Value & Capital, CHAPTER XVI, Section 5

This section examines Marshall's short and long period methods of analyzing the effects on production plans of expected changes in prices of a product.  The discussion uses the following figure for illustration.

Hicks's analysis discusses the actions (in terms of output, plotted on the vertical axis) by an entrepreneur over time (with time being plotted on the horizontal axis).  Initially he assumes that the entrepreneur plans to produce "a steady stream of output" as shown by the flat line AA'.  In the case where the price of the entrepreneur's product experiences a rise in price that is expected to permanent,

[The entrepreneur] would (so it appears) plan a stream such as BB, which would rise while equipment was being adjusted to the new conditions, but would probably settle down in the end to a new 'equilibrium'.

The analysis next turns to the various sources of the total effect of the price increase.  Hicks argues that with elasticity of expectations equal to 1, the total effect "is compounded out of" two types of effects:  the effect of a rise in the current price (with expected prices remaining unchanged), and the effects of a rise in expected price at each particular point in time (with the current price and other expected prices remaining unchanged).  His exposition considers the second type first.

In supposing that an increase in the price of the entrepreneur's product is expected at the date M, the discussion examines two types of consequences of this expectation.  The first type involves the entrepreneur substituting resources that had been intended to be used toward production at other times, either earlier or later, or possibly both, "in order to have as much as possible ready at the critical date."  Various technical characteristics of the product and the equipment used to produce it will affect how easily substitution can be applied.  Among such characteristics, the author lists the durability of the product, the durability of the inputs to production, the initial quantity of available inputs, and so on.  He concludes that "the general shape of the output stream which will be planned" in this type of situation is that shown by the curve ACA'.

The second type of consequence of the expectation of a price increase will be more pronounced when there is less opportunity for substitution.  This might be the case, for example, when "the product is not durable, and the materials which go to make it are not durable."  To meet the expected price increase, the entrepreneur might invest in additional production equipment, which is itself durable.  In this case, "the existence of the equipment will then facilitate increased output at other dates as well.  This is the case of complementarity over time."  In this case, the stream of planned outputs will have a form similar to that of AD.

For the case of a rise in the current price that is not expected to persist, there will typically not be enough time to install additional equipment, so the complementarity effect will be small.  Substitution effects can still occur, but they can only involve substitution of resources that were intended to be used for future output.  If we are truly talking about a rise in the current price (for which there is no advance notice), then no substitution could be done in the past in anticipation.  If there is a substitution effect, the planned output stream will have the form shown by the curve EA'.

Value & Capital, CHAPTER XVI, Section 4

In this section the author begins his discussion of the case in which the elasticity of expectations is unity;  that is, the case in which (as noted in the previous section) "a change in current price will change expected prices in the same direction and in the same proportion."

The auther takes note of two relevant insights from the study of statics.  First, a group of commodities with the same elasticity of expectation can be analyzed as a single commodity.  Second, regarding the production plan of a firm, if the elasticity of expectations is unity, a rise in the price of some commodity X will mean that "there will be an increase in the output of X, brought about either by increased inputs of one sort or another, at one time or another, or by substitution at the expense of other products."

Although a rise in price of a commodity will lead to an increase in planned output of that commodity, the increase may not materialize immediately.  The author notes that limits on capacity and inventory will mean that flexibility of output in response to an increase in price will be small in the near term.  "But," he notes, "there is no such check on the expansion of distant future outputs, or rather the check gets less and less strong as the output recedes into the future."

The author closes this section by indicating that the upcoming section will explore "Marshall's doctrine of the 'short' and 'long' periods."

Value & Capital, CHAPTER XVI, Section 3

This section begins by identifying three categories of influences on price-expectations.  The first is non-economic influences such as "the weather, the political news, people's state of health, their 'psychology.'"  The second category is economic influences that are "not closely connected with actual price-movements."  The author describes this category as ranging all the way from "market superstitions" on one extreme, to market-related news such as crop reports on the other.  Although the author says that we must never forget the existence of these first two categories of influences on prices (which he calls "autonomous causes"), he does not consider them topics for analysis.  The third category, which he begins to discuss in more detail, includes actual experience of prices, both past and present.

For this third category, the author notes that past prices and current prices affect expectations "in very different ways, and so it makes a great deal of difference which influence is the stronger."  The extreme case is that in which the influences of past prices are "completely dominant" and any change in a current price is therefore "treated as quite temporary."  The other cases are those in which the influences of current prices could have different degrees of intensity.

The author lists various cases that characterize the possibilities for influence of current prices on expectations.  He does this by first defining "a measure for the reaction we are studying."  This measure is the elasticity of expectations, which he defines, for a commodity X, as "the ratio of the proportional rise in expected future prices of X to the proportional rise in its current price."  The case of elasticity of 0 corresponds to the case of no influence, described earlier.  If the elasticity were 1, "a change in current prices will change expected prices in the same direction and in the same proportion."  (As a further example, if the elasticity of expectations for some commodity is 0.75, and its current price rises by 20 percent, then we would expect future prices to be only 15 percent higher, instead of 20.)  The author also considers more extreme cases;  for instance, an elasticity of greater than 1 would mean that "a change in current prices makes people feel that they can recognize a trend, so that they try to extrapolate."  Conversely, a negative elasticity makes people feel that a price change is "the culminating point of a fluctuation" (and hence that future prices will be lower than before).

The author concludes that "the second pivotal case (that in which the elasticity of expectations is unity) is of such importance that we ought to make a practice of working out that case whenever it is relevant."  He closes out the current section by previewing that the upcoming discussion will cover the working out of this case.

Value & Capital, CHAPTER XVI, Section 2

In this section, the author briefly reviews the changes that were needed "to convert the static theory of the firm into a dynamic theory of the production plan."  He then describes the most direct and straightforward translations, into the dynamic setting, of "[t]he standard propositions, which define the behavior of a firm in static conditions."  Finally, he summarizes the shortcomings of these direct translations, thus setting up the discussion to come in succeeding sections.

The first of the two "amendments" needed to the static theory of the firm was that "Outputs and inputs due to be sold (or acquired) at different dates have to be treated as if they were different products or factors."  The second was that "actual prices have to be replaced, not merely by expected prices (when that is necessary) but by the discounted values of those expected prices."

The standard propositions that define a firm's behavior could be directly converted from the static case to the dynamic as follows.  To examine the effect of a change in the price of commodity X expected to take place t weeks in the future, the analysis can consider this to be a change in the price of commodity Xt and then apply the static rules.  In the case of a rise in the expected price of Xt, these rules imply that

there must be an increase in the planned output Xt.  This may come about either through an increase of inputs or through the diminution of other outputs, or both.  The inputs may be current or only planned;  the diminished outputs may be of the same kind but differently dated (Xt'), or of a different kind physically (Yt or Yt').  Further, it is always possible that there may be some outputs which are complementary with Xt, so that they will be expanded with it;  and it is possible (though less likely) that there may be some inputs which are regressive against Xt, so that they will be contracted.

The author goes on to argue that we should prefer to use the theory to examine the effects of changes in real prices rather than changes in expected prices.  The effects of changes in the prices of current outputs can be worked directly by the static rules.  But the author points out that such changes would be changes ceteris parabis (or "all other things being equal").  All other price expectations would be assumed to remain the same, even for the commodity whose price is assumed to be changed for the current period.

As the author points out, "if we stick to direct application of the main static rules, we are inhibited from considering any sorts of changes in market prices excepting those which are expected to be temporary.  We are unable to make any allowance for the effect of the current situation on people's expectations."  He then sets up the discussion to come by concluding this section with the statement that "if our theory is to lead to useful results, we must take that effect into account."

Value & Capital, CHAPTER XVI -- PRICES AND THE PRODUCTION PLAN

In this first section of Chapter XVI, the author, Sir John Hicks gives an overview of the discussion the chapter will contain.  He starts by observing that the equilibrium and stability conditions worked out in the previous chapter for a dynamic plan of production "have of course identically the same role as the parallel conditions in static theory."  The current chapter will examine how a production plan changes when prices or price-expectations change.   The following chapter will look at the effects of changes in interest.  The parallelism between the dynamic problem of the production plan and the corresponding static problem will simplify the discussion, so that "the purely formal properties of technical substitution and technical complementarity" can be taken for granted, and the discussion can simply describe these properties "in dynamic terms."

Value & Capital, CHAPTER XV, Section 7

In this section, the final one of the chapter, the author discusses one additional characteristic of the dynamic production plan -- one that, he suggests, "ought perhaps to be reckoned among the stability conditions."  In addition to having a positive net present value initially, the investment plan must also have a positive net present value "at all future dates within the period for which he is planning."  If this were not the case, the planner would recognize that he would lose money by continuing, and he would cut the plan short.  The author notes that "The importance of this condition will emerge fully at a later stage."

He then discusses the ratio of the present value of a stream of capitalized values of a production plan at regular intervals (weeks, in his example) to the present value of the plan itself.  He notes that this ratio "is what we have called the average period of the stream of surpluses."  In an earlier section, he explained that this ratio can be thought of as the weighted average of lengths of times that payments are deferred from the present, with the times of deferment weighted by the discounted values of the payments.  He closes the section by noting that "The significance of this average period will come out when we discuss the effect of changes in interest on the production plan."

Value & Capital, CHAPTER XV, Section 6

This section begins by pointing out that the three categories of equilibrium conditions identified in the previous section are necessary conditions.  In other words, a production plan that fails to satisfy one of these types of conditions cannot maximize profits.  But these conditions are not sufficient to achieve to equilibrium;  "stability conditions have to be satisfied too."  The text identifies three types of stability conditions.

There must be (1)  an increasing marginal rate of substitution between outputs;  (2)  a diminishing marginal rate of substitution between inputs;  (3)  a diminishing marginal rate of transformation of an input into an output.

The author points out that these conditions have the same form as those found for the static equilibrium case.  In addition, there is an analogous condition to the static one that requires a positive surplus;  in the dynamic case, the condition is that "the present value of the stream of surpluses must be positive."

The latter part of this section addresses the conditions needed to ensure the stability of equilibrium under perfect competition.  In the static case, these involved postulating the existence of limitations on increasing the capacity of certain factors of production, such that overall returns were diminishing.  The author then asks what the situation looks like in the dynamic case.  His answer to this question covers two cases

(1) where the entrepreneur, at the date in question, has an already established business, (2) where he is a potential entrepreneur considering whether to set up a business, and, if so, what sort of a business to set up.

In the first case, the author concludes that the "fixity" (or fixed nature) of the resources required for setting up the business is sufficient for providing the necessary diminishing returns.  In the case of the new firm, the author identifies both the difficulties of management and control in the absence of "standing rules" for running the business, as well as the element of risk.

Overall, the author concludes that "we need have rather less compunction" in assuming perfect competition in the dynamic case than in the static case.  This is because "The elements which limit the size of firms in practice are very largely dynamic elements."