Etienne Mantoux died a week before World War II ended. The multiplier is taught in economics 101. Etienne Mantoux was not a fan of the multiplier.
This brings us to the multiplier theory, under which Keynes merely develops some reflections due to R. F. Kahn on the incremental effects of a capital investment. Obviously the movements of capital entailed by investing a certain sum devoted, say, to the execution of a given public works program, will not be confined to the original sum, and a certain amount of additional investments will result, after a varying interval of time, from that initial outlay. The sums invested will more or less rapidly permeate the structure of production, first leading to expenditures among enterprises, and later, when they reach the consumer through payment of wages or other income, causing a demand for consumption goods, which in turn will step up demand for intermediate goods, and so on.
Most analyses of this highly complex phenomenon assume, as we have seen, that all the factors of production are employed. In that case a new investment can only have the effect, in production as a whole, of transferring factors from one branch to another, most often from the consumption goods to the production goods market. It then becomes difficult to speak of net secondary effects of the initial investment, since their addition does not go to augment total output. Kahn’s multiplier measured the ratio of the immediate increment of employment, due to a given investment, to the total increment. Keynes here defines his investment multiplier as the ratio of the total increment of income brought about by a given increment of investments, to this original increment (Y income, I investment, multiplier k=ΔY/ ΔI).
One might first point out that it is very hard to tell what moment to choose for evaluating the final result Y. The interval between the initial outlay and the time when the money invested reaches consumers is not only highly variable, but scarcely amenable to averaging without recourse to some concept like the “Austrian” theory’s “period of production”— apparently not very congenial to Keynes. His “period of production”, defined in terms of the time elapsed before increased demand for a given product expresses itself in a diminished elasticity of employment, looks very much like a petition principii. But the effects of the multiplier, approximate as they are, are indubitable. Far more debatable is the function making the multiplier depend on the propensity to consume. The latter is equal, by definition, to 1-1/k. since income is divided between consumption expenditures and investment expenditures.
Given the definition of the multiplier, the propensity to consume therefore becomes equal to 1-1/k, which amounts to saying that as the propensity to consume approaches unity, meaning if the community applies the totality of its income to consumption expenditures, the secondary effects of a primary investment would approach infinity. Remarkable!