Front Page Titles (by Subject) 6.2.: Inflation and the Taxation of Money Balances: A Land Analogy - The Collected Works of James M. Buchanan, Vol. 9 (The Power to Tax: Analytical Foundations of a Fiscal Constitution)
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6.2.: Inflation and the Taxation of Money Balances: A “Land” Analogy - 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: A “Land” Analogy
To establish the connection between inflation and the taxation of money balances, and to illustrate the crucial role of expectations, we find it helpful to introduce an analogy. We shift attention to “land,” assumed here to be an infinitely durable resource.4 Suppose that government monopolizes the supply of this land, defined in normalized homogeneous units, but that the total supply is more than sufficient to meet the needs of the population. These conditions ensure that some units of land would remain unoccupied even if land were made freely available. The efficiency-generating price would, of course, be zero.
Consider, now, a sequence of periods. Suppose that, in period 1, the monopoly government decides to sell some amount of land, in a setting in which no land has been sold. There are two elements that will enter into the price which the market is prepared to pay for the quantity of land offered for sale: the rental value of that land given the quantity released; and individuals’ expectations about the level of land supply, and hence the market value of land, in future periods. Consider Figure 6.1. In this diagram, we depict the annual marginal value product per unit of land on the vertical axis, and the quantity of land measured in homogeneous physical units (acres) on the horizontal axis. The MVP curve illustrates the way in which this annual marginal value product declines as the quantity of land in use increases. It indicates the price per acre that emerges in a market with free competition among buyers for an annual lease on the services of land, given the quantity of land released. For example, at quantity Q1 the price of an annual lease of 1 acre of land is V1. The aggregate supply of land is given by 0S, and is by construction such that MVP is zero at or before the quantity of land in use reaches 0S.
In our model, however, purchasers do not acquire annual leases but rather buy the right to permanent use. If the quantity of land Q1 is released for sale in period 1 and if Q1 is believed to be the quantity of land that will prevail indefinitely (i.e., if this is believed to be the only sale of land there will ever be), then the price per acre will be the capitalized value, L1 (depicted in Figure 6.2), of the annual marginal value products; that is,
Given that all buyers expect the quantity in each period to be that which will prevail forever, we can show the price per unit of land in Figure 6.2 as V/r with V determined from Figure 6.1. The curve D shows how the price per acre of land changes as the quantity in use changes, and is the same as the MVP curve with the vertical axis denominated in prices, L, for a perpetual flow of annual rentals, V, or V/r. In Figure 6.2, the loss to period 1 purchasers can be depicted as the shaded area (L1 - L2)Q1: this is the additional revenue that government has obtained from being able to “fool” period 1 purchasers.
Of course, if the precise timing of the release of land for sale is known beforehand, each “generation” of buyers will pay for rights to ownership of land only the capitalized value of the future rental streams that the land makes possible. Hence, “generation 1” buyers would be prepared to pay for each unit of land a price, P1, which is
In this case, where the time pattern of release of land for sale is fully known by all purchasers, no capital losses will be sustained by any buyer: each buyer will earn a normal rate of return on land. Obversely, the government cannot obtain additional revenue from unanticipated land sales. In this case of perfect expectations, what would be the government’s (monopolist’s) revenue-maximizing strategy?
Since the time pattern of release is known, the revenue-maximizing arrangement is to maximize the rental value of the land stock in each period. This maximum is depicted in Figure 6.1 as V*, prevailing when the supply of land is Q*, and is derived from MVP in exactly the same way as we derived the maximum revenue solution in the single-period cases analyzed in Chapters 3 and 4 (with the special consideration that here “marginal cost” is zero). Geometrically, with MVP linear, Q* is half Qm. This revenue maximum depends of course on our assumptions that the total quantity of land is more than sufficient to satiate all demands, and that the resource is infinitely durable. The government will release the entire revenue-maximizing supply, Q*, all in the first period. To fail to release any part of that quantity in period 1 would involve an unnecessary sacrifice of revenue in that period.
This revenue-maximizing solution, analogous to the single-period case, depends crucially on the assumption that the future course of land release is completely and accurately predicted by purchasers. But precisely as with the capital tax discussed in Chapter 5, the purchasers of land in this example can only be secure in their predictions about government’s future release of land for sale if government undertakes a binding commitment that purchasers consider to be effectively constraining. If individuals do not really believe that any sale of land will be the final one as long as any land is held by government, they may not purchase land at any price. In this case, we are back in the dilemma-type situation discussed in Chapter 5; both individuals and Leviathan can be made better off by a mutually binding agreement. In the land example, a visible destruction of some part of the total supply might suffice.
Suppose, however, that individuals are not fully “rational” in this expectational sense and that they simply predict that the supply of land in each period will prevail indefinitely without any guarantee to that effect. What is the government’s revenue-maximizing strategy in this imperfect expectational setting? Here, government can obtain the full surplus to be derived from land. By adding an additional unit of land in each period, a set of prices for land will be traced out which follows D in Figure 6.2 exactly—aggregate government revenue will be the area under D.5
[4. ] We do not imply here that the “land” resource as defined in this model has a real-world counterpart. Our purpose is to isolate those features of a resource that may assist in explaining the money-creation power.
[5. ] This assumes that the additional price obtained over the range up to Q* compensates government for the interest it forgoes in postponing the receipt of revenue from the sale of extra units. For example, in period 1, Leviathan could either release Q1 units at price L1, aiming to release an extra (Q2-Q1) units next period, or could release all Q2 units at price L2. In the former case, it obtains (1’) in period 1 values, because it has to wait until period 2 to obtain the revenue from the extra (Q2-Q1) units. In the latter case it obtains Q2L2 (2’) in period 1 values. The former will exceed the latter only if Q2(L1 − L2 > r (L2Q2 − L1Q1). (3’) In the range above L*, the right-hand side of (3’) is positive and may exceed the left-hand side. If so, Leviathan will move instantly to (L*, Q*) and proceed to add successive units beyond Q*. In this range, the right-hand side of (3’) is negative, so that (3’) always holds.