Archive for the ‘Multiplier’ Category

In the chapter 10 of his General Theory, Keynes writes:

For in given circumstances a definite ratio, to be called the Multiplier, can be established between income and investment…”

Below, he writes again:

Let us call k the investment multiplier. It tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment.

A quick look must be enough to see this statement is very odd. Indeed if, generally, an increase of the investment leads to an increase of the income, it is not necessary true: it happens sometimes, it even occurs constantly, that investments turn out to be hazardous and result in a loss. A fortiori, it seems very hard to determine by an aprioristic reasoning any positive « definite ratio » between income and investment.

So, the General Theory reader is bound to think the “multiplier” is only an historical or statistical law. Probably, Keynes studied the economic facts history on a determined period of time and managed, thanks to the available data, to determine what the average efficiency of investment was for this period. Then he considered – a bit hastily – these past average yields would constitute a good approximation of the future returns. So, he called this average efficiency of investment “k” or “the multiplier” (4).

Nevertheless, it appears Keynes doesn’t build up his “multiplier” theory on such statistical analyses. Indeed, in the General Theory, the value of the “multiplier” seems to be completely disconnected from the past average returns; it depends only upon a current data, namely the “(marginal) propensity to consume”, that is, the way in which an income is shared out among consumption and savings:

This quantity [the marginal propensity to consume] is of considerable importance, because it tells us how the next increment of output will have to be divided between consumption and investment. For ΔYw = ΔCw + ΔIw, where ΔCw and ΔIw are the increments of consumption and investment; so that we can write ΔYw = kΔIw, where 1 – (1/k) is equal to the marginal propensity to consume.”

The essence of the demonstration is contained in this paragraph (1).

So, Keynes thinks in this way:

Income = Consumption + Investment

Hence, if Consumption = (1-1/k) x Income,

Income = (1-1/k) x Income + Investment,

And Income = k x Investment

The Keynesian « multiplier » is thus mathematically defined as the reciprocal of the propensity to save.

Let us take the classical example. Let us say that, from an income of 100 $, 80 $ are allocated to consumption, and 20 $ to investment. As a consequence:

Income = 0.8 x Income + investment

0.2 x Income = Investment

Income = 5 x Investment

Thus, according to Keynes, if the propensity to consume is 0.8, the number “5” will constitute the “multiplier of investment”: each unity of investment will give lieu to five units of income. I quote again Keynes’ words: “Let us call k the investment multiplier. It tells us that, when there is an increment of aggregate investment, income will increase by an amount which is k times the increment of investment.

Imagine, dear Reader, you are just earning 100 $. You share out this sum among your right pocket and your left pocket. In the right pocket, you put 80 €, and in the left one, 20 $.

So you have:

Income = Right pocket + Left pocket

Income = 0.8 x Income + Left pocket

0.2 x Income = Left pocket

Income = 5 x Left pocket

Now, I ask you a question: how would you react if a Lord with a mustache approach you in the street and, introducing himself as The-best-economist-of-the-century, tell you: “My friend, I have an infallible plan in order to make you earn money. Since you Left pocket multiplier is 5, instead of putting 20 in this Left pocket, just put 40. As a result, you would have obtained 40 x 5 = 200 €”. You would look at him oddly, wouldn’t you?

This reasoning seems to be so absurd that I repeatedly wonder myself if I don’t misinterpret Keynes’s words. Now, the literal meaning of the sentences quoted above are perfectly clear, so I don’t see how I could have miscontrued them. Nevertheless, the Reader may naturally propose another interpretation of Keynes’s words.

I see numerous errors in what I think Keynes’s reasoning was, but I will focuse on only two of them (in order no to lose myself in incidental criticisms), the two which are the most egregious in my opinion: the confusion about the causality and the unusual monetary illusion.

I.   A Fanciful Causality

The main critique which, in my opinion, must be directed against the “multiplier” concept is that, the earning of the income occurring necessarily before its utilization, the amount of this income cannot be influenced by its utilization.

I know the Reader is exclaiming: “no, the way in which you invest has a direct impact on the amount of the income, because the future income is determined by the investment”.

You are perfectly right, dear Reader, but that is not my point. It is not the future income that the “multiplier” is supposed to determine; it really is the past one.

If you want to be persuaded of it, it is firstly needed to remind that, as I wrote it above, the value of the “multiplier” is computed, nor on the basis of a concrete analysis of the return that can be expected from a determined investment, neither with the average past return that we could expect to obtain again for the next years; the “multiplier” is determined only be examining the sharing out of income among investment and consumption, that is, according to the “propensity to consume”.

Secondly, the Reader must have in mind the fundamental distinction between two orders of things: between, on the first hand, the causal relationships, and, on the second hand, the “functional correspondences” (2).

The beloved Reader must not be frightened by such a barbaric vocabulary: I bet that, if ever he was not aware of this distinction, he will admit its validity very easily. He just needs to read the following two paragraphs.

Causality relationships concern outside reality, in particular the economic laws, and necessarily take place within the time: the cause necessarily comes before the effect, and the effect necessarily follows the cause (Sorry for the repetition of « necessarly », but in this context, I can’t help to do so). It is not possible to make the cause become the effect, nor, the effect, the cause. A handling about the effect cannot have any influence on the cause.

Functional relationships are those of the mathematics. These relationships necessarily take place out of the time, and so, out of the causality. In the equation « 3 x 4 = 12 », « 3 x 4 » is not antecedent to « 12 », and « 12» is not subsequent to « 3 x 4 ». Both terms are synchronous. In the same way, « 3 x 4» is not the cause of « 12 », and « 12 » is not the effect of « 3 x 4 »; indeed, you could inverse the terms, and write « 12 = 3 x 4 ».

If we were logic, we should not use the sign “=” in a causality relationship; we should rather use an arrow (a one direction arrow). Nevertheless, for reasons of convenience, it is evidently authorized to resort to the sign “=” to designate the causality, provided we don’t forget that the two terms, the cause and the effect, cannot be inversed.

We could believe only very dull men are able to err in this respect.

Yet, such a confusion (maybe a voluntary one) seems to be of the essence of the Keynesian theory of the “multiplier”, as I understand it.

The purely descriptive and mathematical relationship is transformed in a causal one, which is itself inversed.

Because “Income = 5 x Left pocket”, Keynes deduces “5 x Left pocket –> Income” (3).

Moreover, the amount indicated in the first term of the equation is the sharing out of the income which is mentioned in the second one; and, as I wrote it above, the earning of the income necessarily precedes its sharing out; as a consequence, the “multiplier” theory implies that the allocation of the income determines the amount of this same income, and so it supposes a real travel through the time.

II.  An unusual monetary illusion.

The charlatan economists of the times by-gone – the monetary cranks – worked out plans where the abundance of wealth was obtained thanks to the printing press. (Actually, Keynes is also an adept of the printing press, but not, or not necessarily, in the part of his theory where he sets out the “multiplier” concept.)

In other words, formerly, the illusion dealt with the quantity of money.

In contrast, the money illusion implied in the “multiplier” concept concerns the velocity of the money.

The “velocity” notion derives from the exchanges equation. This equation is erroneous. Even Keynes managed to criticize it in a thoughtful way. Nevertheless, in this equation, the “velocity” notion had not a too pernicious role. Indeed, it was supposed constant, and so can be tolerated. But, on the contrary, in the “multiplier” theory, this notion becomes the dynamic one; it goes mad.

The “multiplier” theory indeed supposes that some wealth is created (up to the nominal monetary amount of the deal) each time some money shifts in someone else hands.

Thus, if, on an income of 100, we hoard 20 and spend 80, the wealth will have increased by 80. If, on these 80, 64 are spent and 16 hoarded, the total wealth will have again increased by 64, etc, etc. Such is the “logic” of the “multiplier”.

So, according to Keynes (or, at least, according to the implications of “the logical theory of the multiplier”), money is not a mere wealth exchange instrument: it is a wealth creator instrument as well; money creates the wealth by its mere circulation. The use of money in order to exchange goods is the cause of the existence of the exchanged things. In this way, money is different from the other exchange instruments, as wagons or containers, which do not create what they make circulate.

By the way, this explains that, when Keynes speaks about “public investment”, he actually thinks to any public spending, regardless this spending is or is not engaged with a productive purpose. Why to think about the manner to spend the money, since, wherever this money goes, it will create wealth by its mere circulating?


(1)   On the following pages, Keynes speaks only about the factors which could vary at the margins the exact level of the “multiplier”.

(2)   Expression used by Mises in Human Action (Chapter V, 2°).

(3)   A big part of what I’m writing here has already been said by Henry Hazlitt in his  Failure of the New Economics, p135 and ff: “If investment is one-tenth of income, income will be ten times investment, etc. Then, by some wild leap, this “functional” and purely formal or terminological relationship is confused with a causal relationship. Next, the causal relationship is stood on its head and the amazing conclusion emerges that the greater the proportion of income spent, and the smaller the fraction that represents investment, the more this investment must “multiply” itself to create the total income!”.

(4) Thus, Hazlitt wondered, before implicitly concluding by the negative, « Is it an empirical generalization from actual experience?« 

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