CH. 10 THE MARGINAL PROPENSITY TO CONSUME 115

and can easily be stated in a formally complete fashion—into the propositions that ΔCω and ΔY W have the samesign, but ΔYω > ΔCω, where Cω is the consumption interms of wage-units. This is merely a repetition ofthe proposition already established on p. 29 above.

Let us define, then, dCω/dYω as the marginal propensity toconsume.

This quantity is of considerable importance, be-cause it tells us how the next increment of output willhave to be divided between consumption and invest-ment. For ΔYω = ΔCω + ΔIω , where ΔCω and Δlω arethe increments of consumption and investment; so that

we can write ΔYω = kΔIω, where I - I/k is equal to the

marginal propensity to consume.

Let us call k the investment multiplier. It tells usthat, when there is an increment of aggregate invest-ment, income will increase by an amount which is ktimes the increment of investment.

II

Mr. Kahn’s multiplier is a little different from this,being what we may call the employment multiplier de-signated by k', since it measures the ratio of the in-crement of total employment which is associated witha given increment of primary employment in the in-vestment industries. That is to say, if the incrementof investment Δlω leads to an increment of primaryemployment ΔN2 in the investment industries, the in-crement of total employment ΔN =k'ΔN2 .

There is no reason in general to suppose that k = k'.For there is no necessary presumption that the shapesof the relevant portions of the aggregate supply func-tions for different types of industry are such that theratio of the increment of employment in the one set ofindustries to the increment of demand which has