Value & Capital, CHAPTER XII, Section 2

In this section, Hicks notes that two potential "difficulties" in discussing the rate of interest have already been dealt with by the previous analysis.  The first is that calculating the interest rate, not in isolation but "as part of a mutually interdependent system" that includes all the commodity prices, might seem to complicate the problem.  On the contrary, Hicks notes that because the interest rate is a price, like other prices, determining it is part of "the general problem of price-determination in an economy where borrowing and lending are practiced," which makes the problem "a good deal easier to understand."

The second potential difficulty is that of determining "the" interest rate, when in reality there would seem to be many different interest rates in an actual economy.  The simplified models of the previous chapter provided two different ways in which an economy could be analyzed as having only one rate of interest -- either the single-period "short rate" or, alternatively, the "long-rate" corresponding to a spot market in which all loans are assumed to last indefinitely.

Hicks therefore notes that the problem to be discussed in the present context "divides into two sub-problems, according as we assume short lending, or long lending, to be the only kind of lending practiced."  The upcoming sections of the chapter will examine these two cases in turn.

Value & Capital, CHAPTER XII -- THE DETERMINATION OF THE RATE OF INTEREST

The author, Sir John Hicks, begins Chapter XII of Value and Capital by raising the question of what determines the rate of interest.  Among economists, the traditional answer to this question had been the demand and supply of "capital," but Hicks notes that the definition of capital in this context had been somewhat imprecise.

Does capital mean 'real capital' in the sense of concrete goods and the power to dispose over a given quantity of them? ... Or does 'capital' mean 'money capital' in the sense of loanable funds -- power to dispose over a given quantity of money?  It makes a great deal of difference which interpretation we take.

Before addressing this particular question, Hicks notes another apparent controversy among "those who adhere to the monetary approach," namely whether the interest rate is "determined by the supply and demand of loanable funds (that is to say, by borrowing and lending)" versus being "determined by the supply and demand for money itself."

Hicks notes that the latter view is the one proposed by John Maynard Keynes in his General Theory, and Hicks explains that he will endeavor to show that these two views lead to the same results.

Value & Capital, CHAPTER XI, Section 6

In this section, the final one of the chapter, the author summarizes his findings on the behavior of interest rates in an example economy.  In earlier sections he had defined two separate ways of constructing a simple economy having only one market rate of interest.  He argues that each of them has its advantages, so he proceeds to discuss them both in this section ("We shall therefore try to drive them for a while in double harness.")

In the first approach, there is a one-period interest rate (the "short rate") that is used as the unit from which the whole system of interest rates is built.  The author argues that "a system of nothing but short lending would break down in practice because many borrowers would desire the additional security that comes of borrowing for longer periods, and lenders would be prepared to grant them this security in return for a concession of rather higher rates of interest."

In the second example, interest rate is for funds loaned indefinitely.  The author notes that borrowers wanting to borrow for an extended length of time would be content with such a system.  In addition, those lenders "whose object is simply to derive a regular income from their capital, and have no thought of anything else" would likely find indefinite lending to be satisfactory.  In practice, the consideration by a lender of wanting his capital back for other uses will tend to expose the problems with indefinitely long lending.

As we have seen, the rate of interest which can be earned on a loan of any finite duration, by investing in undated debentures, is highly conjectural.  If there is a serious rise in the long-term rate of interest, the effective yield may be completely wiped out. But this is much less likely to happen if the security acquired has a definite maturity, even if it is disposed of at a different date from that at which it falls due.
    Thus lenders will always tend to reduce the risks to which they are subject if they can substitute shorter lending for longer lending ... In general we may suppose that they will be willing to make some sacrifice of interest (which may be great or small) in order to achieve greater security.

So short and medium-term interest rates will tend to be below the prevailing yield on indefinite loans;  the difference will correspond to a risk premium determined by "the estimate put upon the gain in security."  The prevailing yield on loans of indefinite duration "will lie below the current (long-term) market rate when that rate is expected to rise in the future, above it in the contrary case."  When the long-term rate is expected to be stable, "the short rate will lie below it to the extent of the normal risk-premium; when the long rate is expected to rise, the short rate will lie below it still further;  it is only when the long rate is expected to fall that the short rate may lie above the long rate."

These conclusions, based on the analysis of long-term rates, are consistent with those derived from the analysis of short rates.  The only difference is which of the rates (short or long) is the focus of expectations regarding future rate changes.  In both cases, the analysis of this section describes how a significant portion of the borrowing and lending will happen at rates different from the single market rate of interest, in order to accommodate the desire for greater security.  The author concludes the section (and hence the chapter) by noting that "there is a tendency for short and long rates to move in the same direction, but for the movement of short rates to have the larger amplitude."

Value & Capital, CHAPTER XI, Section 5

This section continues the discussion of long lending in the context of a "spot economy."  Earlier in this chapter, the analysis explored a model in which a long-period loan could be built up out of a sequence of one-week loans, with the interest rate for the long loan being the arithmetic average between the current short rate and the forward short rates for the periods comprising the loan duration.  Section 5 describes a different way of simplifying the analysis of interest rates;  this approach views all loans as having indefinite (i.e. infinite) duration.  Another way of viewing this (my own interpretation, not the author's exact words) is that a loan gives the lender the right to an ongoing series of payments from the borrower.  When the borrower wishes to pay off the loan, he or she must buy back that right from the lender (at a price that reflects both the payment size, and the interest rate prevailing at the time of the buy-back).

Once a loan is made, the lender holds an asset -- the right to be paid a fixed amount "in perpetuity, at regular intervals, as interest on the loan."  The value of this asset will change according to the interest rate at any particular time.  If the interest rate goes down, a new loan that generates the same payment as the existing loan would require a greater loan amount (principal), so the capital value of the existing loan would increase with a decrease in interest rate.  Conversely, the capital value would decrease for an increase in interest rates.

Suppose R is the current week's interest rate, and R' is the rate a borrower expects for the following week (the author continues to base his illustrations on the use of one week as a loan period).  The author points out that a loan's capital value "will change in the course of the week in the proportion R/R'."  He then states that the effective rate a lender will have to pay is

R + (R / R') - 1

This expression can be understood as follows:  the first term represents that portion of the return that results from the existing interest rate;  the second and third terms represent the change in capital value expressed as an interest rate.

An individual who wants to borrow can issue new securities (thus becoming obligated to make the associated payments); or he could sell existing securities he already possessed (which has the effect of increasing his net indebtedness).  An individual who wants to lend can do so by buying old or new securities, thus becoming entitled to the associated stream of payments.  A buyer is indifferent between old and new securities (assuming there is "an equal degree of default risk"), so there must be an equivalence between these securities' prices if they generate the same income per period.  We may view this equivalence either as the interest rate on new securities adjusting to the prices of existing securities, or as the prices of those securities adjusting to the new interest rate.  Either way, the new prices of the old securities are completely determined by the new interest rate, which is the only market rate of interest in the system (in the words of the author, there is a "purely arithmetical relation between the prices of old securities and the rate of interest.")

Value & Capital, CHAPTER XI, Section 4

This section continues the discussion of interest rates on loans of various durations, based on the view of a long-duration loan as a series of single-period loans (the text uses a week as the length of a single period).  The text notes that interest rates for loans beginning in a future week "are strictly analogous to the futures prices" discussed in the previous chapter "and are determined in almost exactly the same way."

The previous chapter's discussion of forward trading discusses the role of hedging and speculation in bringing about the coordination of plans in a private enterprise economy. A similar distinction of hedgers and speculators is relevant in discussing the market for long-terms, although the author concedes that "it is not usual" to think of the loan market in this way.  The text notes that, all other things being equal, someone who "[enters into] a long-term loan contract puts himself into a more risky position than he would be in if he refrained from making it;  but there are some persons (and concerns) for whom this will not be true."  For a person or firm already committed to a large project that will require capital over a large number of future time periods, entering into a long-term loan will amount to hedging their future supplies of loan capital.  This opportunity to reduce their risk will give them a strong incentive to borrow long.

The text notes that there does not appear to be a similar incentive on the other side of the market, but it does mention "an important circumstance which demands attention."  The discussion goes on to explain that, essentially, there are some fixed costs of making a loan, regardless of the size of the loan.  Thus "the difficulty of short lending may sometimes have the effect of driving lenders into the long market."  Although this effect may be real, the text implies that it is relatively weak, and therefore, "If no extra return is offered for long lending, most people (and institutions) would prefer to lend short."

The result of these effects on the demand and supply for loan capital will tend toward "a large excess of demands to borrow long which would not be met.  Borrowers would thus need to offer better terms in order to persuade lenders to switch over into the long market (that is to say, enter the forward market)."  As with speculators in the forward commodity market, lenders in the long loan market would only participate if by so doing, they "gain sufficiently to offset the risk incurred."  To balance supply and demand for loanable funds, the interest rate for any particular future week must be high enough to induce a sufficient quantity of loan capital to be available for the loan contracts.  This forward short rate will have to be higher than the short rate the lenders expect to see in that future period, in order to compensate the lenders for the risk they incur.  The excess above the expected rate corresponds to a risk premium analogous to that in forward commodity markets.  If there is an expectation that future rates will rise, the excess will be even greater;  if rates are expected to fall, the premium will be reduced.

The section closes by noting that these rules "must also apply to the long rates themselves, which, as we saw in the last section, are effectively an average of the forward rates."

Value & Capital, CHAPTER XI, Section 3

This section revisits the concept of reducing a long-term loan into a combination of spot and forward transactions.  In particular, the discussion examines a case of a loan made for two weeks, which is equivalent to a loan for one week, plus a forward transaction renewing the loan for the succeeding week.

Looked at in this way, the rate of interest for loans of two weeks ... is compounded out of the 'spot' rate of interest for loans of one week and the 'forward' rate of interest, also for one-week loans, but for loans to be executed in the second week.  If no interest is to be paid until the conclusion of the whole transaction, then the same capital sum must be arrived at by accumulating for two weeks at the two-weeks rate of interest, or alternatively by accumulating for one week at the one-week rate, and then accumulating for a second week at the 'forward' rate."  The two transactions are ultimately identical.

Using the notation R1, R2 and R3 for the current one-, two-, and three-week rates, respectively, and the notation r1, r2, and r3 for the single-week rates for "forward" transactions in weeks one, two, and three, respectively, we have the following equations for the costs of paying back one-, two-, and three-week loans, respectively:

1 + R1 = 1 + r1

(1 + R2)^2 = (1 + r1)(1 + r2)

(1 + R3)^3 = (1 + r1)(1 + r2)(1 + r3)

These relationships are less complicated if we assume simple interest.  In that case the following equations express the costs of interest for the one-, two-, and three-week loans, respectively:

R1 =  r1

 2 R2 = r1 + r2

3 R3 = r1 + r2 + r3

Thus the long rate for a loan of a given length is the arithmetic average between the current short rate and the forward short rates for the periods comprising the loan duration.

Value & Capital, CHAPTER XI, Section 2

This section examines factors that determine the rate of interest on loans.  Given the conclusions of the previous section, the focus is on money rates of interest.  Loans -- even those made at the same time -- may have different interest rates.  There are two main reasons for these differences:  (1) differences in the length of the loan period and schedule of repayment; and (2) differences in the risk of the borrower defaulting on the loan.  According to the author, the second of these reasons "is responsible for the element of 'risk premium' in interest rates as generally understood."

A borrower judged to have poor credit will have to pay a higher interest rate than a borrower with good credit.  This is because of the extra risk that loaning to such a borrower imposes on a lender.

[E]ven if the supposedly untrustworthy borrower does discharge his obligations, he will not pay more than he is obliged; that sets a maximum to the receipts which can be expected by the lender; all the possible variations from it are in one direction.

Therefore a lender will only be induced to lend to a less sound borrower if he is offered better terms than for a loan to a sound borrower.

A borrower's creditworthiness is a matter that individual lenders must subjectively assess.  These types of judgments are likely to vary among lenders.  For a small loan, a business may find it possible to raise the desired amount of funding "by appealing only to that inner circle of potential lenders with which it has good standing, and who thus may be expected to be willing to lend to it on relatively favourable terms."  To raise larger amounts, the business must either appeal to other lenders, who will want a higher rate, or else persuade lenders in the "inner circle" to lend more.  The amount that a particular lender will loan is limited by that lender's willingness to incur risk from "putting all his eggs in one basket."  Offering better terms (such as a higher rate of interest) not only persuades an individual lender to lend more, but it also induces additional lenders to be willing to lend.  The result of this effect is that

Each particular borrower thus finds himself confronted with a sort of 'supply curve for loan capital', analogous to the supply curves of other factors of production which confront a producer when he is in a 'monopsonistic' (or monopoly buyer) position.

The section closes by noting that there is no reason to suppose this supply curve would be perfectly elastic.  Although the author does not go into detail, he notes in passing that "this consideration introduces into the theory of interest questions analogous to those which have been discussed by writers on Imperfect Competition," which a complete theory of interest ought to take into account.

Value & Capital, CHAPTER XI -- INTEREST

In this first section of Chapter XI, the author, Sir John Hicks, references the discussions of the preceding sections to introduce the concept of a loan transaction, as well as that of interest.  Previously, he had introduced the concept of a "Spot Economy" in which all transactions were made for immediate delivery, as well as that of a "Futures Economy" in which "everything was fixed up in advance" for some considerable amount of lead time.  These concepts were helpful exploring potential sources of disequilibrium in an economy.  In this section he notes that "there is no reason why the two sides of a bargain should be due to be executed at the same date."  Thus we have another kind of transaction -- loan transactions -- where the transaction is divided in time;  one side is executed immediately, and the other at some future date or series of future dates.

Any exchange of this sort is technically a loan, but by far the most common in practice is an exchange of money now for money later.  It is uncommon to exchange goods of one sort now for goods of another sort later, for the same reason that barter is not more common:  the inconvenience of searching for someone who wants exactly the goods you have and can offer you goods that you want in exchange.  Transactions involving goods now for money later, or goods later for money now, occur frequently, but Hicks notes that "they are naturally thought of as reducible to a money loan plus a spot transaction (or a forward transaction)."  To illustrate, he imagines a pure-barter case of exchanging "coffee now for coffee a year hence" and notes that it can be reduced to a spot transaction, a forward transaction, and a money loan.  He then goes into a discussion of how a forward market implicitly determines a rate of interest in terms of whatever commodity is being traded.  Using an example in which the price of coffee for delivery in one year is trading at 3 percent above the spot price, and the interest rate on money is 5 percent, he determines the coffee rate of interest to be 105/103, or approximately 2 percent.  The reasoning is as follows:  a person who wants to "lend coffee for one year" could, in this example, sell the coffee in the spot market, loan the money proceeds at 5 percent, and cover the sale of the coffee by purchasing on the forward market.  To put it another way, a person who has coffee now should be able to obtain an increased amount of coffee in a year (even though the price of coffee is expected to increase) because, in this example, money can grow slightly faster.  Hicks concludes the discussion by noting that the coffee rate of interest will be the same as the money rate of interest only if the forward price of coffee is the same as the spot price (i.e. if the denominator of the fraction above is 100 instead of 103).

After concluding the discussion on commodity rates of interest, Hicks summarizes by saying that these rates of interest are of relatively "little direct importance," just as a rate of exchange between two commodities is of relatively little importance "when neither of the two commodities is the standard of value" (i.e. when neither one is being used as money).  With no further assumptions about the properties of money, then, 

[W]e are entitled to assume that all loans are in money terms; for any loan transaction which takes place otherwise is always capable of being reduced to a money loan combined with a spot transaction and a forward transaction.

Value & Capital, CHAPTER X, Section 5

The previous section argued that the first two source of disequilibrium (namely, inconsistent price expectations across individuals and inconsistency between the planned levels of supply and demand) are absent in a "futures economy" where all transactions are conducted via forward trading.  In the present section Hicks argues that it is the desire for hedging (i.e. limiting risk) that limits the extent of forward trading in a capitalist economy.  Thus the ultimate reason why the first two sources of disequilibrium cannot be eliminated is "the unavoidable presence of the third and fourth" sources (namely, imperfect foresight as to wants and hedging behaviors in response to perceived risks).  Recall that in the previous section, these latter two causes are claimed to be present in any type of economic system.

Hicks argues that when the ends of society are certain, socialist organization "has a strong case on grounds of efficiency; but in the ordinary pursuit of peace-time economic welfare, immediate ends are likely to be much less certain, the natural method of economic policy being trial and error."  If a socialist dictator were to find himself "afflicted by those same sorts of uncertainty which impede co-ordination under capitalism," Hicks argues, the wise preference would be for "a loose and decentralized system" even though it may be "open to the charge of planlessness, and not clearly superior in its power of adjusting means to ends."  With these remarks Hicks leaves the "great debate" mentioned at the beginning of the previous section and turns to explaining the significance of this chapter's results for the discussion that will follow in upcoming sections.

He describes the 'Spot Economy' in which only spot transactions are taken into account as being a convenient place to begin, as well as "not really a very drastic simplification of reality."   While we know that "[a] certain proportion of the transactions which take place in reality have to be reckoned (in whole or in part) as forward transactions," we now know "enough about forward markets to be able to take them into account on occasion."

At the other the extreme, the pure 'Futures Economy' could "have no claims to be a good approximation to reality."  Instead its usefulness is theoretical:  the prices that maintain equilibrium over time in such an economy under changing conditions are exactly those that would result in equilibrium for a system in which all traders have perfect foresight.   

Value & Capital, CHAPTER X, Section 4

This lengthy section explores the vulnerabilities to the various sources of disequilibrium (and hence inefficiency) that may exist in different types of economies.  The section notes at the outset that the classification of causes of disequilibrium "has a distinct bearing on the great dispute about the relative efficiency of different types of economic organization."

The text argues that "the third and fourth sources of waste" (namely, imperfect foresight as to wants and hedging behaviors in response to perceived risks) would "be found in every conceivable economic system, Capitalist or Socialist, Liberal or Authoritarian."

In contrast, it is argued, "the first and second sources" (namely inconsistent price expectations across individuals and inconsistency of planned supply and demand quantities) may appear to be "peculiar to a system of private enterprise."  Thus a completely centralized system could, in theory, dictate what future prices would be, and even determine the supply and demand quantities allowed.  But as the text notes, "a completely centralized system is a mere figment of the imagination;  every government delegates its authority to some extent."  As a consequence, some of these delegated actions "can get out of step" and bring about the kinds of inefficiencies described.

The text then goes into an extended discussion on the role of "forward trading" (i.e. trades for future deliveries, and, in fact, all long-term contracts) in bringing about the coordination of plans in a private enterprise economy.  This discussion begins by imagining a system of private enterprise in which there is no forward trading at all.  Instead, all transactions are made for immediate delivery, i.e. delivery "on the spot," (which may be the reason for the name for such a market: a "spot market").  In such a market, it is only in the most ideal, stationary conditions that people could be expected to guess each other's plans with any reasonable accuracy.  Hence in normal circumstances, if "conditions are at all disturbed, a spot economy must be expected to get out of equilibrium to a considerable extent."

At the other extreme, one could imagine an economy in which all transactions were handled by forward trading.  In this type of system, a "futures economy," inconsistent price expectations and inconsistent planned supply and demand quantities (i.e. the first two sources of disequilibrium) would be absent.  Still the possibility of disequilibrium from imperfect foresight about preferences or resources would be present.  As a result, one would expect a spot market to arise to handle mismatches between planned sales and planned purchases.

This discussion transitions into a discussion about hedging.  Noting that traders are aware of the various uncertainties associated with buying and selling in the future, the text argues that

[T]he ordinary business man only enters into a forward contract if by so doing he can 'hedge' -- that is to say, if the forward transaction lessens the riskiness of his position.  And this will only happen in those cases where he is somehow otherwise committed to making a sale or purchase at the date in question ... and if he has already done something which will make it difficult for him to alter his plan.  Now there are quite sufficient technical rigidities in the process of production to make it certain that a number of entrepreneurs will want to hedge their sales for this reason;  supplies in the near future are largely governed by decisions taken in the past, so that if these planned supplies can be covered by forward sales, risk is reduced.

The discussion argues further that we do not see an equivalent hedging effect on the demand side, i.e. with planned purchases.  Such hedging of planned purchases "is almost inevitably rarer" and "less insistent" because of "technical conditions" that give entrepreneurs more freedom in decisions about acquiring the inputs to production than their freedom regarding the completion of outputs.  The text goes on to argue that it is because of this asymmetry that "forward markets rarely consist entirely of hedgers."

Futures prices are therefore nearly always made partly by speculators, who seek a profit by buying futures when the futures price is below the spot price which they expect to rule on the corresponding date; their action tends to raise the futures price to a more reasonable level.  But it is the essence of speculation, as opposed to hedging, that the speculator puts himself into a more risky position as a result of his forward trading -- he need not have ventured into forward dealing at all, and would have been safer if he had not done so.

Similar effects of hedging apply in labor markets as well, where it is in the interest of a worker to "hedge" future sales of his labor by securing long-term employment.  On the other hand, it is typically not in an employer's interest to offer long-term contracts, except in special circumstances such as when an employee is difficult to replace.

Value & Capital, CHAPTER X, Section 3

This section discusses several possible causes of disequilibrium in a dynamic economic system.  One of them comes about when individuals differ in their expectations of prices. But the text argues that unless the expectations are "very definite" there are unlikely to be serious effects (in fact, the text calls this "perhaps the least important" cause of disequilibrium).

A second possibility arises when individuals' plans are inconsistent (even though their price expectations might be consistent).  In particular, when planned supply for some commodity (meaning the total quantity that all sellers plan to sell) is greater than planned demand (the total that all buyers plan to buy), the new price must be lower than it had been expected to be.  The text says this case "is evidently a potent cause of disequilibrium; it is perhaps the most interesting cause of all." 

A third possible cause is incorrect foresight by individuals as to their future preferences, or their estimates of the outputs of production processes.  When these preferences or production outputs are realized, some individuals "will find themselves unwilling or unable to buy or sell those quantities of goods they had planned to buy or sell."  As in the previous case, the new prices will be different from those that had been expected.  Further, as the text notes, "the imperfect foresight of some persons will put others too into disequilibrium."

The text argues that these three possible causes are the only ones that could arise when price expectations are definite.  A fourth possibility arises from the fact that, in real life, price expectations are uncertain.  The discussion notes that the effect from this possibility is not disequilibrium in the sense of instability, but disequilibrium in the sense of being an "imperfect equilibrium."  The explanation goes as follows:

when risk is present, people will generally act, not upon the price which they expect as most probable, but as if that price had been shifted a little in a direction unfavourable to them.  Now this means that even if no disequilibrium in any of the above senses is present ... still the most perfect adjustment of resources to wants may not be reached. ... [T]heir sense of risk may have prevented entrepreneurs from producing those quantities of output, which they would have produced if they had been more confident that their anticipations were right.  In this way, the efficiency of the system may be very seriously damaged, without any of the types of disequilibrium mentioned above coming into question.

The discussion notes next that this lack of confidence is a possible, though not a necessary, source of waste.  "Putting insufficient faith in good judgments is a source of inefficiency; but skepticism about bad judgments may be better than implicit trust."  The section then closes with the intriguing comment that "we shall find as we go on that there are reasons for suspecting that the economic system loses more by mistrust than by over-confidence."

Value & Capital, CHAPTER X, Section 2

This section explores the senses in which the dynamic economic system is either in or out of equilibrium.  In one sense, it is always in equilibrium, because one may think of current supply and demand as being equal in competitive conditions.

Stocks may indeed be left in the shops unsold; but they are unsold because people prefer to take the chance of being able to sell them at a future date rather than cut prices in order to sell them now.  The tendency for the current price to fall leads to a shift in supply from present to future.

The discussion goes on to note that in another wider sense, the economy is always out of equilibrium to some extent.  Beginning with the observation that prices established on the first day of trading will govern the plans and the allocation of resources throughout the intervening time until new prices are determined, the implication is that the second set of prices may differ from the first one.  The discussion argues that constancy of prices should not be required for equilibrium in an economy subject to change;  rather the more important test is whether the second set of prices realized in the economy "are the same as those which were previously expected to rule at that date."  In other words, "In equilibrium, the change in prices which occurs is that which was expected."  Hicks goes on to describe such an economy, in which preferences and resource quantities are what they were expected to be, and plans need not be revised because "no one has made any mistakes" as being "like the sun in Faust."  Here Hicks gives a quote in German without translation.  Fortunately, we have Google Translate to help us get an (approximate) English version, which is "Her predecessed journey she accomplished with thunder."

No economic system exhibits perfect equilibrium over time, as Hicks notes.  He makes the intuitive claim that equilibrium is "usually approached most nearly when conditions are nearly stationary; when people expect prices to remain steady, and they do remain steady."  Conversely, acute disequilibrium (in the sense that "expectations are cheated and plans go astray") is most likely "in times of rapid price-movement."

There are two final points worth noting from this section;  both are topics treated briefly, but both seem significant.  The discussion about the degree of disequilibrium notes that "the expectations of entrepreneurs are in fact not precise expectations of particular prices but partake more of the character of probability distributions."  Therefore "the realized prices can depart to some extent from those prices expected as most probable, without causing any acute sense of disequilibrium."  The second point is that the divergence between expected and realized prices, despite offering some "latitude" in applying the concept of equilibrium, represents economic loss.

Whenever such a divergence occurs, it means (retrospectively) that there has been malinvestment and consequent waste.  Resources have been used in a way in which they would not have been used, if the future had been foreseen more accurately; wants, which could have been met if they had been foreseen, will not be satisfied or will be satisfied imperfectly.

The next section will begin to explore how disequilibrium arises.

Historical note:  The New York Times this morning (22 February 2017) contains the obituary of Kenneth Arrow.  Professor Arrow was mentioned in the second post of this blog.  I am considering blogging on Arrow's 1950 paper, "A Difficulty in the Concept of Social Welfare" as my next topic after finishing the blogging of Value and Capital.

Value & Capital, CHAPTER X -- EQUILIBRIUM AND DISEQUILIBRIUM

In this first section of Chapter X, the author, Sir John Hicks, begins with a summary of the general method he will be using to apply equilibrium analysis to dynamic theory.  As described in Section 4 of the previous chapter, prices will be assumed to be set each Monday.  Everything that has happened up to that time must be treated as data, not subject to change.  In particular, we take as given "the whole material equipment of the community," including finished goods ready for sale, raw materials, and goods at every stage of production in between, along with the physical plant and durable consumer goods already purchased.  "From now on, the economic problem consists in the allotment of these resources, inherited from the past, among the satisfaction of present wants and future wants."

As described in Section 5 of the previous chapter, entrepreneurs and private persons are assumed to draw up plans for their conduct during the current week and in future weeks.  The plans of private persons include quantities of commodities they plan to purchase at present and at future times (and possibly quantities of services to supply).  The plans of entrepreneurs include quantities of inputs to production to be purchased or hired in the current week and future weeks, as well as quantities of outputs to be produced for sale at these times.

As explained in Section 6 of the previous chapter, these plans incorporate expectations about future prices. If the supply and demand in the current week cause the price of some commodity to differ from those expectations, the plans will be revised accordingly.

By assumption, trading happens on Monday and brings supply and demand into equilibrium;  this assumption "is essential in order for us to be able to use the equilibrium method in dynamic theory."  Hicks explains that the current discussion will not focus on the process by which equilibrium prices are formed (referring the reader instead to the end note of the previous Chapter).  "[O]ur method seems to imply that we conceive of the economic system as being always in equilibrium.  We work out the equilibrium prices of one week, and the equilibrium prices of another week, and leave it at that."

Value & Capital, Note to Chapter IX -- THE FORMATION OF PRICES, section 2

The second section of the end note for Chapter IX examines whether Marshall's argument regarding the effectiveness of the trial-and-error process of fixing prices can be extended from the simple "fish market" case Marshall considers to the more general setting that Hicks envisions. The discussion here argues that the effect of "false trading" (meaning trades that happen at prices different from the equilibrium prices) will be to create gains and losses that are "the same in kind as the income effects which may have to be considered even when we suppose equilibrium prices to be fixed straight away."  These income effects have been shown again and again to cause "indeterminateness" in the results derived earlier in the book. (The term "indeterminateness" here appears to mean a lack of precision in the theoretical predictions due to the limitations of the assumptions.)  The text goes on to note that "All that happens as a result of false trading is that this indeterminateness is somewhat intensified.  How much intensified depends, of course, upon the extent of the false trading; if very extensive transactions take place at prices very different from equilibrium prices, the disturbance will be serious."

The discussion goes on to argue that there should not be a large volume of trades happening at "very false" prices.  One of the justifications for this conclusion relies on intelligence in the fixing of prices.  Another justification is explained (perhaps a bit too briefly in the text, in my opinion) by the fact that "gains to the buyers mean losses to the sellers, and vice versa."  There is a footnote reference to p. 64, which is part of Section 2 of Chapter V, where Hicks explains that the income effect of a fall in price tends both to increase demand and to increase supply.  This is because, if sellers are similar to buyers, they will consume some of the commodity they supply, but with lower income they will consume less of it, leaving more to be supplied to the buyers.  Thus the income effect increases both demand and supply, so there is some cancellation of the income effects when it comes to determining excess demand (and hence price at equilibrium).

Hicks concludes the note by explaining that the "arbitrariness" in the practical application of these results is a consequence of assuming the markets to be open only on Mondays, with a relatively long period in which the prices determined that day hold constant.  If we wish to reduce that arbitrariness, he explains that we can do so by thinking of the "week" as being shorter.

Value & Capital, Note to Chapter IX -- THE FORMATION OF PRICES

In this section, the first of two sections comprising the end note for Chapter IX, the author examines Alfred Marshall's argument that (in Hicks's words), "the process of fixing prices by trial and error, necessary when market conditions are changing, need not have any appreciable effect upon the prices ultimately fixed."  The essential step in the argument is the assertion that "a change in price in the midst of trading has the same sort of effect as a redistribution of wealth."  Such a change is illustrated with an example in which an initial "false" price (Hicks's term of convenience for a price other than the equilibrium) is agreed upon for a given commodity:  the false price is chosen to be 10 dollars per pound, whereas the equilibrium price is 6 dollars per pound.  Suppose a person buys 3 pounds at the false price, but the market price soon drops to equilibrium.  This buyer's position is exactly the same as if the price had been 6 dollars per pound all along, but the buyer had been forced to cough up an extra 12 dollars to the seller.  The buyer's demand and seller's supply will be exactly the same in the two scenarios.   The effects of this sort of transfer are income effects, and as noted here, Hicks has repeatedly shown that "income effects can be very frequently neglected."  In Marshall's example the amount spent by the buyer on the commodity in question is assumed to be a small fraction of his resources; thus a price change will not have a large effect on the total value of these resources.  Hicks quotes Marshall as saying that this assumption "is justifiable with respect to most of the market dealings with which we are practically concerned.  When a person buys anything for his own consumption he generally spends on it a small part only of his total resources."  The buyer could be made better or worse off by the initial trading at the false price -- but only slightly in the big scheme of things -- so there will not be a significant effect on his demand for the commodity.  As a result, "the market must finish up very close to the equilibrium price."