This chapter looks difficult. But it’s not really. The reason is that everyone who learns anything about Keynes learns about the multiplier, or how increases in investment boost aggregate income by some multiple of the original increase, because the receivers of the original injection spend most of it on other stuff, and then the people who get that income spend most of it, and so on. Keep in mind that this is basically what Keynes is getting at and you can work through it. My main interest here is to see how closely the chapter as Keynes wrote it matches what we get taught in Keynes 101.
First, Keynes defines the multiplier as the “definite ratio… between income and investment and, subject to certain simplifications, between the total employment and the employment directly employed on investment…” [p. 113] This ratio is ‘definite’ given a certain propensity to consume – if that propensity changes, so does the multiplier. But since we are mainly interested in changes in the rate of investment, we need the concept of the marginal propensity to consume. That is, what proportion of an increase in income will be consumed. Remember from the last two chapters that as income rises, consumption rises, but not as much.
The change in aggregate income equals the change in consumption plus the change in investment. Since the change in consumption is dependent on the change in investment, we can remove consumption from the equation: The change in aggregate income equals the investment multiplier times the change in investment. (Remember everything is denominated in wage-units.)
Note that this investment multiplier is not the same thing as the plain old multiplier defined above, which is about the relationship between the proportion of income consumed and the proportion invested. The investment multiplier is related to the marginal propensity to consume: The marginal propensity to consume is 1 minus [one divided by the investment multiplier].
Keynes doesn’t show how this is derived but it is pretty basic, ignore this if it’s obvious or you don’t care: (In the following Δ represents change; C = consumption; c = marginal propensity to consume; I = investment; Y = income; k = the investment multiplier)
ΔC = c(ΔY) (The change in consumption equals the marginal propensity to consume times the change in income.)
ΔY = kΔI (The change in income equals the investment multiplier times the change in investment)
ΔY = ΔC + ΔI (The change in income also equals the change in consumption plus the change in investment)
→ kΔI = c(kΔI) + ΔI (Therefore, the investment multiplier times the change in investment equals the marginal propensity to consume times the investment multiplier times the change in investment)
→ kΔI – c(kΔI) = ΔI
→ kΔI(1-c) = ΔI
→ 1-c = 1/k
→ c = 1-1/k
(Now I see the ridiculousness of promising to write out the equations in words!)
In the next section, Keynes discusses the relationship between the investment multiplier and Kahn’s ‘employment multiplier’, which expresses the relationship between a change in employment in investment goods industries (directly related to a change in investment spending), and the total flow-on change in employment. There is no reason the two multipliers will be equal, because production in the investment goods sector may be more (or less) labour intensive than production in the consumer goods sector. But this caveat can be ignored to explain the general relationship between investment spending and employment.
In general, then, an increase in investment spending (private or public) will employ people immediately in the investment goods industry, and have a multiplied effect, employing some multiple of additional people elsewhere in the economy. This is just an obvious extension of the idea that spending on investment will be re-spent. But this does hint at another issue – that the real output of the economy is limited (to output at full employment), and spending multiplied past this point will simply raise prices. If people try to spend the whole of their increased incomes triggered by the increase in investment, without saving any, “there will be no point of stability and prices will rise without limit”. [p. 117]
That people in fact do not spend all of additions to their income is an empirical claim – it is not logically necessary. But assuming they increase saving out of the new income, the multiplier tells us how much extra income it takes to bring saving in line with the increase in investment: “If saving is the pill and consumption is the jam, the extra jam has to be proportioned to the size of the additional pill.” [p. 117]
The proportion of additional income spent (i.e. the marginal propensity to consume) is the lever by which investment moves aggregate income and employment: if it is high, a little initial extra investment will raise employment a lot; if it is low, it takes a lot of investment to have a serious impact on employment. Keynes thinks that in reality the propensity to consume is closer to one than to zero:
… with the result that we have, in a sense, the worst of both worlds, fluctuations in employment being considerable and, at the same time, the increment in investment required to produce full employment being too great to be easily handled. Unfortunately the fluctuations have been sufficient to prevent the nature of the malady from being obvious, whilst its severity is such that it cannot be remedied unless its nature is understood. [p. 118]
Next Keynes makes clear that we are talking about additions to net investment. We can’t say for sure that any given investment project (public or private) will raise income and employment with the full force of the multiplier, because that decision to invest may take the place of investment that would have happened in its absence. For example, funding it might raise interest rates and discourage other investments, or compete with other projects for labour. This anticipates notions of ‘crowding out’ which are to this day raised against stimulatory macroeconomic policies. This argument is often thought to be a rebuttal of Keynes, but he was clearly aware of it from the start, though he does not dwell on it.
Here he also raises the issue of foreign trade – that to the extent that spending ‘leaks’ out to foreign producers, it diminishes domestic income and the multiplier. On the other hand, the domestic economy gets the benefit from other countries’ expenditure via exports. Note the classic Keynesian ontology of the world economy as a collection of interrelated national economies. The national economy is conceptualised primarily as a self-contained system, except for flow relationships with other national economies.
So far we have been discussing an equilibrium position following from the logical fact that an increase in investment must increase aggregate income by a greater amount (unless the marginal propensity to consume is zero or less). In the next section Keynes considers the dynamics: how do we get to equilibrium from an initial decision to invest? This is tricky, because the multiplier is a logical relation “which holds good continuously, without time-lag, at all moments of time”. [p. 122] But if an increase in investment is unforeseen, the effect will not be instantaneous. These two statements seem contradictory. I think what Keynes is getting at is that there are two senses in which we are interested in the multiplier: as a logical relation and as an equilibrium relation.
Say we look at a period as short as a day. That day a decision to invest is put into effect: a firm makes a purchase of some piece of machinery. The funds are transferred into the bank account of the machinery manufacturer. And there they stay for the rest of the day. In this period we have an increase in investment, but no multiplier. The multiplier effect still holds – as it logically must. But effectively, the marginal propensity to consume out of this piece of income from investment is zero, for the period of the single day. But on some day soon afterwards, the extra sale figures in the machinery firm’s reckonings, and it employs more staff to increase production. On the day of their first paycheck, consumption rises, this time without any prior increase in investment. The marginal propensity to consume rises.
Of course it is ridiculous to define a period as short as a day. But this is the logic behind Keynes’ statement that unforeseen investment “may cause a temporary departure of the marginal propensity to consume away from its normal value, followed, however, by a gradual return to it.” [p. 123] Keynes’ examples examine periods longer than a day, but in which the initial investment expenditure has taken place without yet being followed by expansion in the consumer goods sector. As those employed in the investment goods sector begin to spend out of the addition to their incomes, at first consumer goods prices will rise, and only later will output follow. In the meantime, higher prices will cause some to defer spending, redistribute income to lower-spending entrepreneurs, etc., so that the propensity to consume temporarily declines.
Eventually, though, production of consumer goods will catch up and the full effect of the multiplier is felt. While it was never suspended, we can distinguish between its operation in shorter periods of time during which the marginal propensity to consume oscillates, and the period of rest once the forces set in motion by the initial increase in investment have fully played themselves out. Over this longer period, the marginal propensity to consume is (more or less) constant.
This dynamic story is not entirely satisfying, especially since Keynes implies that it is partly an explanation for the business cycle – which seems like too long a period over which to be considering the effects of an increase in net investment. But the fundamental point is sound. It is interesting that again there are echoes of Marx’s concept of balanced growth. In regular times, Keynes thinks most expansion of investment will be foreseen and planned for, so that the multiplier effect will play out fairly quickly and not work through this oscillation.
Marginal and average propensities to consume
Keynes notes that at first glance, a poor economy which saves little might be assumed to suffer from very large fluctuations in output and employment, because the multiplier would be so large. But this ignores the fact that in such an economy, investment would also be a much smaller proportion of output (and therefore employment) as a whole, so fluctuations in the rate of investment would have a correspondingly smaller effect on overall income, counteracting the effects of the larger multiplier. He gives a general formula for working out the combined effects on page 126: it is straightforward.
It also follows that for a given economy, the multiplier effect of an increase in investment will be greater if employment is initially low than if it is initially high. So “public works even of doubtful utility will pay for themselves many times over” if unemployment is high, but perhaps not at full employment. [p. 127]
Finally, we get a passage that Keynes is notorious for. For the involuntarily unemployed, employment may have positive utility, instead of being an unwelcome sacrifice. So it may be worth the government investing in producing useless goods just to create employment. He caustically notes that in practice it is often easier to make politically acceptable useless make-work projects, or handing out money in unemployment benefits, than it is to make a case for real public investment, which tends to be judged on commercial grounds.
If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coalmines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez-faire to dig the notes up again (the right to do so being obtained, of course, by tendering for leases of the note-bearing territory), there need be no more unemployment and, with the help of the repercussions, the real income of the community, and its capital wealth also, would probably become a good deal greater than it actually is. It would, indeed, be more sensible to build houses and the like; but it there are political and practical difficulties in the way of this, the above would be better than nothing. [p. 129]
Ouch! Even more cuttingly, he notes that “wars have been the only form of large-scale loan expenditure which statesmen have thought justifiable” and gold-mining helps recovery from recessions because the barbarous relic’s price rises in downturns and motivates expeditions to dig it out of the ground. [p. 130]