Value & Capital, CHAPTER XVII -- INTEREST AND THE PRODUCTION PLAN

 

In this first section of Chapter XVII, the author, Sir John Hicks, describes the topic that the chapter will address, namely the effects that interest-rate changes have on production plans.  As he explains, his discussion in the previous chapter on the effects of changes in prices "had no new major principles to annunciate."  When it comes to the effects of interest-rate changes, however, the situation is different:  "there is no such body of doctrine which is settled and easily acceptable."  Hicks mentions Böhm-Bawerk's "classical" theory (to which he alluded earlier in the book) as well as Frank Knight's "sketch of an opposition theory," but he judges the classical theory's validity to be "widely questioned" and the opposition theory to be "largely unresolved."  He concludes that "the field is therefore open for us to try to discover a new theory."

Hicks proposes to set out such a theory in this chapter by applying the same method used to investigate price-changes.  He explains that "the theory of interest-changes is ... much more difficult than the theory of price-changes" because a change in the interest rate does not result in simple proportional changes of the sort that result from price-changes.  Instead, as he notes, 

A change in interest rates which is expected to be permanent implies a proportionate change in the discount ratio per week for loans of all durations;  and this does not lead to a proportionate change in discounted prices—the prices which are relevant to the determination of the plan. ... [T]he discounted prices of the outputs and inputs further ahead in time are regularly affected more than the discounted prices of the nearer outputs and inputs. 

As a consequence, the only feasible approach to deriving relevant propositions for a theory of interest-rate changes is "by splitting up the general change in interest rates into a number of particular changes in particular rates (just as we split up the general change in prices and price-expectations into a number of particular changes in expectations)."  In a sense, then, Hicks's use of this method in the previous chapter was a bit of a warm-up for its required use in the current chapter.  It wasn't actually necessary for analyzing the effects of price-changes, although, as he notes "we got some illumination from this splitting-up."  When it comes to analyzing interest-rate changes, however, "it is the only line of attack we have open."

Value & Capital, CHAPTER XVI, Section 7

In this final section of the chapter, the author shifts his attention to the effects of changes in the price of an input to production.  (Earlier sections in the chapter had dealt with changes in the price of the output.)  

In general, the effects of changes in input prices are analogous to the effects of changes in output prices.  If the price of an input is expected to increase and to remain at the higher level, then it must be the case that the planned use of that input will decrease.  As with changes in output prices, the effects of changes in input prices need not be spread evenly over future time periods;  likewise, a lasting price change for an input will tend to have a greater effect on input levels at later times than in the near future.

As before, the main reason for these effects comes from the nature of unfinished goods, or work in progress at the time of the price change.  For these goods, the author explains, “work has already been done on them with the object of converting them in the end into a certain kind of product;  if this process is at all far advanced, the degree to which its ultimate object can be changed will be limited.”  As long as the price increase is not too large, it will pay to continue the production process as planned for these goods.  Longer term, more extensive changes to the production process can be expected.

For a decrease in an input price, similar conclusions hold, but the author also mentions an additional possibility — namely that the entrepreneur may start an entirely new process of production.  Technical factors will play an important role in determining the exact shape of the new input stream.  The author states that it is “quite possible for technical factors to induce input streams of any conceivable shape.”  But generally after some time the rate of input will ramp up to its peak.

The author closes the chapter with a remark on the economic importance of the delay in achieving the peak input rate:

Marshall’s doctrine of the short and long periods has familiarized us with the notion of lags on the output side;  it is a pity that the corresponding lags on the input side have not received more attention.  They are closely connected with some of the major social problems that concern the economist — unemployment and the intractability of unemployment;  in this direction above all a theory which leaves out the probability of input lags is likely to be gravely misleading.

Value & Capital, CHAPTER XVI, Section 6

This section continues the discussion of the example introduced in the previous section.  In this example, the price of some commodity is expected to experience an increase at some date M in the future, but all other prices are expected to be unchanged.  The results from this type of model can be used to derive the effect of a price rise that is expected to be permanent, by summing the effects of a set of "partial effects."

In the complementarity case, which as noted in the previous section may involve the investment in additional durable production equipment, the individual increments have the form shown in the figure by the curve AD, and the total effect will have the form shown by the curve BB.

In the case of substitution, for instance of outputs at earlier or later dates in order to have more to sell at a critical date, the effect of a permanent price rise is much less certain, because "the constituent effects are much less simple in character."  The author argues that 

It is still likely, on the whole, that the main increase in output will come at dates in the further future; so that a resultant such as BB is still the most probable.  But variations from the standard form are much more possible;  thus the adoption of a production plan such as bb, with some outputs actually less than the corresponding outputs in the original stream, is not ruled out.

The author notes later that "abnormal" effects, such as those shown by the curve bb, are not likely except when "the character of the initial equipment dominates the whole situation."

In this connection he then makes reference to a historical example of South African gold mining in 1934-35, in which extraction of richer ores fell slightly during a time when new capacity was under construction and expected to enter into production shortly.  Although the author notes that there is some dispute about these facts on which he does not take a position, he points out that "there is no theoretical reason why it should not have happened like that."

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."
 

Value & Capital, CHAPTER XV, Section 5

This section continues explaining some of the details of how "the problem of maximizing the present value of the production plan is formally identical with the problem of maximizing the surplus of receipts over costs in the static problem of the firm."  For given interest rates, future costs enter into the analysis as discounted costs.  Outputs at different dates are treated as different outputs.  "With these adjustments," the author states, "the whole static theory of the firm still holds.  We have nothing to do but translate."

For conditions of equilibrium, the author identifies three kinds of conditions, "corresponding to the three 'elementary' forms of variation."  These are as follows:
(1)  For any two dates, the marginal rate of substitution between an output at those two dates must equal the ratio of the discounted prices.
(2) For any two dates, the marginal rate of substitution between an input at those two dates must equal the ratio of the discounted prices.
(3)  The marginal rate of transformation between any input and output pair must equal the ratio of their discounted prices.

The author goes on to explain that certain other equilibrium conditions stated by other writers are special cases of these three.  In particular, he notes that "the often stated rule that the current rate of wages equals the discounted value of the marginal product of current labour is a special case of our third condition."  Similarly, a rule noted by Wicksell -- that the interest rate equals the relative marginal productivity of waiting -- is a special case of the first condition.

Also, Keynes's statement that "short-period supply price is the sum of marginal factor cost and marginal user cost" corresponds to a combination of the first and third conditions.  Finally, another rule from Keynes, that the marginal cost of a unit of input equals "the present value of the stream of output increments made possible by the marginal input" appears to be (although not stated explicitly in the text) a combination of the second and third conditions.

The author concludes the section by noting briefly that in some cases, groups of inputs or outputs must be chosen in fixed proportions, but "little is to be gained by paying a great deal of attention to these cases ... at this stage of our inquiry."