The Marginal Propensity to Consume and the Multiplier

Superphysics Note: We replace “wage-unit” with “hourly-common-wage” and “labour-unit” with “hourly-common-labour”

Chapter 8 established that employment can only increase pari passu with investment.

The Multiplier in our theory of employment is a definite ratio between:

• income and investment
• total employment and primary employment (employment directly employed on investment).

This establishes a precise relationship, given the propensity to consume, between:

• aggregate employment and income
• the rate of investment

This was originally from Mr. R. F. Kahn in his article on “The Relation of Home Investment to Unemployment” (Economic Journal, June 1931).

• It stated that if the propensity to consume as given and we conceive the government to stimulate or retard investment, the change in the amount of employment will be a function of the net change in the amount of investment.
• It aimed to lay down general principles to estimate the actual quantitative relationship between:
  • an increment of net investment and
  • the increment of aggregate employment which will be associated with it.

Before coming to the multiplier, we must explain the marginal propensity to consume.

The fluctuations in real income result from applying different quantities of worker-hours to a given capital equipment.

• In this way, real income changes with the number of worker-hours employed.

We assume that, as these worker-hours are increased, the margin gets a decreasing return. .

• The income will increase more than the rise of worker-hours used .
• The worker-hours will, in turn, increase more than the amount of real income measured (if that is possible) in terms of product.

Real income measured in terms of product and income measured in terms of hourly-common-labour will, however, increase and decrease together.

Real income, measured in terms of product, might be incapable of precise numerical measurement.

• This is why we should regard income in terms of common-hourly-wage Yw as an adequate working index of changes in real income.

Yw increases and decreases in a greater proportion than real income.

• But in other contexts, they can be interchanged because they always increase and decrease together.

My normal psychological law is:

This is translate into:

• ΔCw and ΔYw have the same sign
• But ΔYw > ΔCw, where Cw is the consumption in terms of hourly-common-wage

This is merely a repetition of the proposition already established above.

The marginal propensity to consume is dCw/dYw

• This quantity tells us how the next increment of output will have to be divided between consumption and investment.

ΔYw = ΔCw + ΔIw

• -ΔCw is the increment of consumption
• ΔIw is the increment of investment

ΔYw = kΔIw

• 1 - (1/k) is equal to the marginal propensity to consume.
• k is the investment multiplier.

This 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.

Mr. Kahn’s multiplier is a little different.

• It is the employment multiplier designated by k', since it measures the ratio of the increment of total employment which is associated with a given increment of primary employment in the investment industries.

If the increment of investment ΔIw leads to an increment of primary employment ΔN2 in the investment industries, the increment 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 shapes of the relevant portions of the aggregate supply functions for different types of industry are such that the ratio of the increment of employment in the one set of industries to the increment of demand which has stimulated it will be the same as in the other set of industries.[1]

The marginal propensity to consume can be widely different from the average propensity. In this case,we can presume in favour of:

• ΔYw/ΔN and
  • This would create a divergent change for consumption-goods
• ΔIw/ΔN2
  • This would create a divergent change for investment-goods

We can rewrite the following argument in a more generalised form. This is useful if we want to take account of such possible differences in the shapes of the relevant portions of the aggregate supply functions for consumption-goods and investment-goods.

But it will be convenient to deal with the simplified case where k = k'.

It follows that if the people choose to consume, then:

• the multiplier k is 10
• the total employment caused by increased public works, for example, will be 10 times the primary employment provided by the public works themselves, assuming no reduction of investment in other directions.

Only in the event of the community maintaining their consumption unchanged in spite of the increase in employment and hence in real income, will the increase of employment be restricted to the primary employment provided by the public works.

If, on the other hand, they seek to consume the whole of any increment of income, there will be no point of stability and prices will rise without limit.

With normal psychological suppositions, an increase in employment will only be associated with a decline in consumption if there is at the same time a change in the propensity to consume — as the result, for instance, of propaganda in time of war in favour of restricting individual consumption; and it is only in this event that the increased employment in investment will be associated with an unfavourable repercussion on employment in the industries producing for consumption.

This only sums up in a formula what should by now be obvious to the reader on general grounds. An increment of investment in terms of wage-units cannot occur unless the public are prepared to increase their savings in terms of wage-units. Ordinarily speaking, the public will not do this unless their aggregate income in terms of wage-units is increasing, Thus their effort to consume a part of their increased incomes will stimulate output until the new level (and distribution) of incomes provides a margin of saving sufficient to correspond to the increased investment.

The multiplier:

• tells us by how much their employment has to be increased to yield an increase in real income sufficient to induce them to do the necessary extra saving, and is a function of their psychological propensities.[3]

If saving is the pill and consumption is the jam, the extra jam has to be proportioned to the size of the additional pill. Unless the psychological propensities of the public are different from what we are supposing, we have here established the law that increased employment for investment must necessarily stimulate the industries producing for consumption and thus lead to a total increase of employment which is a multiple of the primary employment required by the investment itself.

It follows that, if the marginal propensity to consume is not far short of unity, small fluctuations in investment will lead to wide fluctuations in employment; but, at the same time, a comparatively small increment of investment will lead to full employment.

If, on the other hand, the marginal propensity to consume is not much above zero, small fluctuations in investment will lead to correspondingly small fluctuations in employment; but, at the same time, it may require a large increment of investment to produce full employment. In the former case involuntary unemployment would be an easily remedied malady, though liable to be troublesome if it is allowed to develop.

In the latter case, employment may be less variable but liable to settle down at a low level and to prove recalcitrant to any but the most drastic remedies.

In actual fact, the marginal propensity to consume seems to lie somewhere between these two extremes, though much nearer to unity than to zero. The result is that we have the worst of both worlds:

• fluctuations in employment being considerable
• 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.

When full employment is reached, any attempt to increase investment still further will set up a tendency in money-prices to rise without limit, irrespective of the marginal propensity to consume; i.e. we shall have reached a state of true inflation.[4] Up to this point, however, rising prices will be associated with an increasing aggregate real income.