Value & Capital, CHAPTER XIX, Section 3

In this section, the author begins describing special cases of analysis to help address the general question of how an individual will distribute his funds between money and securities.

The first and simplest case is defined so that the individual involved will have a demand for money that is "nil."  Or, put another way, the individual will choose to hold all of his funds in the form of securities instead of money.

Suppose that the interest on the securities he possesses at the planning date, together with any other kinds of revenue which may be due him, is expected to yield a constant flow of receipts, the same amount in every future week.  Suppose, further, that he plans to spend, in every future week, the same amount as he receives, no more and no less.  Then, if he is perfectly confident that he can carry out his plan, his demand for money will be nil.  All the money he receives will be paid out again at once; he will need to keep over from one week to another no money balance at all to finance his transactions.

The author goes on to discuss two reasons why this example is unrealistic.

The first is that expenditures and receipts "do not come in at exactly the same moments."  Thus some money balance would typically be held because trying to invest it in securities is not worth the trouble.  The author argues that these effects, from the standpoint of the economy as a whole, probably cause the holding of "a fairly constant amount of money, only liable to some quite regular fluctuations at quarter-days and Christmas and so on."  Moreover, he indicates that this source of demand for money is not much affected by interest rate changes.

The second reason why money is held is that even if expenditures and receipts tended to coincide, there is always uncertainty to be guarded against.  Because the costs associated with selling securities on the spur of the moment could be considerable, "the mere risk of needing to do this would be sufficient to offset a moderate gain in interest."  The degree to which an individual will choose to hold money for this reason will depend on "the individual's attitude to the risk and upon the size of the gain offered by investment in securities."  Therefore this effect is sensitive to interest rates, "but it is also very susceptible to changes in the risk factor."

An important example of a business needing to hold money for the purpose of paying claims on short notice is that of banks.  The author calls this "the clearest case" of a business incurring liabilities that it may be called on "to meet at dates which cannot be quite certainly predicted."  But, as he notes in closing this section, "the holding of money against uncertain future expenditures ... is practiced to some extent by all businesses, and by many private individuals as well."

Value & Capital, CHAPTER XIX, Section 2

In this section the author reviews several of his conclusions from the analysis of money in Chapter XIII.  In many cases money and securities function as close substitutes for one another.  While securities pay interest and money does not, people still prefer to hold some money.  As the author notes, "Even the safest and most negotiable securities, which are not money, involve some risks to their holders, and some costs of acquisition and disposal, from which money is free."

Thus the demand for money depends strongly on the rate of interest (or, as the author elaborates, "on the system of interest rates").  Because of the existence of a wide variety of securities which "form a chain of very close substitutes" between money and other securities, money and securities tend to "behave as very close substitutes, from the point of view of the economy as a whole."  A rise in the interest rate would tend to decrease the demand for money (and increase the demand for securities).

The author closes the section by asking, "If rates of interest are given, what determines the way in which an individual will distribute his funds between money and securities?"  He then previews the discussion in upcoming sections by noting that this question can be approached "most easily if we consider a number of special cases."

Value & Capital, CHAPTER XIX -- THE DEMAND FOR MONEY

In this section, the first one of the chapter, the author, Sir John Hicks, sets up his discussion of what determines an individual's demand for money.

He begins by noting a deficiency in the discussion up to this point of the individual's consumption plan.  This is the simplifying assumption made earlier that any difference between an individual's receipts and expenditures in a time period (e.g. a week) will be made up entirely by an incremental change in his or her holding of securities.  This assumption was made for convenience, but according to Hicks "it would let us down badly in the applications we want to make later on."  And of course it is not truly realistic.

In reality, individuals typically hold some money along with securities and can react to surpluses or deficits by adjusting their holdings of both.  Hicks notes that "It is a matter of considerable importance which form the balancing takes," so he seeks a way of addressing this question within the structure of his theory.  His analysis could easily accommodate money, if money can be treated as though it were some sort of durable consumer good.

It is a condition of equilibrium for the individual that the marginal rate of substitution between acquisitions of any commodities at given dates must equal the ratio of their discounted prices; this rule could be taken as applying to money as well.  The marginal rate of substitution between money now and any other commodity now would equal the current price of that commodity (just the same rule as we found for the standard commodity in statics); the marginal rate of substitution between the acquisition of money now and the acquisition of money at a later date would equal the discount ratio over the period of deferment.  This implies that the interest charge over a period would measure the sacrifice involved in postponing the acquisition of a marginal unit of money to the end of the period .... In other words, the rate of interest would measure the impatience to possess money now instead of money in the future.

The rules for how interest rate changes affect the demand for present commodities would also apply to the demand for money in the present.  Therefore, an interest rate increase "may be expected to diminish the demand for money." Also, a general rise in commodity prices should tend to increase the demand for money.

Hicks concludes the section by stating that these rules for the behavior of money that would apply if it were a durable consumption good are "very reasonable," and that "it would be surprising if more careful attention to the true nature of money were to make it necessary to alter them very considerably."

Value & Capital, CHAPTER XVIII, Section 6

In this section, the final one of the chapter, the author summarizes his analysis of the effects of interest rate changes on expenditures.  He notes that his approach is different than that of other writers but that he is "preparing the ground for an attempt to apply to the general dynamic problem the same sort of reasoning as we used in statics."  The key insight here appears to be his grouping of "the relevant forces in a particular way."

He notes that the traditional way of deriving the effects of interest rate changes on expenditures would be "(i) to inquire how the amount spent out of a given income would be affected; and (ii) ... to inquire how the level of income would be affected" by the interest rate changes.

He then notes that "the effect on the level of income is not at all a simple effect."  He clarifies matters by decomposing this effect into two components:

(ii a) the effect on the incomes of entrepreneurs which would accrue even if they kept their production plans entirely unchanged; and (ii b) the effect on their incomes and on those of other people as well which results from any changes they may make in their production plans.

He points out that his analysis involves grouping the effects (i) and (ii a) together, which allows him to avoid dealing with the concept of income, which as he notes, "We ourselves have learnt to mistrust."  With this simplification, he is able to conclude that, when prices and production plans are given, "a change in the rate of interest will affect the volume of current expenditure in the opposite direction," although he states that it is "quite another matter to say how large this effect may be."

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.

Value & Capital, CHAPTER XVII, Section 5

 In this section, the author provides a fairly straightforward proof of his assertion, made in the previous section, that a fall in the rate of interest lengthens the average period of a stream of surpluses.

His proof begins by defining the concept of the marginal stream, based on the streams of surpluses before and after the change in the interest rate.  In his notation, (S0, S1, S2, ..., Sn) is the stream of surpluses under the production plan corresponding to the old interest rate, and (S'0, S'1, S'2, ..., S'n) is the stream that would be planned at the new rate of interest.  The marginal stream then consists of the stream of differences

S'0 – S0 , S'1 – S1 , S'2 – S2 , ..., S'n – Sn

where each difference could be positive or negative.

The new stream equals the old stream plus the marginal stream.  The author explains that the average period of the new stream is the average of the average period of the old stream and the average period of the marginal stream. He expresses the average period of the new stream as

(CP + cp) / (C + c)

where P and p are the average periods of the old and marginal streams, respectively, and C and c are the capital values of the old and marginal streams, respectively.  He then considers the particular marginal stream at an interest rate for which the capital value is arbitrarily close to zero.  He argues that the quantity cp is still positive.

We saw in an earlier chapter that the product of the average period of a stream by its capital value equals the capital value of an auxiliary stream formed by capitalizing, in each successive week, the items in the stream of surpluses which remain over after that week.  We saw too that every item in this auxiliary stream must be positive (otherwise it would never pay to go through with the production plan implied in the stream);  consequently the capital value of the auxiliary stream must be positive.

Thus in his formula above, c can be neglected, "but the term cp must not be neglected."  The expression then becomes

(CP + cp) / C  =  P + (cp / C)

which is strictly greater than P.  The author also gives a (much) more mathematical proof in the book's Appendix

Value & Capital, CHAPTER XVII, Section 4

In this section, the author begins to give an exact definition to the "broad sense" in which there is an upward tilt to the stream of future surpluses if there is a general fall in interest rates.  In particular, he seeks "a numerical index" characterizing the production plan -- an index that changes "in a given direction when the rate of interest varies."

The author spends some length reviewing both the search by Böhm-Bawerk for such an index, leading to the concepts of "average period of production" and "average period of investment," as well as Knight's objections to Böhm-Bawerk's arguments for these concepts.

Hicks then argues that the needed concept corresponds to his average period of a stream, already derived in an earlier section.  The stream of concern is then "the expected stream of surpluses and deficits (the differences between value of output and value of input in successive periods)," with the weights in the average corresponding to discounted values.

Hicks concludes the section with an explanation of a technical detail about how to calculate the effect on the production plan from an interest rate change. 

What we must do is to start with a certain rate of interest, a certain production plan drawn up in vew of that rate, and an average period calculated from the production plan at the rate of interest.  Then we must suppose the rate of interest to fall, and the production plan to be varied in consequence.  Finally, we must calculate the average period of the new plan, using the same rate of interest in its calculation as before—that is to say, the old rate of interest.  Then our proposition is that the new, average period calculated in this way, must be longer than the old.  A fall in the rate of interest lengthens the average period.

Value & Capital, CHAPTER XVII, Section 3

In this section, the author generalizes the effect of a change in interest rate, which was discussed in the previous section for a specific case.  The previous section considered the interest rate for loans of a given duration, with all other rates of interest assumed to be unchanged.  The current section generalizes this analysis "so as to give the effect of a general shift in interest rates."  In general the effect is as follows:

If rates of interest per week fall for loans of all periods ... this in itself induces a direct tendency for substitution in favour of future surpluses, against the current surplus.

For example, in the context of production planning, a fall in interest rates would (other things being equal) make it more favorable to borrow today to make investments that would lead to a given increase in production at some future date.  The author explains that the effect is not proportional for all future time periods;  instead the effect would be compounded over time.  "Thus we should expect to find the greatest expansion in those surpluses which are farthest away in time."   He also notes that the effects of other surpluses may exhibit a negative effect ("a pull making for contraction") on a given surplus.

He summarizes the effect on surpluses as follows:

The whole effect on the stream of surpluses may be expressed by saying that it is given a tilt;  it is lowered at one end and raised at the other;  it is rotated, as it were, about some point in the middle. 

He includes the following illustration to show the effect on output streams over time (starting with the current period):

Input streams, conversely, are affected in the opposite way, hence the following illustration:

The relative strengths of these tilting effects would depend on technical conditions present in each specific case.

The author mentions that a similar tilting effect on output streams was encountered in an earlier section.  But the effect there (which arose in the context of a price rise assumed to be permanent) was one that was "owing to technical rigidities and the specificity of initial equipment."  In the present setting the tilting effect arises instead from "the very nature of interest itself."

Although technical rigidities and other factors will have an effect here, any stimulus to current production will likely not be very significant.  Therefore the author concludes the following:

The precise distribution over time of the new production plan depends upon technical conditions, for they decide when it will be possible to increase the futurity of output, and diminish the futurity of input.  It is not possible to lay down any hard and fast rule about the output or input of any given date (or even the surplus of any given date);  all we can say is that there must be an upward tilt to the stream of surpluses, in some broad sense or other.

In the next section, the author will begin to give an exact definition to this "broad sense."

Value & Capital, CHAPTER XVII, Section 2

In this section, the author examines the effect of a supposed change in the interest rate for loans of a given duration, assuming that the interest rates for loans of all other durations remain unchanged.  (In the next section, he will generalize from this particular case, to look at "the effect of a general shift in interest rates.")

As a helpful illustration of the effect of interest rate changes, suppose that one's goal is to save up, so as to have a certain quantity of money accumulated at some certain future date.  If interest rates fall, then this means that one must set aside more money now to achieve the planned savings goal.

In the author's discussion, the effect on prices of a fall in the interest rate for loans of t weeks will be to raise the discounted prices of "outputs and inputs planned for the week starting t weeks ahead."  The production planner would also find it profitable to increase the planned outputs for that week and decrease the planned inputs.  The author notes that "This would involve, as a counterpart, either an increase in the inputs planned for other weeks, or a decrease in the outputs, or both."

In general, because of indirect effects of increased demands for some inputs or outputs on the demands for other inputs or outputs, "it is not absolutely certain that any particular output of the date in question will be increased, nor that any particular input will be diminished."  But because the affected inputs and outputs are those of a given week (i.e. contemporaneous), "a change in the rate of interest will change all their discounted prices in the same proportion."

The author thus argues that we can "lump" these contemporaneous commodities into a single commodity that he calls the surplus, which is the value of the outputs minus the value of the inputs.  He then arrives at the central conclusion of his example, which is the following:

The absolutely definite rule, which gives without any exception the effect of a fall in the rate of interest for loans of t weeks, is simply this:  the surplus planned for the (t + 1)th week must be increased.

From this conclusion he goes on to argue that

We can simplify down the problem of the production plan, and regard it merely as the problem of choosing the most profitable stream out of a set of possible streams of surpluses; the list of possible streams being given by technical conditions, and converted into value terms by the assumption of given prices and given price-expectations.  The effect of interest-changes can then be regarded as consisting in substitution among surpluses, using this as a shorthand expression for substitution and transformation among the outputs and inputs, from which the surpluses are built up.

The author closes the section by noting that an increase in one surplus must come about "by substitution at the expense of  other surpluses (it is only possible for one surplus to be expanded if others are contracted)."  It may be possible, however, for a limited number of complementary surpluses to increase at the same time.