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."