George L. S. Shackle, “The Multiplier in Closed and Open Systems”

Shackle’s article is a compact theoretical reconstruction of the Keynesian multiplier. Its central aim is to separate the multiplier as a logical ratio from the dynamic process through which output, stocks, expectations, and entrepreneurial decisions actually change. He begins by insisting that the relevant magnitudes are flows, not stocks: income, consumption, investment, and accumulation must be read as rates per unit of time.

That is to say, each of these variables represents a speed (or time-rate) and is measured as so many units of money value per unit of time, or so many units of physical quantity per unit of time.

This temporal vocabulary matters because Shackle treats the multiplier as an ex ante relation among intended rates. In its first form, the theorem follows from the marginal propensity to consume: when income changes, income-receivers divide the increment between consumption and accumulation. The multiplier ratio is therefore immediately implied by behavior toward additional income, but it does not yet explain how production comes to adjust.

In the first it is an immediate inference from an assumption about the tastes of individuals in the choice between consuming and accumulating income.

The crucial distinction is between the conduct of income-receivers and the conduct of entrepreneurs. Consumers may wish to spend a determinate fraction of additional income, but that fact alone cannot cause firms to expand the production of consumption goods. The multiplier becomes a theory of output only when one adds assumptions about entrepreneurial reactions to sales, inventories, expected income, and intended investment.

This inherent behaviour-pattern of income-receivers is not capable by itself of explaining why an increase in the output of goods intended as additions to equipment should give rise to an increase in the output of goods intended to be consumed.

Shackle’s criticism is therefore directed against overly mechanical presentations of the multiplier. The standard doctrine often writes the equality between intended accumulation and actual saving as if it were automatic. Shackle instead stresses the possible divergence between what entrepreneurs intend to add to equipment and what income-receivers, through their spending decisions, permit to be accumulated.

Hitherto in expressing the multiplier principle authors have assumed equality.

In the closed-system model, this divergence appears most clearly when entrepreneurs attempt to raise the rate of accumulation. The additional production becomes income; recipients spend part of it on consumption; and unless consumer-goods output also rises, inventories of consumer goods are run down. The multiplier process is thus a sequence of adjustments, not an instantaneous identity.

If a larger proportion than $1 - \lambda$ of the increment of general output is intended by entrepreneurs to constitute a growth of equipment, then stocks of goods ready for consumption will begin to be depleted.

The article’s middle sections generalize the argument beyond a one-good economy. Output must be valued, separated into consumption goods and equipment goods, and related to the changing composition of stocks. Shackle’s use of ex ante concepts is deliberate: actual income over a future interval depends partly on what individuals expect their incomes to be, since those expectations affect current spending. The multiplier is therefore intertwined with expectations rather than independent of them.

The open-economy extension adds the export surplus to the same analytical field as investment. Goods produced at home but not consumed at home, when exported in excess of imports, function like additions to accumulation from the standpoint of the domestic propensity to consume. A rise in the export surplus can therefore initiate expansion in the same formal way as a rise in investment, while a fall in exports or rise in imports can transmit contraction.

Shackle’s enduring contribution is to preserve the Keynesian multiplier while denying that it is a complete dynamic mechanism by itself. The ratio follows from the marginal propensity to consume; the path of income depends on entrepreneurial adjustment, inventories, investment inducement, international leakages, and expectations. The article is thus a clarification of Keynesian theory: it shows why the multiplier is logically powerful but empirically incomplete unless embedded in a theory of time, plans, and changing anticipations.