The Online Library of Liberty

A project of Liberty Fund, Inc.

• Foreword
• Geoffrey Brennan
• Preface
• Acknowledgments
• The Power to Tax
• 1.: Taxation In Constitutional Perspective
• 1.1.: The Notion of a “constitution”
• 1.2.: The Logic of a Constitution
• 1.3.: The Means of Constitutional Constraint
• 1.4.: The Wicksellian Ideal and Majoritarian Reality
• 1.5.: The Power to Tax
• 1.6.: The Enforceability of Constitutional Contract
• 1.7.: Normative Implications
• 2.: Natural Government a Model of Leviathan
• 2.1.: Leviathan As Actuality and As Contingency
• 2.2.: Monopoly Government and Popular Sovereignty
• 2.3.: The Model of “leviathan”: Revenue Maximization
• 2.4.: The Model of Leviathan As Monolith
• 2.5.: The Constitutional Criteria
• 3.: Constraints On Base and Rate Structure *
• 3.1.: Government As Revenue Maximizer Subject to Constitutional Tax Constraints
• 3.2.: Tax-base and Tax-rate Constraints In a Simple Model
• 3.3.: One Among Many
• 3.4.: Tax Limits and Tax Reform
• Appendix: Progression In the Multiperson Setting
• 4.: The Taxation of Commodities
• 4.1.: The Conventional Wisdom
• 4.2.: Constitutional Tax Choice
• 4.3.: Alternative Forms of Commodity Tax: the Choice of Base
• 4.4.: Uniformity of Rates Over Commodities
• 4.5.: Uniformity of Rates Over Individuals
• 4.6.: Discrimination By Means of the Rate Structure
• 4.7.: Summary
• Appendix
• 5.: Taxation Through Time Income Taxes, Capital Taxes, and Public Debt
• 5.1.: Income Taxes, Capital Taxes, and Public Debt In Orthodox Public Finance
• 5.2.: The Timing of Rate Announcement
• 5.3.: Income and Capital Taxes Under Perpetual Leviathan
• 5.4: Leviathan’s Time Preference
• 5.5.: The Time Preference of the Taxpayer-citizen With Respect to Public Spending
• 5.6.: The Power to Borrow
• 5.7.: Conclusions
• 6.: Money Creation and Taxation
• 6.1.: The Power to Create Money
• 6.2.: Inflation and the Taxation of Money Balances: a “land” Analogy
• 6.3.: Inflation and the Taxation of Money Balances
• 6.4.: Inflationary Expectations Under Leviathan
• 6.5.: Inflation, Wealth Taxation, and the Durability of Money
• 6.6.: The Orthodox Discussion of Inflation As a Tax
• 6.7.: The Monetary Constitution
• 6.8.: Inflation and Income Tax Revenue
• 6.9.: Monetary Rules and Tax Rules
• 7.: The Disposition of Public Revenues *
• 7.1.: The Model
• 7.2.: Public-goods Supply Under a Pure Surplus Maximizer: Geometric Analysis
• 7.3.: The Surplus Maximizer: Algebraic Treatment
• 7.4.: The Nonsurplus Maximizer
• 7.5.: Toward a Tax Policy
• 8.: The Domain of Politics
• 8.1.: Procedural Constraints On Political Decision Making
• 8.2.: The Rule of Law: General Rules
• 8.3.: The Domain of Public Expenditures
• 8.4.: Government By Coercion
• 9.: Open Economy, Federalism, and Taxing Authority
• 9.1.: Toward a Tax Constitution For Leviathan In an Open Economy With Trade But Without Migration
• 9.2.: Tax Rules In an Open Economy With Trade and Migration
• 9.3.: Federalism As a Component of a Fiscal Constitution
• 9.4.: An Alternative Theory of Government Grants
• 9.5.: A Tax Constitution For a Federal State
• 9.6.: Conclusions
• 10.: Toward Authentic Tax Reform Prospects and Prescriptions
• 10.1.: Taxation In Constitutional Perspective
• 10.2.: Tax Reform As Tax Limits
• 10.3.: Tax-rate Limits: the Logic of Proposition 13
• 10.4.: Tax-base Constraints
• 10.5.: Aggregate Revenue and Outlay Limits: Ratio-type Proposals For Constitutional Constraint
• 10.6.: Procedural Limits: Qualified Majorities and Budget Balance
• 10.7.: Toward Authentic Tax Reform
• Epilogue

6.3.

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, D_m. 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:

• 1. The current or initial-period portion of the “price,” which is simply the initial-period $1 held in the form of monetary assets; plus
• 2. The present value of the increments to the initial allocation of resources to money balances that will be required in order to maintain the same real (and desired) stock of real balances. (Since no increments need be added in the noninflationary regime, this second term becomes zero; hence, as noted above, the capital value of a dollar’s worth of real balances in perpetuity is $1.)

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
     (4)
Hence, the “price” for a dollar’s worth of real money balances, in M₀ dollars, is

The revenue-maximizing government will select that rate, i*, which given the demand for money, D_m, will maximize
     (5)
because money is costless to produce.6 This maximum is obtained when
     (6)
or when
     (7)
a familiar condition requiring that the price elasticity of the D_m curve in Figure 6.3 be unity. Note that this problem is again almost equivalent to that confronting the land monopolist discussed above. The one difference is that the value placed on any stock of real money balances can only be altered by changing i, rather than some independently measurable physical quantity.

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.