A constituent monetary unit within a larger unified holding can be deployed against a broader range of an economy’s product than the same nominal unit within a smaller holding.
Someone with a larger holding might therefore ask: “Why should a unit of my money transact at par with an identical unit of yours when, by virtue of my wealth, the next unit of money I receive can be redeemed against more of the economy’s output than can that same unit received by you?” Why should we suppose that nominal equivalence of identical money should equal real equivalence when in different hands?
The difference is not merely a property of the holding as a whole: it attaches to the constituent monetary unit while it participates in that holding. A unit within the larger holding therefore possesses purchasing possibilities unavailable to the same nominal unit within the smaller holding. The facial nominal equivalence of the two units alone provides no reason to presume real equivalence between them.
If reducing a holding by one monetary unit leaves each of the remaining monetary units, individually and collectively, capable of commanding a lesser portion of the real economy than they previously could, then the real economic loss cannot be confined to the monetary unit that was transferred. A nominal transaction records the unit that moved; it does not record the change in the real purchasing capacity of all the units that did not move, nor the change in the real purchasing capacity of the unit as it passes between holdings of different scale.
A transfer between holdings of greater and lesser aggregation may therefore entail not merely the nominal transfer observed, but a further transfer of real purchasing power arising from the change in aggregation—not apparent from the nominal transfer, as with tax incidence. As money circulates through aggregation and disaggregation, real purchasing command may consequently be redistributed whilst the fact of that redistribution remains nominally undetected.
Smaller holders routinely transfer monetary claims containing latent purchasing possibilities they cannot themselves exercise. Concentrated holders aggregate those same claims, make the latent possibilities exercisable, and thereby acquire greater command over production. Because that concentrated demand directs what gets produced, wealth concentration operates as a private system of economic planning.
The apparently one-dimensional monetary scalar may therefore fail to represent the real economic properties of money across different scales of aggregation.
If the size of the holding to which a monetary unit belongs alters the real purchasing power of that unit, then existing monetary theory and extant general theories of microeconomics and macroeconomics would appear to be incomplete.
The proposition is simple to state but remarkably difficult to think through consistently. The presumption that the nominal equivalence of two monetary units entails their real equivalence is so deeply embedded in ordinary economic thought that even an inquiry intended to test it can quietly reintroduce it.
We have followed the proposition considerably further than we have attempted to do here. Confined strictly to economics, the questions are, needless to say, numerous: whether nominal fungibility conceals an asymmetry in real fungibility across different scales of monetary aggregation; what shape the relationship between nominal holding size and real purchasing command takes; whether, in practice, that relationship is continuous or instead changes at critical thresholds at which new baskets or combinations of goods, assets, or transactions become accessible; whether arbitrage tends to produce a constant slope in the seigniorage-like return across scales of aggregation, or whether market power of different kinds curves that relationship; whether the monetary sovereign stands apart because it has no superior monetary domain; what the real money supply is, and how it should be conceptualized and measured; whether a payment from a larger holding entails the surrender of further opportunities for disaggregation, and whether that forgone purchasing command enters into price; whether a loan, by moving a holding across an aggregation threshold, increases the purchasing command of the holding as a whole, and, if so, what charge is levied for that leverage, where that charge appears, and whether conventional interest captures it at all; whether the aggregation effect survives even in the absence of conventional transaction costs or market frictions, since the relevant distinction concerns the opportunity set of the unified holding itself; whether attempts to arbitrage away differences between lesser and greater holdings necessarily require aggregation, such that the mechanism required to eliminate the advantage of aggregation is aggregation itself; whether corporate forms, joint-stock ownership, mergers, conglomeration, and internal capital markets can be understood partly as institutions for preserving or increasing the purchasing possibilities created by unified monetary control, independently of conventional economies of scale or productive synergy; whether some portion of the value conventionally attributed to corporate scale therefore represents a return to unified monetary control itself; whether the services by which monetary claims are aggregated are themselves subject to the aggregation effect, such that a larger holding may acquire further aggregation, or finance the aggregation of lesser holdings, at a lower relative cost than those lesser holdings could achieve independently; whether this produces increasing or recursive returns to monetary aggregation independent of economies of scale in production; where the incidence of gains and losses arising from aggregation and disaggregation ultimately falls, and whether it appears in price itself or elsewhere; how these relationships interact with inflation, consumption, investment, monetary velocity, and countless other economic variables; whether changes in monetary aggregation and disaggregation, and their role in transfer, bear any systematic relationship to macroeconomic fluctuations; what governs the relationship between the scale of monetary holdings and the scale of real resources transferred over time; and how much organized human capacity—and how much human well-being—can a sufficiently large monetary holding command through an ongoing aggregate holding advantage? And so forth, and forth again.
Insight is not merely preliminary to the detailed work that follows. An idea that changes the terms of a problem—what may be assumed, what must be explained and what conclusions remain available—has already done substantive work. Its further formalization, testing and extension may belong to others. The ideas posted here are the contribution.