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."

Value & Capital, CHAPTER IX, Section 7

This section provides a short summary of the three fundamental concepts used in the dynamic model, along with brief justifications and descriptions of their use.  Using the notion of a week allows the analysis "to treat a process of change as consisting of a series of temporary equilibria;  this enables us still to use equilibrium analysis in the dynamic field."  In the case of the plans that the firms (and private persons) are assumed to make each week, and that are assumed to unfold over the course of the week,

we find ourselves able to conceive of the situation at the end of the week being different from the situation at the beginning;  thus the new temporary equilibrium which is established in a second week must be different from that which was established in the first;  going on in like manner, we have a process under way.

Using the device of definite expectations enables the use of the same type of analysis as that used in the static case of determining an equilibrium for a private individual or firm.  In the dynamic case, however, we are determining the effects of both current prices and expected prices on the plans that firms and individuals make.

These three fundamental notions enable the concept of market equilibrium in the dynamic case to be explored using the "machinery" of the static case ("without abandoning our model to stationariness").

Value & Capital, CHAPTER IX, Section 6

This section discusses two aspects in which the assumptions about individuals' expectations in the dynamic model are "excessively rigid."  The plans made by producers and consumers in each time period are assumed to depend on "definite" ideas of the prices of all goods of interest in any future time period.  One erroneous aspect of this kind of assumption is that people don't have expectations of specific prices, so much as they have "expectations of market conditions."  Therefore, the text argues, "the assumption of precise price-expectations is really one aspect of the assumption of perfect competition, which we have maintained throughout, and shall continue to maintain here."

The second aspect in which the assumptions are overly rigid occupies the remainder of the discussion in this section, and it relates to the fact that people don't have precise price expectations but instead have a range of prices they consider possible.  Such a price range includes some value considered to be the most probable, "but deviations from this most probable value on either side are considered to be more or less possible."  The text argues that it is sometimes sufficient to look only at the most probable value of a quantity of interest, although "for most purposes the dispersion has a very real importance."

When we think of the choices the individuals must make in determining their plans, we should expect that "a person's readiness to adopt a plan which involves buying or selling" at a given price on a given future date "may be affected, if he becomes less certain about the probability of that price, if the dispersion of possible prices is increased."  In general, even if the most probable price were to remain unchanged, we would expect an increase in price dispersion to make individuals less willing to commit to buying or selling at the most probable price.  For individuals planning to buy, an increase in price dispersion will have the same effect as an increase in the expected price;  for those expecting to sell, "an increased dispersion will have the same effect as a reduction of the expected price."  Therefore, the text argues, "we must not take the most probable price as the representative expected price."  Instead we should use the most probable price, plus or minus an allowance for risk.

This adjustment for risk underlies the analysis of the dynamic model that will follow.  The author acknowledges that this "is not an absolutely satisfactory way of dealing with risk" and expresses the opinion that "there ought to be an Economics of Risk on beyond the Dynamic Economics we shall work out here."  Given that this book was originally written in the 1930's, it is not surprising that the decades since its publication have seen extensive developments in the economic analysis of risk.

The discussion next makes two final points about the analysis of risk.  One is that the allowance for risk depends not only on the degree of uncertainty, but also on the decision maker's preferences -- in particular his willingness to bear risks.  The second point (and the author describes it as "the most serious weakness of our treatment") is that the willingness to bear any particular risk "will be appreciably affected by the riskiness involved in the rest of the plan.  I can do very little about this on present methods," he states, "though some consequences of the interrelations of risks will come to our notice now and then."  (The text does not state this, but a particularly important consideration is the extent to which various risks may be correlated, meaning that the realization of one risk implies that certain other risks are more likely to come to fruition -- as opposed to a situation in which risks are independent.)

The section concludes by restating that the analysis will "formally assume that people expect particular definite prices."  On occasion, though, these expectations will be interpreted as "those particular figures which best represent the uncertain expectations of reality."

Value & Capital, CHAPTER IX, Section 5

This section explores a "second property of the week" in the dynamic model described in preceding sections.  Since the previous section's description of the model made the simplifying assumption that markets were open only one day per week (say Monday), the discussion in the present section makes the further assumption that "Mondays are the planning dates too."  The author notes the fundamental importance of realizing that the planning decisions about buying and selling "nearly always form part of a system of decisions which is not bounded by the present, but has some reference to future events."

The discussion goes on to note some aspects in which the treatment of planning in the model is unrealistic.  For example, it would be more realistic to describe firms as "making plans at irregular intervals."  Furthermore, the assumption "that every firm more or less reconsiders the whole situation every Monday" likely implies greater efficiency than the system would actually possess.  (The author notes that "an inefficient firm will make major plans as rarely as possible, and do all its planning by small adjustments of detail, which take only a few elements of the situation into account, and do not need much thinking.")  The author argues that these assumptions do not matter much for the model.

Thus this section arrives at the assumption that "firms (and private persons) draw up or revise their plans on Mondays in light of the market situation which is disclosing itself;  and that any minor adjustments made during the week can be neglected."  At the close of business on Mondays, then, markets "have reached the fullest equilibrium which is possible on that date;  not only have prices settled down, but every one has made the purchases and sales which seem advantageous to him at those prices."  Plans have been adjusted to these prices as well as they can be, given the imperfect efficiency of the planners.

Value & Capital, CHAPTER IX, Section 4

This section begins to describe how Alfred Marshall's framework for analyzing the dynamic model of a simple one-good economy can be generalized to study "a whole economic system."  Hicks explains that it is not worthwhile to retain Marshall's "tripartite division" of the model into Temporary Equilibrium on the first "Day," "Short Period" equilibrium, and "Long Period" equilibrium.  He bases his choice not to retain the tripartite classification on questions about the actual tendency toward stable equilibrium, as well as concerns about the length of time that adjustments to equilibrium could require.  He states his intent, instead, "to keep the truth it embodies (the time taken in adjustment) clearly in mind."

Hicks chooses to work in terms of a "week" (chosen, somewhat arbitrarily, for illustration and also "to distinguish it from Marshall's Day").  He assumes it to be "that period of time during which variations in prices can be neglected."  For illustration Hicks supposes "that there is only one day (say Monday) when markets are open, so that it is only on Mondays that contracts can be made."  Contracts can be fulfilled during the week (goods can be delivered, payments made, etc.) but any new contracts would have to wait until the following Monday to be drawn up (as would any revisions to existing contracts). In this scenario the prices set on Monday will "rule throughout the week, and they will govern the disposition of resources during the week."

During the week, when markets are not open, there is no opportunity for prices to change, hence they will remain constant.  But Hicks goes on to argue that changes in price are also "negligible" on Mondays "when the market is open and dealers have to fix market prices by higgling and bargaining, trial and error.  This implies that the market (indeed, all markets) proceeds quickly and smoothly to a position of temporary equilibrium -- in Marshall's sense.  Marshall gave certain grounds for supposing this to be a reasonable assumption under the conditions of his model;  I shall examine in the note at the end of this chapter how far these grounds are available to us."

For the sake of the present discussion, Hicks asks the reader to accept his assumption of "an easy passage to equilibrium" as being similar to other common assumptions in economic reasoning (he cites the specific example of assuming "that every one knows the current prices in all those markets which concern him").  He will explore the properties that follow from his assumptions in subsequent sections.

Value & Capital, CHAPTER IX, Section 3

In this section the author, Sir John Hicks, describes his approach to analyzing the dynamic problem as being similar to the approach of Alfred Marshall (as opposed to the Austrian approach that relies on the stationary state model).  One difference between Hick's approach and Marshall's is that Marshall only analyzed the determination of value for a single commodity, whereas Hicks is "concerned with the determination of the whole system of values."

Marshall's analysis considers a supply of goods being brought forward for sale on a particular day (which Hicks calls Day I).  This supply is considered to be completely determined by past expectations (which may or may not match the actual supply and demand conditions that exist on Day I).  The demands, on the other hand, "will be determined by the preferences and income conditions that actually exist on Day I; they may also be affected by the expectations which exist on Day I, particularly if the commodity is durable, and some persons expect an increased demand (or diminished supply) in the future."

Hicks then explores the extent to which the price that results on Day I is "determinate," i.e. conclusively determined.  Hicks notes that Marshall uses "an ingenious argument" to show that the price is determinate -- namely that "in the end, supply and demand must be equated." At the price that results, buyers buy the quantity they want to buy at that price, and sellers sell the quantity they want to sell at that price.  Hicks states in a footnote that he will return to this point in a note at the conclusion of this chapter.

Hicks next explores what happens to the supply of goods on some "Day II, or perhaps some 'days' later."  There will begin to be effects from the price that results on Day I, in addition to the continuing influence of decisions made before Day I.  The Day I price will have different effects in the long run than in the short run.  In the short run the supplies of machinery, specialized skills, and other capital, along with "the appropriate industrial organization" have not had sufficient time to adapt to demand; instead, producers must make the best adjustments to demand that they can.  In the long run, these investments in productive capacity "have time to be adjusted to the incomes which are expected to be earned by them."  Given the price on Day I, producers may begin to plan for increasing output, and may make short-term or long-term plans in this direction.

The section concludes by explaining that, for given Day I and Day N, one could "inquire what output producers will plan to produce on Day N, if they expect the price on Day N to be such and such."  The different pairs of expected price and expected output will form a curve.  "Such a curve could be drawn up for each particular future date;  Marshall's short and long period curves are samples taken out of this potentially large collection."