Value & Capital, CHAPTER XVIII, Section 5

In this rather lengthy section, the author examines the effects of changes in interest rates.  He notes that they can be handled, similarly to changes in prices, by dividing the effects into separate income effects and substitution effects.  Because a rise in the rate of interest will lower the discounted prices of future purchases as compared with present purchases, such a rise "will cause a general substitution all along the line" from present purchases to less distant future purchases, to more distant future purchases.  In other words, the substitution effect will cause "a general postponement of expenditure."  The author does note, however, that "there is plenty of opportunity for all sorts of cross-effects, and all sorts of complementarity to muddle things up."

Regarding income effects, the net result of a rise in interest rates will depend on how the change affects the discounted values of the planned series of expenditures (including the amount that is planned to be left over at the end of the planning period) versus the discounted value of the planned stream of receipts.  For a rise in interest rates, both of these capitalized values will be reduced, but it is not immediately clear which one will be reduced more.  The author notes that this question is "formally identical" with the question addressed in the context of income examining "the relative movement of the capitalized values of two streams (previously of the same capitalized value), when the rate of interest changes."  In that context, the relative changes in capitalized values of these streams depended on the average periods of these streams (weighted by the discounted values of the various payment amounts).  A rise in the interest rate will make the individual better off if the average period of his stream of receipts is less than the average period of his expenditure stream.

When the period of expenditures is greater than that of receipts, the individual, in effect, "plans to spend less than he receives in the near future, to 'spend' more than he receives in the remoter future" (recalling that the capital sum to be accumulated at the end of the planning period is considered part of spending).  Such a person, whom the author describes as "planning to be a lender," is made better off when interest rates rise.  Because these individuals are made better off, they may then decide to consume more.  Thus, "the income effect and the substitution effect go in opposite directions" for such persons, and "either may be dominant.  We cannot say whether their present expenditure will be increased or decreased by a rise in the rate of interest."

The author goes on to discuss the nature of these results, and he explains that they arise "from the same cause as in the effect of changes in wages on the supply of labour, or of changes in the price for one commodity on the demand for another."  But he notes that "the most important thing which emerges is the way in which this indecisiveness depends upon the assumption that the individual 'plans to be a lender.'"

In what the author calls "the contrary case," someone whose average period of expenditure is less than the average period of receipts will be made worse off by a rise in interest rates.  For such a person, the income effect and substitution effect both work in the same direction, namely, to reduce current expenditure in response to an increase in the rate of interest.

These individuals, whom the author describes as people who "plan to be borrowers," include entrepreneurs who are undertaking investments (as well as "spendthrifts" whom he dismisses from further consideration).

In the remainder of the section, the author considers the implications of lenders' and borrowers' income effects for the supply and demand sides of the market for securities.

While those persons who plan to be lenders have an income effect increasing their present expenditure when the rate of interest rises, those who plan to be borrowers have an income effect reducing it.  If these income effects cancel out, then there is nothing left but the two substitution effects, each of which tends to reduce current expenditure.

The author then asks the question, "Are the income effects likely to cancel out?"  He notes that there is "one broad reason" to expect that they will tend to, but that this tendency "is subject to two sorts of exceptions."

The broad reason to expect them to cancel out is that current lending and current borrowing must always be equal when the market for securities is at equilibrium.  But this isn't sufficient for concluding that the aggregate income effects among borrowers and lenders will exactly balance out.  And this gets at the first of the two sorts of exceptions: namely, the possible inconsistency between the planned quantity of  borrowing/lending and the actual current borrowing/lending.

[P]lanned borrowing and lending, being mainly inside people's heads (and not very definite even there), are not matched on the market.  There may be an excess on one side or on the other; though, if there is, it spells inconsistency between plans, and consequent potential disequalibrium.

The second of the two exceptions, which the author deems "doubtless" more important, relates to the possible relative speeds with which borrowers and lenders adjust their expenditure to new conditions.

If borrowers are quicker to adapt themselves than lenders (I should judge that in practice this is probably the case), the income effect on the borrowers' side is likely to be stronger than ... on the lenders' side.  This would make the net income effect work in the same direction as the total substitution effect, and reinforce the conclusion that, for the market as a whole, a rise in the rate of interest will reduce current expenditure, a fall in the rate of interest increase it.

Value & Capital, CHAPTER XVIII, Section 4

In this short section, the author reviews the analysis of changes in commodity prices, addressing the cases in which the price change is, or is not, expected to be permanent.  The purpose of this review is to set up the analysis of changes in rates of interest, which he discusses in the next section.

His analysis begins with the case in which the price of some commodity X rises, and the effect is expected to be permanent (and interest rates do not change). 

There will be a substitution effect against X in favour of other goods;  and there will be an income effect, which must also run against X, save in the exceptional case where X is an inferior good. ... But ... there is no definite rule about the way in which the reduction in demand will be spread over time.

The next case he considers is that in which the rise in the price of X is not expected to be permanent.  In this case, "the income effect will usually be very slight or indeed quite negligible.  The substitution effect, however, may well be much more considerable than in the preceding case."  The reason for this is that the consumer may choose to substitute both other commodities, as well as future consumption of X, for current consumption of X.

The final case he discusses is that in which "the price of X rises, and this rise is interpreted to mean that the price will rise still further in the future (elasticity of expectations greater than unity)."  Depending on the level of the elasticity of expectations, this rise in the price of X could actually lead to an increase in current demand for X (from both substitution and income effects).  The author notes that "This is the familiar case of speculative demand."

Value & Capital, CHAPTER XVIII, Section 3

The author, Sir John Hicks, begins this brief section by noting that once we distinguish between transactions made on different dates, and we replace actual prices by discounted prices, "the whole static theory of value becomes directly applicable" to the analysis of expenditure plans.  The analogous conditions of equilibrium and stability apply.

Another similarity discussed is that of the effects of changes in prices.  When analyzing the effects of such changes, which, in the present context of expenditure planning, also include interest-rate changes, we can divide the effects into two types, substitution and income effects, just as was done in the static theory case.

The substitution effect results from the individual deciding to substitute some planned purchases for others, due to the changes in their relative discounted prices.

The income effect, or more precisely, the effect that the author describes as "corresponding to" the income effect in the static case, results from "the extent to which the individual is made better or worse off by the change in question."  In short, the individual is better off if he can plan the same set of purchases at the various dates (and have something left over) as before the change.  Conversely, he will be worse off if he cannot expect to make the same purchases as before but must instead "retrench somewhere."  This effect depends on the capital values of the streams of both his planned expenditures and his expected receipts.  As a result, the author notes that it actually "would be more logical to call it a 'capital effect', or something of that sort, rather than than an 'income effect,'" but he does not consider it worth the trouble to make that change in terminology.  He does note, however, that "we must remember the precise meaning which has to be given to it from now on."

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.

Value & Capital, CHAPTER XVII, Section 7

In this section, the author reviews what he has written in this chapter by noting that, "I may have laid myself open to the charge of having done nothing but state simple things in a complicated way." He justifies this, however, by the need of explaining where Böhm-Bawerk went wrong in developing the "Austrian theory."

He also restates the general conclusion of this chapter, namely "that changes in the rate of interest affect the 'tilt' or crescendo of the production plan."

He then turns to explaining a further point, which he says is "of much greater practical importance than those with which we have been labouring." This point has to do with the conditions under which the interest rate has a significant influence.

For near-term planning, he asserts that changes in interest rates within the normal range (such as between 2 and 7 percent) probably do not have much of an effect on business decisions. If entrepreneurs are "living from hand to mouth," interest rate effects will not be significant.

Conversely, for longer-term decisions, interest rate changes do have a signficant effect; but, as the text explains, considerations of risk will have an even greater effect.

As we have often seen, the effective 'expected price' of a future output ... is not the most probable price, but the most probable price minus an allowance for risk. Now the farther ahead the future output is, the larger this risk-allowance is likely to become, just because the uncertainty of the future price increases; after a certain point, therefore, the risk-allowance will become so large as to wipe out any possible gains, and the effective 'expected price' will become nil.

Thus, the author concludes that in near-term planning, interest will not have a significant influence, and "risk is too strong to enable interest to have much influence on the far future." He suggests that between these two extreme cases, there is likely a range of intermediate cases in which interest can have a significant influence. The extent of this range depends on the prevailing attitude toward risk.

Value & Capital, CHAPTER XVII, Section 6

In this section the author, Sir John Hicks, explains what was mistaken in Böhm-Bawerk’s concept of the ‘average period of production’ (which Hicks also refers to as ‘the Austrian theory’).  Böhm-Bawerk had reasonably focused on a simple case of production:  namely, “the case where all the input is utilized at one given date, and all the output comes to fruition at another given date.”  The analysis is correct in this case, but, as Hicks notes, the result “does not generalize in the sort of way in which it might have been expected to generalize.”

Instead, in the general case,

The absolute length of the true average period has no significance whatsoever; it depends only in part upon the character of the production plan; it will be lengthened and shortened in an entirely arbitrary manner according as we calculate the average period of the same plan at different rates of interest. Change in the average period is important, but not the length of the period itself. The average period measures nothing else but the crescendo of the plan; and that has nothing to do with the technical methods of production employed.

To clarify the point further, Hicks gives a simple example to illustrate the properties involved.  His example considers a particular firm whose production consists of a number of separate processes, each of which takes n weeks to complete. In any given week, some of the previously started processes are completed, and new ones are started to take their place.  He assumes that the firm is initially in a stationary equilibrium state, with m processes finishing each week, and m new ones begun to replace them.  Thus mn of these processes are being conducted each week, and “the streams of total inputs and total output are both constant over time.”  The firm is assumed to have chosen the number mn "for reasons of risk;  risk-coefficients increase as the scale of output expands; the entrepreneur declines to undertake extra processes, because their capitalized value (allowance being made for risk) would be negative."

If there is a fall in the interest rate, it may be profitable to start some new processes that were not profitable before.  The author states that the inception of these new processes, undertaken only because of the fall in the interest rate, "must raise the average period of the plan."  To explain this, note that these less profitable processes may have, in a sense, a longer payback period.  Even if they do not (that is to say, even if they have the same properties as the other processes), the increased investment in them (in exchange for later profits) will have the effect of diminishing the current surplus and increasing some later surpluses.  In other words, as the author concludes, "the stream is given a crescendo."

Personal note:  Just over 24 hours ago, I was vaccinated against COVID-19, so my hope is that in two weeks or so, I will have escaped the recent global pandemic.