Value & Capital, CHAPTER XVIII, Section 2

In this section, the author starts from the assumption, made near the end of the previous section, that people "do plan, more or less consciously, and more or less definitely, those parts of future expenditure which are relevant to current expenditure."  He therefore argues that the assumption of a complete plan of future expenditures, if used only for determining "the details of current expenditure alone," is not unreasonable.

His analysis works by assuming "an individual who possesses, at the planning date, a certain stock of durable consumption goods;  who is receiving a sum of money R₀ in the current week ... and who expects to receive a series of sums R₁, R₂, R₃, ... in the same way in the following weeks."

The individual's expenditures in the coming weeks are assumed to be (in monetary terms) the sums E₀, E₁, E₂, E₃, ... .  The difference between receipts and expenditures in each week will cause an incremental change in the individual's holding of money or of securities (for simplicity, Professor Hicks assumes only the latter). 

Hicks asserts that the stream of differences R₀ - E₀, R₁ - E₁, R₂ - E₂, R₃ - E₃, ... may be regarded as a stream of lendings (which is reasonable terminology since investments in securities are made in hopes of receiving future payment).   

If the plan is to be carried on for a fixed but arbitrary number of weeks, say n, then at the end of that time the individual can expect to have accumulated, from carrying out his plan, a sum C_n that is available as part of his resources for future consumption or investment.  As the author then explains,

If we regard the provision of such a capital sum as one of the things to which expenditures can be devoted in the last week of the plan, we have an accounting device which enables us to reduce the whole problem to one of distributing expenditure between the n weeks.

Using this sum with the notation defined above, the author's "stream of lendings" becomes

R₀ - E₀, R₁ - E₁, R₂ - E₂, R₃ - E₃, ... , R_n - E_n - C_n

If the sum of E_n and C_n were indeed spent in the last week, then the stream of receipts and the stream of expenditures (adjusted to include C_n) would exactly cancel out, and the capital value of the adjusted stream of lendings must equal zero.  (The author spells out in a footnote his assumption that "the securities initially held are expected to retain the same value at the end as they possessed at the beginning.")

The author concludes the section by describing the equality of the streams of receipts and (adjusted) expenditures as "the clue which enables us to reduce the planning of expenditure (just as we reduced the planning of production) into terms of a problem we have already solved in static theory."

Value & Capital, CHAPTER XVIII -- SPENDING AND LENDING

In this section, the first of this chapter, the author, Sir John Hicks, begins by placing in context the problem to be studied in this chapter.  This problem is the dynamic problem of individual spending decisions.  He begins by reminding the reader of the earlier topics of firms making decisions in both the "static case" and the "dynamic case." 

The static problem of the firm consisted in maximizing the surplus of receipts over costs which could be earned by exploiting a given productive opportunity in given technical conditions; the corresponding dynamic problem consisted in maximizing the capital value of the stream of surpluses which could be expected to accrue, in the present and in the future, from the exploitation of such an opportunity.

For an individual consumer, the static problem involved "choosing the most preferred collection of commodities which could be purchased out of a given sum of money."  By reasoning in a way that is parallel to the arguments for the firm, one might conclude that the dynamic problem for the individual consumer consists of "the choice of a most preferred collection of streams of commodities, out of the various collections of streams which the individual could expect to be able to purchase out of a given expected stream of receipts."

The author acknowledges that "one cannot help feeling considerable qualms" regarding this line of reasoning.  The assumptions about the kinds of plans that firms draw up for their future investments may seem reasonable enough.

But when we turn to the case of the private individual, whose 'plan' (if he has a plan) must be directed solely to the satisfaction of his wants in the present and in the future, then the fact that he will ordinarily not know what his future wants are going to be (and will know that he does not know) becomes very upsetting.  It is possible to plan ahead when one's plan is directed towards a given end (such as profit), but it is not possible to plan ahead when the object of planning is unknown.  For this reason the whole method of analysis threatens to break down.

The author reassures the reader, however, that this perceived problem is not too serious.  Although people may not know the details of their future wants, there is certainly an awareness of a tradeoff between the ability to spend now and the ability to spend in the future.  Moreover, when people buy durable consumer goods, there is an understanding that such goods can satisfy both present and future wants.  Such purchases are, in a sense, making explicit a part of an individual's future policy.  Thus the author states that "People do not plan their future expenditure as a whole; but they do plan, more or less consciously, and more or less definitely, those parts of future expenditure which are relevant to current expenditure."  Such parts of future expenditure include both "particular items of current expenditure" (such as durable goods), as well as a general idea about the size of their total future resources.