Value & Capital, Notes to Chapter XIV -- A. SAVING AND INVESTMENT

Regarding saving and investment, the author states in the preliminary paragraph of his notes on Chapter XIV that "I think the reader has a right to demand some expression of opinion on that controversial topic."  He then begins his note on the topic by explaining that the principal difficulty "evidently arises from the multiplicity of ways in which the terms can be defined."  He observes that saving can be defined in a way that corresponds to each of the definitions of income discussed in the preceding chapter (each of which would, in turn, give rise to a corresponding definition of investment).  He also states that saving can be defined ex ante or ex post.  He argues that the choice of which definition of income to use is not important to the analysis, but he states that "the ex ante - ex post distinction is of course very important."  (One wonders whether the author thought this should be obvious.)

For his explanation the author chooses to use Income No. 1 as his basis for defining saving and investment;  he notes that if he chose another definition of income, "the whole argurment would be exactly duplicated."  Using this definition of income (and the same kind of one-week model he has used in earlier analyses) he defines a person's savings ex ante to be "the difference between his actual consumption during the week and that level of consumption which would leave the money value of the prospect he can expect to have at the end of the week the same as it actually was at the beginning."  If the week is assumed to be a short enough time that "the accretion of interest" is negligible , then saving can also be said to be "the increment in the money value of his prospect planned to accrue during the week."  If any changes in his earning power are ruled out, then "his saving may also be written as the planed increment in the value of his property.  All this is saving ex ante; saving ex post will be the realized increment in the value of his property."

Regarding saving and investment ex post, the author gives an argument for the equality of their aggregate amounts that is so straightforward that I prefer to reproduce it in full:

Savings ex post may be aggregated for all members of the community.  Their sum total will equal the total increment in the money value of all persons' property which accrues during the week.  Now property has three forms:  it may consist of physical goods (real capital), or securities, or money.  But money, as we have seen, is either a physical good, like gold, or a security, like notes or bank deposits.  Our three categories thus reduce to two.  Further, securities are simply debts of various sorts from one person (or concern) to another; and therefore, when all property is aggregated, they cancel out.  Total savings ex post therefore reduce to nothing else but the increment in the value of physical capital; which is what seems to be meant by investment -- of course investment ex post.

While the author notes that this equality is a "mere truism," indicating only that "all the capital goods in the economy belong to somebody," the relationship between saving and investment ex ante is more interesting.  For the simple one-week model that the author uses, in which all demands and corresponding supplies are assumed to be equal during the week, it is indeed true that savings equal investment ex ante, but this is a property of the one-week model, and it will not hold for a longer time period.  As the author explains, "The ex post magnitudes will be equal whatever period we take, but the ex ante magnitudes will only be necessarily equal if plans are consistent."  Over a longer time period, planned saving could exceed planned investment.  "If an attempt is made to carry through the plans without readjustment, supplies of commodities will begin to exceed demands, and (so far as we can see at present) prices will tend to fall.  Similarly, if planned investment exceeds planned saving, there will be a tendency for prices to rise."

Toward the end of this note, the author exclaims "What a tricky business this all is!"  He then goes on to note four statements that John Maynard Keynes made regarding savings and investment:
(1) In his Treatise on Money, that they are only equal in conditions of equilibrium, and
(2) that an excess of investment over saving means rising prices, and vice versa;
(3) in the General Theory, that savings and investment are always equal, and
(4) that this is a mere identity or truism, without significance for the determination of prices.

"As far as I can make out," Hicks notes, "there are relevant and important senses in which all four of these statements are each of them right and each of them wrong."

Value & Capital, CHAPTER XIV, Section 8

This section begins by noting a dilemma that confronts anyone wanting to calculate social income:  "The income he can calculate is not the true income he seeks;  the income he seeks cannot be calculated."  The text explains that the only real way out of this dilemma is to start with the objective quantity, Social Income ex post, and to adjust it "for those changes in capital values which look as if they have had the character of windfalls."  The author argues that such an estimation procedure is perfectly reasonable, but he emphasizes that the result is only a statistical estimate, not a true measurement of an economic quantity.

In discussing the problem of estimating income, the author proposes one method, which is

to take the actual capital goods existing at the end of the period, and to value them at the prices which any similar goods would have had at the beginning;  any accumulation of capital which survives this test will be an accumulation in real terms.  By adding the amount of consumption during the period, we get at least one sense of income ex post;  by then correcting for windfalls we get a useful measure of real social income.

In closing this section, the author expresses the hope that this chapter has made clear the important influence of income calculations on economic conduct, both at the individual level and the social level.  At the same time, he expresses the hope that the chapter has made clear that "income is a very dangerous term, and it can be avoided."  Finally, he previews future discussions by noting that "a whole general theory of economic dynamics can be worked out" without using income.  Even when a need arises "at a very late stage in our investigations," an exact definition will not prove necessary;  "something quite rough" will be sufficient.

Value & Capital, CHAPTER XIV, Section 7

This section begins with an issue that emerges when considering social income, i.e. the aggregate of individual incomes.  As seen earlier, the concept of individual income depends on the expectations of the particular individual.  Furthermore, as explained in the discussion of equilibrium and disequilibrium, the expectations of different individuals may not be consistent.  As the author notes, "one of the main causes of disequilibrium in the economic system is a lack of consistency in expectations and plans."  So it is obviously problematic to be considering an aggregate based on these possibly inconsistent expectations.  But if this is not what social income is, the author asks, what is it?

He answers this question by noting that the various "definitions of income that we have hitherto discussed are ex ante definitions -- they are concerned with what a person can consume during a week and still expect to be as well off as he was.  Nothing is said about the realization of this expectation."  If the value of the individual's prospect at the end of the week is greater than expected, he is said to have experienced a "windfall" profit for that week (conversely, if less, then a windfall loss).  If the value of the windfall profit is added to the income ex ante (or the windfall loss is subtracted from it), the result is defined as the income ex post.  As the author notes, if this is applied to the concept he earlier termed Income No. 1, then "it equals Consumption plus Capital Accumulation."

The author goes on to note that this particular income concept "has one supremely important property" -- namely that "it is almost completely objective."  As long as the capital accumulation deals with income from property and not with changes in "human capital" then income ex post can be measured objectively.  The author notes that "this is a very convenient property" but argues that it does not justify extensive use of the income ex post concept in economic theory.

The income ex post of any particular week cannot be calculated until the end of the week, and then it involves a comparison between present values and values which belong wholly to the past.  On the general principle of 'bygones are bygones', it can have no relevance to present decisions.

Value & Capital, CHAPTER XIV, Section 6

This section reaches an important and somewhat surprising conclusion about the definition of income.  Recalling that the "central criterion" is "that a person's income is what he can consume during the week and still expect to be as well off at the end of the week as he was at the beginning," the author notes that the various approximations to this criterion indicate "how unattractive it looks when subjected to detailed analysis."  Indeed, he goes on to explain why the approximations raise doubt as to whether the central criterion "does, in the last resort, stand up to analysis at all."

His explanation compares two "prospects" of an individual possessing a certain stock of consumption goods at the beginning of a week and expecting "a stream of receipts that will enable him to acquire in the future other consumption goods, perishable or durable."  The two prospects, which he calls Prospect I and Prospect II, are related in that Prospect II is the new prospect that emerges, one week after having started with Prospect I.  Prospect II "will have a new first week which is the old second week, a new second week which is the old third week, and so on."  The author argues that if both prospects were available at the beginning of the same week, the individual would know which one he preferred.  "But to inquire whether I on the first Monday is preferred to II on the second Monday is a nonsense question; the choice between them could never be actual at all."

He then concludes the section with the following summation of the key insight of this chapter:

This point ... has the same sort of significance as the point we made at a much earlier stage of our investigations, about the immeasurability of utility.  In order to get clear-cut results in economic theory, we must work with concepts which are directly dependent on the individual's scale of preferences, not on any vaguer properties of his psychology.  By eschewing utility we were able to sharpen the edge of our conclusions in economic statics;  for the same reason, we shall be well advised to eschew income and saving in economic dynamics.  They are bad tools, which break in our hands.

Value & Capital, CHAPTER XIV, Section 5

This section continues the discussion of the definition of income.  Whereas the previous section examined the definition in the context of interest rates that are expected to change, the present section considers what happens when we expect prices to change.  In this case, the author introduces a new definition (the third one of the chapter):

Income No. 3 must be defined as the maximum amount of money which the individual can spend this week, and still expect to be able to spend the same amount in real terms in each ensuing week.

The author considers an individual who plans to spend £10 each week.  If prices are expected to rise each week, then the individual must expect to be less well off as time proceeds (because the rising prices imply that he is getting less for his money each week).  If prices can fluctuate up or down, and £10 is to be the individual's weekly income (in the sense of Income No. 3 as defined above), then "he will have to expect to be able to spend in each future week, not £10 but a sum greater or less than £10 by the extent to which prices have risen or fallen in that week above or below their level in the first week."

As the author notes, this sort of correction is "obviously desirable," but in general there is no completely satisfactory solution.  One could take a set of planned expenditures and expected prices, to compare with a given income to see "whether it is such that the planner is living within his income," but unless expenditures exactly equalled income, it would be unclear "exactly how much his income is."

As the author notes, this indeterminateness is not the only difficulty with Income No. 3; there is also the matter of durable consumption goods.  By definition, a given amount of expenditure on durable goods does not constitute that amount of consumption of such goods.  The definition of income should really refer to an amount that can be consumed (not spent) during a period of time while expecting to be as well off at the end of the time period as before.  "It is only if ... the acquisition of new consumption goods just matches the using up of old ones, that we can equate consumption to spending, and proceed as before."  If these things do not match, if the individual is drawing down his stock of durable goods, he must take other steps so that his planned consumption leaves him as well off at the end of the planning period as at the beginning.

Value & Capital, CHAPTER XIV, Section 4

This section continues -- seemingly in mid-paragraph -- the discussion of the previous section, by beginning, "For consider what happens, first, if interest rates are expected to change."  In this case, the author argues, "a definition based upon constancy of money capital becomes unsatisfactory."  He then constructs a numerical example in which the interest rate becomes fixed in the second time period at a rate that is twice the rate in the first period (and it remains at the second-period rate thereafter).  In his example, the individual can make the stream of expenditures

 £10, £20, £20, £20, ...  

and maintain his same quantity of capital, whereas that quantity of capital being available at the beginning of the second time period allows the individual to spend the stream

 £20, £20, £20, £20, ...  

The author notes that "It will ordinarily be reasonable to say that a person with the latter prospect is better off than one with the former."

Accordingly, the author arrives at the definition he calls "Income No. 2."  Namely, it is "the maximum amount the individual can spend this week, and still expect to be able to spend the same amount in each ensuing week."  For constant interest rates, this definition is the same as Income No. 1, but not when interest rates are expected to change.  The author concludes, "Income No. 2 is then a closer approximation to the central concept than Income No. 1 is."

Value & Capital, CHAPTER XIV, Section 3

This section considers the first of several approximations to the "central meaning" of the term income.  This first approximation "would make everything depend on the capitalized money value of the individual's prospective receipts."  The author explains by use of an example (in terms of pounds sterling, denoted by £):

Suppose that the stream of receipts expected by an individual at the beginning of the week is the same as that which would be yielded by investing in securities a sum of £M.  Then if he spends nothing in the current week, reinvesting any receipts which he gets ... he can expect that the stream which will be in prospect at the end of the week will be £M plus a week's interest on £M.  But if he spends something, the expected value of his prospect at the end of the week will be less than this.  There will be a certain particular amount of expenditure which will reduce the expected value of his prospect to exactly £M.  On this interpretation, that amount is his income.

It might be easier to understand this explanation by seeing it expressed mathematically.  Let r denote the rate of interest earned by investments; let M (as above) be the initial sum available for investment, and let y denote income.  Based on the author's description of income as an expenditure that will reduce the expected prospect to M, we have the following equation:

(M − y)⋅(1 + r) = M

Performing one step of multiplication, we get

M + r⋅M − y⋅(1 + r) = M

Subtracting M from both sides and rearranging, we get

r⋅M = y⋅(1 + r)

Therefore,

y = M⋅r / (1 + r).

The author notes that this definition makes sense in the case of income derived from property.  He goes on to note that it is "less obviously sensible" in the case of labor income but "is still quite consistent with ordinary practice."  The author refers to this definition as "Income No. 1" and notes that it is "the maximum amount which can be spent during a period if there is to be an expectation of maintaining intact the capital value of prospective receipts (in money terms)."  Looking at the equation above, we can see that y is less than a single period of interest on the original investment M because of the term of 1 + r in the denominator (assuming r is positive).  This makes sense because the expenditure of y would cause interest to be earned on less than the full investment of M.

The section concludes by noting that this definition is likely the one that "most people do implicitly use in their private affairs;  but it is far from being in all circumstances a good approximation to the central concept."