Value & Capital, Chapter XX, Section 6

In this section, the final one of the chapter, the author, Sir John Hicks, addresses the importance of the analysis in this chapter and relates it to similar work by other economists studying similar problems, namely Knut Wicksell and John Maynard Keynes.  

He begins by claiming that "The proposition which we have thus established is perhaps the most important proposition in economic dynamics."  He is referring, of course, to his conclusion from the previous section that the case of elasticities of expectations equal to unity marks a sort of "dividing line between stability and instability."  He attributes its importance not to its assumed conditions being commonplace, nor even to their being realistic.  (He does assert, however, that its assumptions are "quite plausible" simplifications of the sort that economists commonly make when constructing an analytical model.)  The importance of the proposition is, instead, a consequence of its having "a strong bearing upon one's whole conception of the economic system, considered as a process in time."

I think it's reasonable to say that the second paragraph of this section is one of the more important paragraphs in the entire book:

So long as economists were content to regard the economic system in static fashion, it was reasonable to treat it as a self-righting mechanism.  A static economy is inherently stable; small causes produce small effects; the system is therefore not liable to large disturbances, excepting those which originate definitely outside itself.  But this appearance of stability was only achieved by leaving out part of the problem.  As soon as we take expectations into account (or rather, as soon as we take the elasticity of expectations into account), the stability of the system is seriously weakened.  Special reasons may indeed give it a sufficient amount of stability to enable it to carry on, ... but it is not inherently and necessarily stable. It is henceforth not at all surprising that the economic system of reality should be subject to large fluctuations, nor that these fluctuations should be so very dangerous.

Hicks goes on to note that his proposition is an extension of a similar proposition by Wicksell, regarding his 'cumulative process.' He notes, however, that it is more widely associated with Keynes, and his arguments in The General Theory of Employment.  Keynes's proof "assumes a unity elasticity of expectations only for prices expected to rule in the near future; for prices expected in the further future he assumes that they move with money wages."  Hicks argues that this makes Keynes's proof less general than his own:  "Expected prices can depend on current prices in any way whatsoever—so long as a proportionate rise in all current prices raises all expected prices in the same proportion—and my proof holds." 

Hicks also explains that his proof makes it clear that the instability is not due to Keynes's assumptions about expectations and their connection with money wages.  "The instability is not a property of wages; it is a property of money and of securities, those awkward things which are not demanded for their own sake, but as a means to the purchase of commodities at future dates."

In a footnote at the end of this section, Hicks mentions two lines of relevant research that appeared after the publication of the first edition of Value and Capital.  One is by Oskar Lange and Jacob Mosak who examined the arguments in this chapter.  From their work, Hicks concludes that his treatment could be improved, but he chose to leave the current chapter unaltered and has "set out the qualifications I should now desire to make in an additional note at the end of the volume."

A separate line of inquiry that Hicks considers potentially relevant is that of Paul Samuelson in addressing "process analytics."  He states that "I am still not convinced that it has a very close relevance, but it deserves more discussion than I gave it in 1938.  I have therefore included a further note on this subject."

I plan to address each of these additional notes in upcoming posts.

Value & Capital, Chapter XX, Section 5

In this section, the author reverts to his earlier assumption that the economy being analyzed includes the circulation of money, which does not bear interest.  He then sets up a test of stability for a system in which elasticities of expectations are unity, and the interest rate is fixed, while the price of some commodity, which he calls commodity X, rises by 5%.  If the system is to remain stable, the price rise in commodity X should induce price changes in the other commodities, such that the result is an excess supply of commodity X.  If only some of the other commodity prices are analyzed, there is not a problem.

But when we consider the repercussions on all other markets (but not the market for securities, since the rate of interest is taken as given, and not the market for money, since it is not independent from the rest), then we seem to move into a different world.  Equilibrium can only be restored in the other commodity markets if the prices of the other commodities all rise by 5 per cent. too.

The problem is that under these assumptions, the ratios of prices between given commodities remain unchanged, and therefore "there is no opportunity for substitution anywhere."  As the author describes it, such a system is "in 'neutral equilibrium'; that is to say, it can be in equilibrium at any level of money prices."

As he goes on to explain, if elasticities of expectations are greater than unity, the system is definitely unstable."  The case in which elasticities of expectations are equal to one is therefore a rather important special case.  

Technically, then, the case where elasticities of expectations are equal to unity marks the dividing line between stability and instability.  But its own stability is a very questionable sort.  A slight disturbance will be sufficient to make it pass over into instability.

The author concludes this section by going through a simple argument, based on a rise in demand for a single commodity, to conclude that "when elasticities of expectations are equal to unity, the system is liable to break down at the slightest disturbance."

Value & Capital, Chapter XX, Section 4

The previous section concluded by noting that "substitution over time will be strongly stabilizing" for the dynamic system being analyzed.  The author therefore begins this section by asking "whether the system will still be stable if the opportunity for substitution over time is withdrawn."  He explains that such a condition would mean that "elasticities of expectations become all equal to 1."  (In other words, changes in current prices will cause changes in expected prices in exactly the same proportion.)

The author notes that this assumption would seem to be extremely plausible and for that reason has been "taken for granted by the majority of economists."  But as he also notes,

Just for this reason, it has caused an immense amount of trouble.  The most natural assumption which one can make for dealing with dynamic problems is one of the most dangerous assumptions, for it involves treading on the very borderland between stability and instability.

He blames the reliance on this assumption for "much of the bewilderment of 'monetary theory'" in the first half of the twentieth century (recall that the first edition of Value and Capital was published in 1939).

The author credits Knut Wicksell, with giving "the first indication that something was wrong" in his book Interest and Prices, published in 1898.

Roughly, what his central argument amounts to is this.  In equilibrium, there corresponds to a particular rate of interest a particular relation between current prices in general and expected prices in general.  If the rate of interest is lowered, current prices will rise; if expected prices had remained unchanged, this process would restore equilibrium with current prices bearing a higher ratio to expected prices.  But if expected prices rise pari passu ["in even step"], the equilibrium tendency is defeated; current prices can never catch up.  The system is involved in the famous 'cumulative process'.

On a closer look, however, the author points out that Wicksell's system involves a pure credit economy, with all transactions involving payment in interest-bearing bills.  Thus "there is no place in his system for a money that does not bear interest; it is neither demanded nor supplied."  So the mathematical conditions for temporary equilibrium involve one fewer equation than those in Hicks's system.  If each system had n ‒ 1 real commodities, then because Hicks's system additionally includes both money and interest-bearing securities, his equilibrium conditions involve n + 1 equations and n + 1 unknowns (although as we have seen, one of them is redundant, so they reduce to n equations and n unknowns). 

In Wicksell's system, however, there is no supply or demand for money, so one equation is dropped from his equilibrium conditions (as compared with Hicks's system).  Another equation is dropped as before, because accounts must balance, so there remain n ‒ 1 equations, which are insufficient to determine n unknowns.

The author (Hicks) goes on to explain that Wicksell's conditions do determine the relative prices of the various commodities, along with the rate of interest, but "The general level of money prices (the value of money) is left indeterminate." He illustrates this with an example in which there is an increase of 5% in all prices (emphasis on all).  This change "will leave every one's position unchanged, so long as the rate of interest does not vary."  Prices are up, but incomes are up by the same amount.  Demands and supplies thus remain the same.  Since the 5% increase is an arbitrary choice, the conclusion is that the system could be in equilibrium "at any level of money prices."

As Hicks puts it, "Wicksell's price-system consists of a perfectly determinate core‒—the relative prices of commodities and the rate of interest‒—floating in a perfectly indeterminate aether of money values."  The implication of the "utterly arbitrary" nature of the money-price level is that "any slight and temporary disturbance of data may shift it about to a large extent."  Even "slight divergencies" between the rate of interest as determined by 'real' causes and the "momentary money rate ... are sufficient to set up large changes in the price-level."

Hicks concludes that the belief, among Wicksell and his immediate followers, in a possible discrepancy between the money rate of interest and the natural rate is a rather unfortunate "delusion." 

If the theory is interpreted strictly, the possible discrepancy is only a virtual discrepancy;  as soon as the discrepancy becomes actual, the theory breaks down.  For this reason the theory is of very little use as a guide to banking policy, the field in which it was thought to have direct applicability.

He concludes the section by previewing another way to look at "the whole matter ... which incidentally enables us to dispense with Wicksell's assumption of a Pure Credit Economy."

Value & Capital, Chapter XX, Section 3

In this section, the author goes through the exercise that he previewed at the conclusion of the previous section -- namely, setting up "a particular case of the temporary equilibrium system which has the same formal properties as the static systems already known to be stable" to see whether it passes the same set of stability tests as the static systems.

To set the context, he begins by noting that the main difference between these two types of systems is the presence of the buying and selling of securities in the dynamic case (and of course its absence in the static case).  Because securities are a kind of commodity, their presence in a temporary equilibrium model "only changes the formal properties of the system in so far as this special kind of commodity fails to observe the static rules of behavior."

The author notes that a key condition, identified earlier, for the static system stability rules to hold is that preferences between commodity choices are independent of the scale of prices.  And he goes on to explain that "This condition will continue to hold, even in a dynamic system, so as long as elasticities of expectations are zero, that is to say, so long as all price-expectations and interest-expectations are given."  Under these conditions, securities will behave exactly like ordinary commodities.

The author next goes into an explanation of this principle, using an example economy in which all lending is of one short duration, namely one week. If expected prices are given, and expected interest rates are given, then discounting prices to the current week (which involves multiplying them by the discount ratio) leaves the ratios of any two prices unaffected.  This enables us to have a commodity we may call 'securities' whose price is the discount ratio for one week and which behaves the same as any ordinary commodity.

He then argues that the same conclusions hold in an economy with long lending.  Rates of interest will adjust, and there will be new income effects based on past lending contracts, but he concludes that none of these effects would be "seriously destabilizing."

The author sums up this section by concluding that "So long as elasticities of expectations are zero, the temporary equilibrium system works exactly like a static system and is as stable as that is. ... So long as all changes in current prices are regarded as being temporary changes, any change in current prices will induce very large substitution effects in a large number of markets ... [These effects] will be strongly stabilizing ... indeed, the forces making for stability are likely to be so potent that it will take a very violent disturbance of data to have any considerable effect on the price-system at all."

Value & Capital, Chapter XX, Section 2

The author begins this section by noting that he hopes to provide clarity on such "topically interesting problems" as "the effects of saving and investment on the rate of interest" as well as "the effects of general changes in money wages."  But he observes that it is difficult to determine the correct answers to these questions.  The reason for this difficulty, he explains, involves the phrase he placed at the beginning of the previous section—essentially used as a subtitle of the chapter—namely that "the temporary equilibrium system is liable to be imperfectly stable."

As part of his discussion, the author reviews the results of his earlier analysis of stability in exchange.  He summarizes these results as follows:

In order for a system of multiple exchange to be perfectly stable (and the temporary equilibrium system is simply an extended system of multiple exchange), the following conditions must be satisfied.  A rise in the price of any commodity must make the supply of that commodity exceed the demand (a) if all other prices are given, (b) if some other prices are adjusted so as to preserve equality between demand and supply in their respective markets, (c) if all other prices are so adjusted.

He describes this last condition as being "indispensable."  Without it, "the system is not stable at all, but will break down at the slightest disturbance."  Assuming this condition is met, either of the other conditions could fail to hold, and the system would still be "stable in the end ... but we have to be prepared for its working to show queer anomalies."

When the author applied these stability tests to static systems, he "found no significant reason to suppose that they gave any particular trouble."  Hence, his analysis treated them as perfectly stable.  In the current chapter he addresses the question of "What happens when we apply the same tests to the dynamic system—or rather to the system of temporary equilibrium?" 

His plan for answering this question is to try "to construct a particular case of the temporary equilibrium system" in such a way that its formal properties match those of the static case.  This particular case will then be perfectly stable.  He will then compare the particular case with the general (imperfectly stable) case, in order to "see whether there is anything in the general case likely to upset its stability—and if so, what the disturbing element is."

Value & Capital, CHAPTER XX -- THE TEMPORARY EQUILIBRIUM OF THE WHOLE SYSTEM

In this first section of the chapter, a section titled "Its Imperfect Stability," the author, Sir John Hicks, introduces the analytical methods he will use to analyze the effects of changes in data, such as prices, on the workings of a dynamic economy.

He begins by noting how his method of analysis allows for an easy transition from analyzing the behavior of a single individual or firm to analyzing "the great issues of the prosperity or adversity, even life or death, of a whole economic system." His method works by deriving laws of market behavior for idealized, representative individuals and firms.  These laws, elaborated for what he calls "those tenuous creatures" then 

become revealed 'in their own dimensions like themselves' as laws of the behavior of great groups of economic units, from which we can readily evolve the laws of their interconnexions, the laws of the behaviour of prices, the laws of the working of the whole system.

The author then notes that an earlier chapter laid out the conditions for a (temporary) equilibrium of an economy during a particular 'week' although the discussion in that chapter did not use the "representative economic units" described above.  These equilibrium equations define the prices that will result when conditions such as preferences, resources, and expectations are specified.  The author's goal in this chapter is to "begin to set the equations to work" to determine what happens when some of the conditions change.

He explains that the analytical process will "follow out a programme exactly parallel to that which we previously followed when dealing with a static price-system," but with an important difference.  In the present context, "the laws of the working of a temporary equilibrium system" are not the ultimate goal of the analysis in the same way that the corresponding laws of a static system were.  For a temporary equilibrium system, the changes in data that will be analyzed are only hypothetical.  But investigating these changes is a necessary precondition for being able "to examine the ulterior consequences of changes in data."

He also defends the value of the short-term analysis used in the theory of temporary equilibrium.  "For many purposes, what we want to know is exactly what the theory of temporary equilibrium tells us—what immediate alteration in the course of events will follow from a particular change in data."  He also revisits the use of a 'week' as the planning period for his analysis;  he points out that such usage is rather arbitrary and that 

The main problems where it is necessary to consider more than one 'week' are those where we are specially interested in the consequences of accumulation or decumulation of capital.  These have to be held over for later consideration;  they belong to a part of dynamics which falls outside temporary equilibrium theory.

He concludes the section by discussing the distinction between two kinds of effects from price changes, namely those effects that "result simply from people's awareness of the initial effects" and "those effects which depend on capital accumulation" (and whose speed may be limited by the "duration of the processes needed to bring about changes in productive equipment.")  He explains that his method of analysis will "[suppose] the first sort of effect to go through with the maximum of rapidity," and that while this may not be realistic, it poses no great difficulty.

Value & Capital, CHAPTER XIX, Section 5

In this section, the final one of the chapter, the author begins by noting that the preceding discussion of an entrepreneur's expenditures assumed these expenditures to include both those expenses going toward running the business, as well as spending on consumption goods.

The author explains that it was a "theoretical convenience" to suppose the entire financial aspect of the business to involve transfers into or out of the entrepreneur's private account, although in practice this supposition is unrealistic.  For a private firm, the distinction between the firm's account and the individual's account may be somewhat artificial; for a joint-stock company, however, the situation is different.

There is a real line of division;  the financial side of the firm's operations has an existence of its own quite separate from the private accounts of the shareholders—a separation maintained by the legal principle of limited liability.

The analysis of the present chapter would apply "perfectly well" to a firm's financial account being treated as a sort of private account, but there is a remaining difficulty when it comes to joint-stock companies, namely their decisions about payment of dividends.  The author concludes this section (and the chapter) by explaining the difficulty as follows:

No clear principle is left to determine on what scale dividends should be paid—that is to say, how much should be paid out in dividends in the current period and how much should be 'ploughed back into the business'.  Nor does there seem to be any theoretical device by which this arbitrariness can be removed;  it is a ... real peculiarity of the joint-stock company. ... [T]he only implication for the general dynamic theory ... is that we must be prepared sometimes to treat dividend policy as an independent variable.

Value & Capital, CHAPTER XIX, Section 4

In this section, the author adds to his preceding discussion of the reasons for holding money in stationary conditions.  The additions in this section amount to two further reasons for holding money when conditions are not stationary.

The first reason is the result of a person's planning to undertake "some considerable increase in his expenditure in the near future."  Because of uncertainty about when such funds would be needed, as well as the convenience of transferring needed funds in a single transaction, a person planning on such a rise in future expenditure will very likely prepare for it by increasing his demand for money in the present.

A second reason results from having plans, not for increased consumption, but for increased investment in securities in the near future.  As the author implies, the reason an individual would make such investments is "to be able to be able to spend more than he receives at some distant and probably conjectural future date." For the near term, however, such increased holding of cash reflects a plan to purchase securities, given an assumption that such investments are cheaper when multiple 'weeks' of 'savings' are consolidated into a single transaction.

The author summarizes his findings thus far as being that "we should not go far wrong if we said that the demand for money depends on the rate of interest, and upon the volume of planned expenditures in the near future (in money terms), some attention being paid to the confidence with which it is expected that this expenditure and no more will be carried out."  This summary, as he notes, does not apply to his last reason for holding money, namely, "an increase in the amount of securities that the individual plans to buy in the near future."  He calls this "an awkward exception" to his rule for the demand for money but states that, "I do not see any convenient way of reformulating the rule by which it can be avoided."

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