Fritz Machlup, “Period Analysis and Multiplier Theory” (1939)

Machlup’s essay is a theoretical intervention into Keynes-Kahn multiplier analysis, written to show that the multiplier cannot be treated as a timeless relation among investment, income, saving, and consumption. Its central claim is methodological: multiplier theory becomes misleading when it states final ratios without analyzing the temporal process by which income is received, spent, and re-received.

This article is not an exegesis of the theory of the Multiplier; nor is it a critique; it attempts merely to be an analysis of some essentials of that theory.

The article’s first task is therefore to replace vague simultaneity with period analysis. Machlup distinguishes transaction periods, income periods, plan adjustment periods, and equilibrium adjustment periods, because each captures a different lag in the propagation of expenditure. Keynesian terminology, he argues, is too blunt for this purpose: it does not adequately separate the dates of payment, receipt, planning, and adjustment. The multiplier must be studied as a sequence rather than as an instantaneous algebraic multiple.

For a discussion of time lags, transition phases, and other intertemporal relationships, Keynesian terminology is not well suited.

Machlup’s road-building example gives the argument its practical force. Public wages become consumer purchases; those purchases become shop or factory receipts; only later do they become wages, profits, or other incomes to be spent again. Between the initial outlay and later income rounds lie inventories, wholesale transactions, production schedules, pay dates, and individual expenditure habits. The crucial analytical object is thus not one person’s pay interval, but an average “income propagation period” that measures how long it takes expenditure to become income again.

This temporal reconstruction changes the meaning of the multiplier. Machlup does not deny that a final multiplier can be written down under simplifying assumptions. He insists, however, that the final multiple is not reached at once. The higher the propensity to consume, the larger the eventual multiplier, but also the longer the adjustment path. For fiscal policy, this distinction matters: a government concerned with the coming quarter or fiscal year may receive only a fraction of the eventual cumulative income effect.

The statement that an increase in the rate of investment will raise the rate of income by an amount which is a certain multiple of the amount of the additional investment can be true only after the lapse of a certain period of adjustment.

Machlup also separates a behavioral propensity to consume from an ex post accounting ratio. If the propensity is meant to describe how households plan expenditure out of received income, it cannot be identical with a tautological relation observed after income and investment have adjusted. This distinction allows him to criticize overly neat versions of multiplier theory without abandoning its core insight. The process is driven by plans, expectations, and habits that may remain stable for a time, but that may also change under the impact of public works, altered confidence, credit conditions, prices, inventories, or interest rates.

The concept of a plan adjustment period rests on the fact that plans remain unchanged over a certain time interval, even if conditions change.

His treatment of “leakages” follows the same logic. Saving out of secondary income need not mean literal hoarding; it may repay debt, purchase securities, finance government borrowing, or alter liquidity positions. For the immediate consumption multiplier, the common feature is that the money is not spent on consumers’ goods in the next round. But Machlup warns that these financial channels can later affect interest rates, credit availability, and private investment, so they cannot be permanently ignored.

The essay also complicates the common view that imports are simple leakages. Imports create income abroad, and that foreign income may induce demand for exports from the original country. Only in special cases, such as a very small country with negligible feedback from foreign expenditure, can imports be treated as a straightforward subtraction from the domestic multiplier.

Machlup’s conclusion is neither anti-Keynesian nor anti-multiplier. Rather, he demands that multiplier theory become explicitly temporal, institutional, and conditional. Its usefulness depends on specifying propagation lags, adjustment periods, saving behavior, foreign-trade feedbacks, financial reactions, and induced private investment. The final multiple is less important than the dated path by which it is approached.