. Government can add to the nominal stock of money without limit and without necessarily driving the value of additional increments to zero. For example, if the population systematically believes that each current addition to the money stock is the last that will ever be made, the real revenue that the government can obtain approaches 0JCS (Figure 6.3) in each period. By an appropriately large increase in the number of units of nominal money, the government can reduce the value of all previously existent units to insignificance. On each occasion all individuals believe the increase in the money stock to be a once-and-for-all denumeration of the currency; but such a “once-and-for-all” denumeration occurs each period. Of course, no such set of expectations is in the least plausible, but the point remains that with an analogous set of expectations the same outcome could not emerge in the land case.
The crucial question in all this is clearly the delineation of a set of expectations that is plausible. What would it be reasonable for the taxpayer-money holder to believe about government monetary strategy? What expectations are “rational” in this setting? The answer clearly depends on the maximand which the taxpayer-money holder attributes to government, and the severity of the constraints (electoral and otherwise) which he believes to apply—that is, on the particular “public-choice” model which implicitly informs taxpayer-money holder-citizen actions. In keeping with our discussion elsewhere in this book, we wish to explore the implications of one particular model of “public choice”—the Leviathan model—which we believe to have considerable relevance, both potential and actual, to the real political world.
[6. ] The same capitalized price can be determined by asking the question: What is the present capitalized value of the revenue that the government obtains under an inflation rate, i, if the real money stock held each period is ? Now and is measured in some real numéraire. The real revenue that government obtains in each period is rM by virtue of interest on M that it does not have to pay, plus iM by virtue of deflating the real liability that money represents. This revenue stream is in terms of some real numéraire and must be capitalized by the real rate of return to yield to
[7. ] This solution is emphasized by Milton Friedman, “The Optimum Quantity of Money,” in The Optimum Quantity of Money and Other Essays (Chicago: Aldine-Atherton, 1969), pp. 1-50.