This is a single-author, article-length theoretical essay in monetary macroeconomics, marked as previously unpublished. Its scope is a conceptual correction of multiplier theory: Mahr does not deny that expenditure generates income, but argues that the conventional Keynesian/geometric multiplier is unusable so long as it sums an income sequence without a definite accounting period.
Der entscheidende Mangel der herrschenden Multiplikatortheorie liegt in der Vernachlässigung des Zeitfaktors.
English translation: The decisive defect of the prevailing multiplier theory lies in the neglect of the time factor.
Mahr’s first move is to bind the multiplier to national-income measurement. Since income is always calculated for a period, normally a year, the multiplier must also be annual. The relevant delays—between receipt of income, expenditure of it, and renewed income formation—are expressed by the circulation velocity of money, not by an abstract propensity alone.
Die Zeitdimension läßt sich aus dem Begriff des Volkseinkommens nicht wegdenken.
English translation: The time dimension cannot be thought away from the concept of national income.
For multiplier analysis the decisive magnitude is the marginal velocity of newly circulating money. Mahr defines it through the “Einsatzperiode des Geldes,” the time for which invested money is tied up in production and sale.
Dabei kommt es für die Multiplikatortheorie auf die marginale Kreislaufgeschwindigkeit an, d. i. die Zahl der einkommensbildenden Umsätze des zusätzlich in Umlauf gesetzten Geldes innerhalb eines Jahres.
English translation: For multiplier theory what matters is the marginal velocity of circulation, i.e. the number of income-creating turnovers of the additionally issued money within a year.
The essay’s central numerical example—a depressed economy falling from 20 to 12 billion monetary units, with a one-billion state injection and marginal velocity of 4—shows the consequence. Without hoarding, the annual income increase is four billion and then persists at the higher level. With repeated hoarding, the multiplier quickly dwindles; the indefinite sum produced by the standard formula gives little practical guidance for annual national-income calculation. Mahr therefore replaces the inherited formula with a monetary-flow definition.
Der Multiplikator ist vielmehr zweckmäßigerweise zu definieren als der Koeffizient, welcher die Zunahme des Volkseinkommens während eines Jahres im Gefolge einer Vermehrung der zirkulierenden Geldmenge zum Ausdruck bringt.
English translation: The multiplier is rather to be defined expediently as the coefficient which expresses the increase of national income during a year in the wake of an increase in the circulating quantity of money.
The thesis follows as $k = K_m = \Delta E / \Delta G$: the multiplier is the marginal circulation velocity, the ratio of annual income growth to the increase in circulating means of payment. This repositions Keynes’s investment multiplier within the broader problem of supplying a growing market economy with money.
Das Problem des Investitionsmultiplikators ist im Grunde nur ein Teil des weit umfassenderen Problems der angemessenen Versorgung einer wachsenden Wirtschaft mit Zahlungsmitteln.
English translation: The problem of the investment multiplier is fundamentally only one part of the far broader problem of the adequate supply of a growing economy with means of payment.
Mahr then widens the argument historically and institutionally. Before 1914 private banks enlarged the money-income stream in booms and contracted it in crises through reserve and credit policy; postwar statistical knowledge, reserve regulation, and central-bank practice moderated those swings. The core distinction is between temporary credit and durable additions to circulation. Short-term credit has a multiplier only if it remains available beyond one circulation period; otherwise it creates income once and disappears.
From this standpoint, public investment, open-market purchases, bank purchases of securities, active balance-of-payments effects, and the dissolution of hoards are variants of the same mechanism when they add circulating money without offsetting cuts elsewhere. Conversely, reserve accumulation, open-market sales, passive external balances, and private hoarding generate a negative multiplier by shrinking the money-income stream. Keynesian public works are important, but not foundational.
Der Keynes'sche Investitionsmultiplikator und der Exportmultiplikator sind nur Spezialfälle dieser Erscheinung.
English translation: Keynes's investment multiplier and the export multiplier are only special cases of this phenomenon.
The treatment of hoarding shows Mahr’s most important conceptual move. “Leakage” is not an external correction to a timeless formula; it lowers the average marginal velocity of additional money within the year.
Die Lösung ist hier ziemlich einfach: das Versickern senkt die durchschnittliche Kreislaufgeschwindigkeit des zusätzlichen Geldes.
English translation: The solution here is rather simple: the leakage lowers the average velocity of circulation of the additional money.
The essay’s relevance is therefore its integration of multiplier and velocity analysis. It preserves the policy significance of public spending in depression—especially when central-bank instruments fail—while demoting the investment multiplier from a special Keynesian law to one case of a general principle: annual changes in monetary national income depend on how much additional money circulates and how often it becomes income-forming.
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