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."

Value & Capital, CHAPTER XIV, Section 2

This section begins to discuss the meaning of the term income, in the context of dynamic economics.  In the stationary state of the dynamic model, as well as in the static case, the meaning is much easier to specify.  For a person who expects to receive “the same amount in every future week as he receives this week, it is reasonable to say that that amount is his income.”  

In the more general dynamic case, complications arise.  The author uses the example of a person being paid more in the current week than in some other weeks (if, for example, “this week’s receipts may include wages for several weeks’ work”);  in such a case “we should not regard the whole of his current receipts as income.” Similarly, for someone paid once every four weeks, if “the present week was one in which his salary was not paid, we should not regard his income this week as being zero.”

If not zero, then what should the income be in this example?  In proceeding to try to answer this question, the author notes that

The purpose of income calculations in practical affairs is to give people an indication of the amount which they can consume without impoverishing themselves.  Following out this idea, it would seem that we ought to define a man’s income as the maximum value which he can consume during a week and still expect to be as well off at the end of the week as he was at the beginning.

He concludes that this definition of income “is what the central meaning must be,” because “the practical purpose of income is to serve as a guide to prudent conduct.”

He closes the section by noting that “business men and economists alike are usually content to employ one or other of a series of approximations to the central meaning.”  The next several sections of the book will look at examples of such approximations.

Value & Capital, CHAPTER XIV -- INCOME

In this section, the first of the chapter, the author, Sir John Hicks, notes that his discussion of interest has concluded, and that he has thereby "concluded all that it is absolutely necessary to say about the foundations of dynamic economics."  He further notes his intention, ultimately, "to analyse the working of the dynamic system, proceeding on parallel lines to those on which we analysed the working of the static system in Part II."  Meanwhile, he notes a possible objection to the discussion so far, namely that it has not addressed topics such as Income, Saving, Depreciation, or "Investment (with a capital I)."

He explains that he deliberately omitted these concepts from the previous five chapters.  He finds "far too much equivocation in their meaning" and believes essentially that "they are not logical categories at all;  they are rough approximations, used by the businessman to steer himself through the bewildering changes of situation which confront him."

He states that "eminent authorities" have confused "each other and even themselves, by adopting different definitions of saving and income, none quite consistent, none quite satisfactory."  He concludes the section by noting the need to bring out the reason for such confusion.  He will spend the remainder of this chapter discussing various definitions of income.  In supplementary notes at the end of the chapter he will discuss the relation between Saving and Investment, as well as the effect of interest rate changes on the calculation of Depreciation, and hence Income.

Value & Capital, CHAPTER XIII, Section 5

In this section, the final one of the chapter, the author summarizes the chapter as having given a "preliminary survey of the relation between money and interest."  The author notes that "The fact that money and securities are close substitutes is absolutely fundamental to dynamic economics."  And he goes on to note that "This close substitutability is much the most important property of actual money which we shall need in our further inquiries."

Money serves as a standard of value, although from the point of view of economic analysis, it is straightforward to consider some other standard commodity "selected from the rest to serve as standard of value."  The author notes that actual money also has two other important properties, "considered for the first time in this chapter," namely "the familiar properties of being a 'medium of exchange' and a 'store of value.'"  He concludes the section, and the chapter, by stating that the "important consequence" of these properties of money "for the working of the price system is simply this:  they explain why there is such a close relation of substitution between money and securities, that is to say, they explain the phenomenon of interest -- money interest."