6: The Definition of Income, Saving and Investment

This is the longest chapter yet, including the appendix, and the first one so far to give me a major headache, though I think I puzzled it out in the end. I thought I would breeze through it quickly since it was all about definitions, but oh no! Bloody user cost! Apologies for any incoherence – I was writing as I read, so it is partly a record of my confusion. I went back and changed some things once I had a better idea about what was going on, but I did not have the energy at the end to completely rewrite.

Income

Income is first defined from the point of view of entrepreneurs. In a given period it equals [total revenue] plus [the value of capital equipment, working capital and stocks of finished and unfinished goods retained at the end of the period] minus [payments between entrepreneurs] minus [the contribution to the product made by equipment inherited from the previous period].

This last element can be calculated in two ways. The first focuses on the value of capital goods sacrificed by using them in production during the period. This is not simple to calculate, because some value is lost from capital goods whether or not they are used – through obsolescence, for example. So Keynes deals with the issue by defining it as the difference between the actual value of capital equipment at the end of the period, and the value capital equipment would have had at the end of the period had it not been used, assuming entrepreneurs would have carried out the optimum level of maintenance, etc., even in that case.

User cost thus equals [payments between entrepreneurs] plus [the counterfactual “maximum net value which might have been conserved from the previous period” (p. 53) if production had not taken place] minus [the value of capital equipment actually existing at the end of the period]. It is “the measure of what has been sacrificed (one way or another) to produce” finished output. [p. 53]

Note there is no reference to the value of capital equipment, etc., at the start of the period, so this is subtly different from the accounting concept of ‘depreciation’. It is all about the counterfactual.

After much confusion, later in the chapter I realised how Keynes is very deliberately making ‘user cost’ different from ‘depreciation’. Depreciation implies a loss of wealth on the part of the entrepreneur. There is an element of this loss of wealth that is not included in user cost: that is, the part of depreciation that happens regardless of whether the equipment is used or not. For example, depreciation due to obsolescence or catastrophe. This is excluded from user cost because it is irrelevant to entrepreneurs’ decisions about how much productive capacity to use.

If user cost is confusing at this point, read the first section of the chapter’s appendix and it becomes clearer. I think in fact it is analogous to Marx’s constant capital rather than ‘depreciation’.

The rest of the definitions are straightforward:

Factor cost equals the amount paid by entrepreneurs to other factors of production (unspecified at this point, but presumably being mainly labour).

Prime cost equals factor cost plus user cost.

Entrepreneurial income equals output minus prime cost.

The income of the rest of the community equals factor cost.

Aggregate income equals entrepreneurial income plus the income of the rest of the community, so equals output minus user cost.

Aggregate consumption equals output minus that bought by entrepreneurs.

Aggregate investment equals [sales between entrepreneurs] minus [user cost]. I have to admit this definition did my head in a little bit, since the definition of user cost includes [payments between entrepreneurs] as a term. So we end up with a statement that aggregate investment equals [the value of capital equipment actually existing at the end of the period] minus [the counterfactual maximum net value that could have been conserved from the previous period if production had not taken place]. So ‘aggregate investment’ here is net investment, not including what is spent to maintain the existing capital stock. And ‘payments between entrepreneurs’ includes all such payments within a period, both those for goods used up immediately (Marx’s circulating capital) and those which become part of the capital equipment (Marx’s fixed capital). This becomes much clearer in the appendix.

Effective demand is that level of aggregate income which entrepreneurs expect, when employment decisions are made, to prevail in the coming period.

Keynes explains that this set of definitions are consistent with the (neo)classical postulate that marginal income equals marginal factor cost. This justifies the tortuous treatment of ‘user cost’ – other economists ignore it, and therefore forget there is a gap between the prices facing consumers and the prices motivating entrepreneurs. From the point of view of the firm, user cost is a deduction from revenue, and it is revenue less user cost that they try to maximise. (So, in a footnote, he shows that a change in employment equals the change in income minus the change in user cost – both measured in wage-units.)

Without pause for a breath, we move straight into the alternative way of conceptualising the contribution of equipment inherited from the previous period. (Remember Keynes was going to give us two!) Here he adds the concept of ‘supplementary cost’ to refer to that part of depreciation which is foreseen but not part of user cost – due, for example, to predictable obsolescence and ‘insurable risks’ (in fact an accountant might count the insurance costs themselves).  He also adds the concept of ‘windfall loss’, to refer to loss of capital value which is unpredictable – for example, from sudden obsolescence (a new invention) or catastrophe.

Recall that Keynes excluded these costs from ‘user cost’ because they did not influence the decision of how much capacity to employ – they are incurred regardless of production decisions. They are important not from the point of view of aggregate supply, but from the point of view of aggregate demand, because they influence the consumption decisions of entrepreneurs. According to Keynes, in working out net income we subtract supplementary cost from entrepreneurs’ gross profits, but not windfall losses. This is because windfall losses will not affect consumption decisions to the same degree, given that entrepreneurs do not expect them to recur. Therefore he assigns them to the capital account – they are considered mainly to lower wealth rather than income. The line between supplementary cost and windfall loss is thus blurry and psychological – if unexpected windfall losses continually eat into wealth, entrepreneurs are at some point likely to revise their expectations of loss and thus expand what they consider to be supplementary cost – to expect the unexpected.

As if this wasn’t enough, we are then treated to a discussion of how Inland Revenue treats these matters, and how it influences (and is influenced by) the declaration of dividends. All I can say is, it is interesting how far institutional and behavioural considerations intrude into a discussion of definitions! We can see why Marshall might have been led to “take refuge in the practices of the Income Tax Commissioners and – broadly speaking – to regard as income whatever they, with their experience, choose to treat as such.” [p. 59]

Saving and Investment

Keynes begins:

So far as I know, everyone is agreed that saving means the excess of income over expenditure on consumption. Thus any doubts about the meaning of saving must arise from doubts about the meaning either of income or of consumption. [p. 61]

Income was clearly defined above – as output minus user cost. It is open to interpretation which kinds of purchases are consumption and which are investment, and Keynes writes that any interpretation will do “provided that it is consistently applied”. [p. 61] He then proceeds to give a precise interpretation of his own. It must be consistent with the income definitions above; specifically, it must keep the same distinction between ‘entrepreneur’ and ‘consumer’. Consumption is, therefore, any purchase/sale that is not between entrepreneurs, or total output minus sales between entrepreneurs.

Investment is any purchase between entrepreneurs that is not part of user cost.

Saving follows logically as aggregate income minus purchases from entrepreneurs by non-entrepreneurs. Because [aggregate income] equals [output] minus [user cost], [saving] equals [sales between entrepreneurs] minus [user cost].

Net saving equals [sales between entrepreneurs] minus [user cost] minus [supplementary cost]. This considers depreciation in the broader sense to be a form of consumption.

This means that by definition, current investment is equal to saving, because, above, Keynes defined aggregate investment as also equal to [sales between entrepreneurs] minus [user cost]. Similarly, net investment is equal to [sales between entrepreneurs] minus [user cost] minus [supplementary cost]. To restate:

Income is created by the value in excess of user cost which the producer obtains for the output he has sold; but the whole of this output must obviously have been sold either to a consumer or to another entrepreneur; and each entrepreneur’s current investment is equal to the excess of the equipment which he has purchased from other entrepreneurs over his own user cost. Hence, in the aggregate the excess of income over consumption, which we call saving, cannot differ from the addition to capital equipment which we call investment. Saving, in fact, is a mere residual.

This last sentence emphasises what is new with Keynes: savings may still be equal to investment, but there is no implication that savings generates investment. As yet, we have no causal mechanism going either way – investment could cause saving. In fact, the way the definitions have been expressed, that is what Keynes is emphasising – he states that “the act of investment cannot help causing the residual or margin, which we call saving, to increase by a corresponding amount”. [p. 64] But this could happen either by expanding income or squeezing consumption. We need to wait for the behavioural parts of the theory – at the moment we only have definitions.

Appendix on User Cost

No major surprises here, though the discussion gets increasingly complex; the first part confirms the interpretation of the concept I got (eventually) from the rest of the chapter. It becomes much easier to think about user cost as equal to all payments between entrepreneurs in the current period, other than investment in capital equipment.

This becomes clearer because Keynes states outright that investment is defined in terms of that counterfactual as: [the value of capital equipment actually existing at the end of the period] minus [the maximum net value which might have remained from the previous period if production had not taken place].

So the confusing counterfactual is now embedded in the concept of investment, and it is easier to think of user cost as something different from ‘depreciation’. It is, in Marxian terms, constant capital. Note that zero investment according to this definition means that during the period the entrepreneur is exactly replacing the value of the capital equipment worn out by production – if this is allowed to wear down, investment is considered negative.

Keynes now explains why he thinks this tortured definition is important – it avoids problems involved with trying to separate the contribution of factors of production (primarily labour) to the value of goods sold in the current period from their contribution to the value of entrepreneurs’ stocks of equipment, etc. Therefore, it is less tortured than the alternatives.

A little reflection will show that all this is no more than common sense. Some part of [an entrepreneur’s] outgoings to other entrepreneurs is balanced by the value of his current investment in his own equipment, and the rest represents the sacrifice which the output he has sold must have cost him over and above the total sum which he has paid out to the factors of production. If the reader tries to express the substance of this otherwise, he will find that its advantage lies in its avoidance of insoluble (and unnecessary) accounting problems. There is, I think, no other way of analysing the current proceeds of production unambiguously.

It seems to me that the counterfactual – the value of inherited capital equipment if production did not take place – still leaves some room for ambiguity, but there you are.

Just when we thought we were getting it, Keynes dives into microeconomics. He points out that while it is alright to treat the short-period supply price as equal to the marginal factor cost – i.e., net of user cost – in the aggregate, this will not do for the analysis of relative prices, because user cost is part of observable prices.

Also, in dealing with relative prices, we need to consider the long-period supply price. Clearly in the long-run the entrepreneur needs to cover not only prime cost, but also supplementary cost (those other aspects of depreciation considered above), and in order to get a normal profit, needs to get an additional return exceeding the rate of interest on loans of term and risk comparable to the entrepreneur’s outlay. (Note that Keynes is working with a standard neoclassical conception of the equality of profit and interest.)

This discussion is difficult going, to say the least. But we can take comfort from the fact that this is mostly irrelevant to Keynes’ macroeconomic analysis. As he explains above in the discussion of supplementary cost, factors that do not influence the aggregate employment decision can be ignored. It is interesting, though, that this is the first time profitability is mentioned, and it turns out to be irrelevant to employment. We can trace this back to Keynes’ acceptance of the neoclassical theory of distribution, where revenues are based on marginal productivity and therefore not independent causes.

The next section discusses further the determination of the hitherto mysterious counterfactual element in user cost, with the delightful maxim: “To-day’s user cost is equal to the maximum of the discounted values of the potential expected yields of all the tomorrows.” Essentially, what the entrepreneur gets in not employing a given part of capital during the period, is the postponement of having to pay to replace it later. So if there are no spare stocks of the item, its user cost is partly determined by the replacement cost of the capital item, and partly by the “amount by which the life or efficiency of the equipment will be shortened if it is used”.

If there are spare stocks, the replacement cost is below the cost of production. The rate of interest and the supplementary cost (i.e. that part of depreciation that happens regardless of whether a stock is used or not) are also relevant. The rate of interest is relevant because whoever is holding the spare stock can anticipate its price will rise back to its cost of production as the spare is eliminated, and will therefore set its present price with reference to the interest rate. Supplementary cost is relevant because spare stocks will still depreciate in value at this rate. This discussion is relevant not only to capital equipment but also to raw materials used in production – note Keynes’ copper example, and his closing statement:

It is an advantage of the concepts of user cost and supplementary cost that they are as applicable to working and liquid capital as to fixed capital. The essential difference between raw materials and fixed capital lies not in their liability to user and supplementary costs, but in the fact that the return to liquid capital consists of a single term; whereas in the case of fixed capital, which is durable and used up gradually, the return consists of a series of user costs and profits earned in successive periods.

The last influence in the case of spare stocks is the time before the excess is expected to be eliminated. In normal times this element of user cost will not vary too much, because the capital goods will be fairly evenly spread out in terms of age. In a general slump, though, user cost depends on how long entrepreneurs expect the slump to last, and as expectations pick up, user cost may rise suddenly as they anticipate the excess stocks being absorbed quickly.

And we are finally done with this monster chapter!

Published in: on 11 October, 2007 at 2:54 pm  Comments (5)  

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5 CommentsLeave a comment

  1. […] Meantime, if you are smart, you’ll read Roughtheory’s fabulous series of posts on the first chapter of Capital, the latest of which here, and Scandalum Magnatum’s insightful notes on Keynes, the latest of which is here. […]

  2. Hi, I’m a layman trying to read and understand Keynes General Theory. Without wanting to bother you, I’d like to ask you some questions about definitions given in chapter 6 (in particular, about the terms of the user cost formula). If you don’t mind, please contact me at isveztia@gmail.com. Or I could post the question here if you prefer. I’d be very grateful in any case.

  3. In the General Theory, Keynes set out the Marginal Efficiency of Capital approach to
    investment. This was essentially an elaboration of the Classical approach as previously
    set out by Irving Fisher and others. We have covered the MEC approach already when we
    discussed the irr method of investment appraisal. At this juncture, it is critical to grasp
    that investment is a flow of spending in a given period (e.g. a quarter or a year). The
    capital stock, Kt, is the stock of usable capital equipment standing in the economy due to
    previous investment. Gross investment is a flow of capital expenditure which adds to the
    size of the capital stock. However.

  4. Pretty! This has been an incredibly wonderful post.
    Thank you for supplying this information.

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