10: The Marginal Propensity to Consume and the Multiplier

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.

Dynamics

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]

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Published in: on 17 October, 2007 at 4:52 pm  Comments (34)  

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34 CommentsLeave a comment

  1. Hey I love your blog. I have a question regarding the Marginal Propensity to Invest. If you could please help me, it would be dearly appreciated.

    a = 100
    Io = 100
    b = .9
    c = .15

    C = a + bY
    I = Io + cY

    a :autonomous consumption

    b :marginal propensity to consume

    c :marginal propensity to invest, change investment in response to a change in income.

    Io :autonomous investment

    Question #1
    What is the investment multiplier?

    Question #2
    What interpretation (scenario) could you come up with to describe this multiplier? Be creative.

    And this is how far I have gotten with the problem….

    Y = C + I
    Y = a + bY + Io + cY

    *** It’s an extra credit problem and my Professor told me not to plug in the a or Io (autonomous consumption and autonomous investment). I just don’t get what the process is to derive this. If you could be of help that would rock!

  2. Hi Beau,

    The reason this one is tricky is because the marginal propensity to consume and the marginal propensity to invest add up to more than one. That means any autonomous increase in investment (or consumption) will generate more and more spending (and therefore income) without limit. Usually the marginal propensities are presumed to be less than one, in which case each round of income generates less additional spending, so it eventually peters out to give a finite multiplier. Also note than Keynes himself treated all investment as autonomous from income – i.e. no ‘marginal propensity to invest’.

    This is a thoroughly unrealistic situation so I’m not sure what kind of scenario your professor has in mind. Possibly a situation of explosive inflation, which would need to be financed by continually increasing debt, since at each round households and firms are together spending more than they receive in income.

    In case you’re wondering about the more general way of determining the multiplier:

    The first thing you need to do is get all the Ys on one side of the
    equation:

    Y – bY – cY = a + Io

    Then get everything else back to the other side:

    Y(1 – b – c) = a + Io

    Y = (a + Io)/(1 – b – c)

    The multiplier is the amount by which Y changes for every unit of increase in Io. That is dY/dIo: the derivative. The original equation can be written like this:

    Y = a/(1 – b – c) + Io/(1 – b – c)

    Because a, b and c are constants, they do not change as investment increases. So to get the derivative you drop the first term completely (it’s nothing but constants) and you are left with this:

    dY/dIo = 1/(1 – b – c)

    In other words, for every additional unit of extra autonomous investment, income rises 1/(1 – b – c) units.

    Note that if you plug in your numbers for b and c you get a large negative multiplier, really a nonsense result. It’s possible I’m totally misinterpreting what your professor has in mind, so you might want to get a second opinion on this one!

  3. I have a BS economics 1975 lewis and clark college. MBA 1986 University of Washington. That being said: 1. Keynes had it wrong. multiple propensity to save or multiple propensity to invest. Fiscal policy to grow economy is a hoax. Milton Friedman had it right.Its all about the money supply. or the velocity of money. When we pass this currnt phase of deflation we are going to have rampant inflation.By goldm solomon had it right. You don’t need arcane high school algebra distributive properties and first derivatives to figure this out. You can use integration by parts if you like. Economics is not physics, its a social science trying to pass itself off as real science. too many variable that are not underhstood. Macro enconomics is voodoo. If you want to understand micro economics study price theory. Indiffernece curves and so on. Any one remember the phillips curve? thats a joke now. forget keynes. remember Marx “From each according to his ability to each according to his need” the commies are in charge. watch out for your wallet all you producers…………we have had a bloodless revolution. capitalism is dead. Dingly hairy, the commie nancy pelosi and the faggot barnie frank have us by the balls.

  4. well said.

  5. Holy batshit insane Batman. Did Garrison just congratulate himself for his own dumb ass rant?

  6. The point is if i could understand this in a simpler language or in a simple way i mean to say just the investment multiplier and then gradually introducing other concepts it would be very easy.
    I simply want to say that all this seems to be a mere jargon and I hardly got the concept
    I would appreciate if I would get the concept that why is investment multiplier written as inverse and not like the other multipliers

  7. THANK YOU.I USED AS A REFERENCE FOR HIGH SCOOL STUDENTS IN ADDIS ABABA.I GOT IMPORTANT AND TO THE POINT.

    • Thankyou so much.

  8. [...] Sumber : [...]

  9. Thanks helped me pass my exams in campus (kenya)

  10. Thanks!

    It helped me lot in prepairing for my MBA exam. nice explanation.

  11. why is marginal propensity to consume high of Ghana like other developing countries,yet,the size of the national income is low.explain with examples from Ghana

  12. The marginal propensity to consume is generally high for Ghana, like other developing countries, yet the size of the national income is low. Explain this with examples from Ghana.

  13. Pls, why is that in Ghana and other developing countries Marginal Propensity to Consume is high yet their National Income is low?
    Please, explain with examples from Ghana or…

  14. why is the propensity to consume high but national income is low?

  15. Hey – the basic answer is this: the propensity to consume is a proportion to income, so in theory any propensity is compatible with any absolute level of income. In practice, poorer countries are likely to show a higher propensity to consume (and higher marginal propensity) because there are greater unmet consumption needs, so people are much more likely to consume more of additional income and save less.

  16. hi this is Usama.can someone tell me government expediture multilplier and marginal prosperity to consume with examples????
    plz also send to my e-mail.
    thankyou

  17. I am a relative newbie to economics and am attempting to slog through Keynes’ General Theory on my own. I’m getting most of it-but without an instructor or class discussions, it’s tough.

    It’s obvious you put a great deal of time and effort into this. Thank you.

  18. Hey cheers Steve! I’m glad people find it useful. I’ve been thinking lately about finally finishing it off (so far it only goes up to Chapter 16).

  19. Hey, Can anyone help me in understanding the implications of different multipliers i.e. employment multiplier, investment multiplier and fiscal multiplier, to setting of government policy and to businesses.

    Thank you in Advance…

  20. please help me, i can’t understand the examples in my book. I understand everything except on how to find the marginal propensity to consume. i have an assignment, it requires me to find the MPC giving only the marginal propensity to save at 0.2 and investment at 72. please help me.tnx

  21. Hi Christina,

    The marginal propensity to consume is just one minus the marginal propensity to save. Any extra income is either spent or saved – the marginal propensity to save is the proportion saved out of an increase in income, and the marginal proportion to consume is the proportion consumed.

  22. What is the difference between marginal propensity to consume and multiplier

  23. Fixed Rate Savings

  24. can any one please help me out in deriving the MPC multiplier by differentiation with respect to “c”

    plz i am in great need thnxxx….. :))

  25. Hi Tom Here,
    I sat through a couple of years worth of economics but graduated in philosophy. So my question if you progress do you actually find out how to make a model in the Keynsian sense with an actual MPC and multiplier?
    So say you aggregated all Bank Balances at the beginning of a financial year added deposits, then subtracted the aggregated balances at the beginning of the following year. Then take this difference in savings add it to the difference in credit card balances and the difference Finance Company loans and so on. Would all these sum to the (Gross Domestic Product) multiplied by the MPC?

  26. i need help with this question ;
    (Simple Spending Multiplier) For each of the following values for the MPC (marginal propensity to consume), determine the size of the simple spending multiplier and the total change in real GDP demanded following a $10 billion decrease in spending: a. MPC = 0.9 b. MPC = 0.75 c. MPC = 0.6

  27. Hi, J here. To Ms. Sylvia, this might be the answers:
    for MPC = 0.9, multiplier = 1/0.9 = 1.11; total change in GDP = $ 11.11 B
    for MPC = 0.75, SSM = 1.33; GDP = $ 13.33

  28. in keynesian model the price level is assumed to be exogeneous and remaining constant or increasing or endogeneous remaining constant and gradually increasing?

  29. Please help me :)

    For each of the following values for the MPC, determine the size of the simple spending multiplier and the total change in real GDP demanded following a $10 billion decrease in spending:
    a. MPC = 0.9
    b. MPC = 0.75
    c. MPC = 0.6

  30. want to know the interpretation of the multiplier?

  31. wana know what will be the value of a multiplier when investment increase with $20m……

  32. hi guys,i love your site it helps me a lot.
    Please help me solve the following questions,am gonna be very gratefull.
    Q1 Assume a model with no government and no foreign sector. If we had savings function that is defined as S=-200 + 0.1Y and autonomous investment increases by 50,
    By how much will consumption change?

  33. hae! please answer for me this:
    what is the relationship between simple multiplier and marginal propensity to consume


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