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.