The Marginal Propensity to Consume and the Multiplier

The previous section explained a foreseen change in aggregate investment for the consumption industries to advance pari passu with the capital-goods industries without adding disturbance to the price of consumption-goods than is consequential, in conditions of decreasing returns, on an increase in the quantity which is produced.

There are cases where the initiative comes from an increase in the output of the capital-goods industries which was not fully foreseen.

• This only produces its full effect on employment over a period of time.

This, however, creates some confusion between:

• the logical theory of the multiplier, and
  • This holds good continuously, without time-lag always
• the consequences of an expansion in the capital-goods industries
  • This has a gradual effect, subject to time-lag and only after an interval.

This is resolved by:

1. An unforeseen, or imperfectly foreseen, expansion in the capital-goods industries does not have an instantaneous effect of equal amount on the aggregate of investment but causes a gradual increase of the latter.

2. It may cause a temporary departure of the marginal propensity to consume away from its normal value, followed, however, by a gradual return to it.

Thus, an expansion in the capital-goods industries causes a series of increments in aggregate investment occurring in successive periods over an interval of time, and a series of values of the marginal propensity to consume in these successive periods which differ both from what the values would have been if the expansion had been foreseen and from what they will be when the community has settled down to a new steady level of aggregate investment.

But in every interval of time the theory of the multiplier holds good in the sense that the increment of aggregate demand is equal to the increment of aggregate investment multiplied by the marginal propensity to consume.

The explanation of these two sets of facts can be seen most clearly by taking the extreme case where

This is seen in the expansion of employment in the capital-goods industries which is entirely unforeseen that there is no increase in the output of consumption-goods.

• In this event, the efforts of those newly employed in the capital-goods industries to consume a proportion of their increased incomes will raise the prices of consumption-goods.
• This willl happen until a temporary equilibrium between demand and supply is created partly by:
  • the high prices causing a postponement of consumption
  • a redistribution of income in favour of the saving classes as an effect of the increased profits resulting from the higher prices, and
  • the higher prices causing a depletion of stocks.

When the balance is restored by a postponement of consumption, there is a temporary reduction of the marginal propensity to consume.

• The multiplier itself is reduced proportional to the depletion of stocks.
• Aggregate investment increases for the time being by less than the increment of investment in the capital-goods industries.
• The thing to be multiplied does not increase by the full increment of investment in the capital-goods industries.

As time goes on, however, the consumption-goods industries adjust themselves to the new demand.

• When the deferred consumption is enjoyed, the marginal propensity to consume rises temporarily above its normal level to compensate for the extent to which it previously fell below it.
• It eventually returns to its normal level.
• The restoration of stocks to their previous figure causes the increment of aggregate investment to be temporarily greater than the increment of investment in the capital-goods industries (the increment of working capital corresponding to the greater output also having temporarily the same effect).

Unforeseen change only exercises its full effect on employment over a period of time. This fact is important when it plays a part in the analysis of the trade cycle.

But it does not in any way affect the significance of the theory of the multiplier as set forth in this chapter; nor render it inapplicable as an indicator of the total benefit to employment to be expected from an expansion in the capital-goods industries.

Moreover, except in conditions where the consumption industries are already working almost at capacity so that an expansion of output requires an expansion of plant and not merely the more intensive employment of the existing plant, there is no reason to suppose that more than a brief interval of time need elapse before employment in the consumption industries is advancing pars passu with employment in the cap ital-goods industries with the multiplier operating near its normal figure.

V

We have seen above that the greater the marginal propensity to consume, the greater the multiplier, and hence the greater the disturbance to employment corresponding to a given change in investment. This might seem to lead to the paradoxical conclusion that a poor community in which saving is a very small proportion of income will be more subject to violent fluctuations than a wealthy community where saving is a larger proportion of income and the multiplier consequently smaller.

This conclusion, however, would overlook the distinction between the effects of the marginal propensity to consume and those of the average propensity to consume. For whilst a high marginal propensity to consume involves a larger proportionate effect from given percentage change in investment, the absolute effect will, nevertheless, be small if the average propensity to consume is also high. This may be illustrated as follows by a numerical example.

Let us suppose that a community’s propensity to consume is such that, so long as its real income does not exceed the output from employing 5,000,000 men on its existing capital equipment, it consumes the whole of its income; that of the output of the next 100,000 additional men employed it consumes 99 per cent., of the next 100,000 after that 98 per cent., of the third 100,000 97 per cent. and so on; and that 10,000,000 men employed represents full employment. It follows from this that, when 5,000,000 + n x 100,000 men are employed, the multiplier at the margin is 100/n, and n(n + 1)/2.(50 + n) per cent. of the national income is invested.

Thus when 5,200,000 men are employed the multiplier is very large, namely 5o, but investment is only a trifling proportion of current income, namely, 0.06 per cent.; with the result that if investment falls off by a large proportion, say about 2/3, employment will only decline to 6,900,000,[*] i.e. by about 2%.

On the other hand, when 9,000,000 men are employed, the marginal multiplier is comparatively small, namely 21, but investment is now a substantial proportion of current income, namely, 9 per cent.; with the result that if investment falls by two-thirds, employment will decline to 6,900,000, namely, by 23 per cent. In the limit where investment falls off to zero, employment will decline by about 4 per cent. in the former case, whereas in the latter case it will decline by 44 per cent.[6]

In the above example, the poorer of the two communities under comparison is poorer by reason of under-employment. But the same reasoning applies by easy adaptation if the poverty is due to inferior skill, technique or equipment. Thus whilst the multiplier is larger in a poor community, the effect on employment of fluctuations in investment will be much greater in a wealthy community, assuming that in the latter current investment represents a much larger proportion of current output.[7]

It is also obvious from the above that the employment of a given number of men on public works will (on the assumptions made) have a much larger effect on aggregate employment at a time when there is severe unemployment, than it will have later on when full employment is approached. In the above example, if, at a time when employment has fallen to 5,200,000, an additional 100,000 men are employed on public works, total employment will rise to 6,400,000.

But if employment is already 9,000,000 when the additional 100,000 men are taken on for public works, total employment will only rise to 9,200,000. Thus public works even of doubtful utility may pay for themselves over and over again at a time of severe unemployment, if only from the diminished cost of relief expenditure, provided that we can assume that a smaller proportion of income is saved when unemployment is greater; but they may become a more doubtful proposition as a state of full employment is approached.

Furthermore, if our assumption is correct that the marginal propensity to consume falls off steadily as we approach full employment, it follows that it will become more and more troublesome to secure a further given increase of employment by further increasing investment.

It should not be difficult to compile a chart of the marginal propensity to consume at each stage of a trade cycle from the statistics (if they were available) of aggregate income and aggregate investment at successive dates. At present, however, our statistics are not accurate enough (or compiled sufficiently with this specific object in view) to allow us to infer more than highly approximate estimates.

The best for the purpose, of which 1 am aware, are Mr. Kuznets’ figures for the United States (already referred to in Chapter 8 above), though they are, nevertheless, very precarious. Taken in conjunction with estimates of national income these suggest, for what they are worth, both a lower figure and a more stable figure for the investment multiplier than I should have expected. If single years are taken in isolation, the results look rather wild.

But if they are grouped in pairs, the multiplier seems to have been less than 3 and probably fairly stable in the neighbourhood of 2.5. This suggests a marginal propensity to consume not exceeding 6o to 70 per cent. — a figure quite plausible for the boom, but surprisingly, and, in my judgment, improbably low for the slump. It is possible, however, that the extreme financial conservatism of corporate finance in the United States, even during the slump, may account for it. In other words, if, when investment is falling heavily through a failure to undertake repairs and replacements, financial provision is made, nevertheless, in respect of such wastage, the effect is to prevent the rise in the marginal propensity to consume which would have occurred otherwise.

This factor may have played a significant part in aggravating the degree of the recent slump in the United States. On the other hand, it is possible that the statistics somewhat overstate the decline in investment, which is alleged to have fallen off by more than 75 percent. in 1932 compared with 1929, whilst net “capital formation” declined by more than 95 per cent.; — a moderate change in these estimates being capable of making a substantial difference to the multiplier.

VI

When involuntary unemployment exists, the marginal disutility of labour is necessarily less than the utility of the marginal product. Indeed it may be much less. For a man who has been long unemployed some measure of labour, instead of involving disutility, may have a positive utility. If this is accepted, the above reasoning shows how “wasteful” loan expenditure[8] may nevertheless enrich the community on balance. Pyramid-building, earthquakes, even wars may serve to increase wealth, if the education of our statesmen on the principles of the classical economics stands in the way of anything better.

It is curious how common sense, wriggling for an escape from absurd conclusions, has been apt to reach a preference for wholly “wasteful” forms of loan expenditure rather than for partly wasteful forms, which, because they are not wholly wasteful, tend to be judged on strict “business” principles. For example, unemployment relief financed by loans is more readily accepted than the financing of improvements at a charge below the current rate of interest; whilst the form of digging holes in the ground known as gold-mining, which not only adds nothing whatever to the real wealth of the world but involves the disutility of labour, is the most acceptable of all solutions.

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 if there are political and practical difficulties in the way of this, the above would be better than nothing.

The analogy between this expedient and the goldmines of the real world is complete. At periods when gold is available at suitable depths experience shows that the real wealth of the world increases rapidly; and when but little of it is so available, our wealth suffers stagnation or decline. Thus gold-mines are of the greatest value and importance to civilisation. just as wars have been the only form of large-scale loan expenditure which statesmen have thought justifiable, so gold-mining is the only pretext for digging holes in the ground which has recommended itself to bankers as sound finance; and each of these activities has played its part in progress-failing something better. To mention a detail, the tendency in slumps for the price of gold to rise in terms of labour and materials aids eventual recovery, because it increases the depth at which gold-digging pays and lowers the minimum grade of ore which is payable.

In addition to the probable effect of increased supplies of gold on the rate of interest, gold-mining is for two reasons a highly practical form of investment, if we are precluded from increasing employment by means which at the same time increase our stock of useful wealth. In the first place, owing to the gambling attractions which it offers it is carried on without too close a regard to the ruling rate of interest. In the second place the result, namely, the increased stock of gold, does not, as in other cases, have the effect of diminishing its marginal utility. Since the value of a house depends on its utility, every house which is built serves to diminish the prospective rents obtainable from further house-building and therefore lessens the attraction of further similar investment unless the rate of interest is falling part passu. But the fruits of gold-mining do not suffer from this disadvantage, and a check can only come through a rise of the wage-unit in terms of gold, which is not likely to occur unless and until employment is substantially better. Moreover, there is no subsequent reverse effect on account of provision for user and supplementary costs, as in the case of less durable forms of wealth.

Ancient Egypt was doubly fortunate, and doubtless owed to this its fabled wealth, in that it possessed two activities, namely, pyramid-building as well as the search for the precious metals, the fruits of which, since they could not serve the needs of man by being consumed, did not stale with abundance. The Middle Ages built cathedrals and sang dirges. Two pyramids, two masses for the dead, are twice as good as one; but not so two railways from London to York. Thus we are so sensible, have schooled ourselves to so close a semblance of prudent financiers, taking careful thought before we add to the “financial” burdens of posterity by building them houses to live in, that we have no such easy escape from the sufferings of unemployment. We have to accept them as an inevitable result of applying to the conduct of the State the maxims which are best calculated to “enrich” an individual by enabling him to pile up claims to enjoyment which he does not intend to exercise at any definite time.

Transcriber’s Footnote

• This is correct against the published text, but the figure must be 4,900,000 not 6,900,000, for an approximately 2% decline from a base level of employment of 5,000,000.

Author’s Footnotes 8. In some passages of this section we have tacitly anticipated ideas which will be introduced in Book IV.

1. More precisely, if ee and e’e are the elasticities of employment in industry as a whole and in the investment industries respectively; and if N and N2 are the numbers of men employed in industry as a whole and in the investment industries, we have

ΔYw = Yw/(ee.N) . ΔN

and

ΔIw = Iw/(e’e.N2) . ΔN2,

so that

ΔN = (ee/e’e).(Iw/N2).(N/Yw).k.ΔN2,

i.e.,

k’ = (Iw/e’eN2).(eeN/Yw).k.

If however, there is no reason to expect any material relevant difference in the shapes of the aggregate supply functions for industry as a whole and for the investment industries respectively, so that Iw/(ee’.N2) = Yw/(ee.N), then it follows that ΔYw/ΔN = ΔIw/ΔN2 and, therefore, that k = k'.

2. Our quantities are measured throughout in terms of wage-units.

3. Though in the more generalised case it is also a function of the physical conditions of production in the investment and consumption industries respectively.

4. Cf. Chapter 21, p. 303, below.

5. Cf., however, below, p. 128, for an American estimate.

6. Quantity of investment is measured, above, by the number of men employed in producing it. Thus if there are diminishing returns per unit of employment as employment increases, what is double the quantity of investment on the above scale will be less than double on a physical (if such a scale is available).

7. More generally, the ratio of the proportional change in total demand to the proportional change in investment

= (ΔY/Y)(ΔI/I) = (ΔY/Y).(Y - C)/(ΔY - ΔC) = (1 - C/Y)/(1 - dC/dY)

As wealth increases dY/dY diminishes, but C/Y also diminishes. Thus the fraction increases or diminishes according as consumption increases or diminishes in a smaller or greater proportion than income.

8. It is often convenient to use the term “ loan expenditure “ to include both public investment financed by borrowing from individuals and also any other current public expenditure which is so financed. Strictly speaking, the latter should be reckoned as negative saving, but official action of this kind is not influenced by the same sort of psychological motives as those which govern private saying. Thus “loan expenditure” is a convenient expression for the net borrowings of public authorities on all accounts, whether on capital account or to meet a budgetary deficit. The one form of loan expenditure operates by increasing investment and the other by increasing the propensity to consume.