Value & Capital, CHAPTER XVII, Section 4

In this section, the author begins to give an exact definition to the "broad sense" in which there is an upward tilt to the stream of future surpluses if there is a general fall in interest rates.  In particular, he seeks "a numerical index" characterizing the production plan -- an index that changes "in a given direction when the rate of interest varies."

The author spends some length reviewing both the search by Böhm-Bawerk for such an index, leading to the concepts of "average period of production" and "average period of investment," as well as Knight's objections to Böhm-Bawerk's arguments for these concepts.

Hicks then argues that the needed concept corresponds to his average period of a stream, already derived in an earlier section.  The stream of concern is then "the expected stream of surpluses and deficits (the differences between value of output and value of input in successive periods)," with the weights in the average corresponding to discounted values.

Hicks concludes the section with an explanation of a technical detail about how to calculate the effect on the production plan from an interest rate change. 

What we must do is to start with a certain rate of interest, a certain production plan drawn up in vew of that rate, and an average period calculated from the production plan at the rate of interest.  Then we must suppose the rate of interest to fall, and the production plan to be varied in consequence.  Finally, we must calculate the average period of the new plan, using the same rate of interest in its calculation as before—that is to say, the old rate of interest.  Then our proposition is that the new, average period calculated in this way, must be longer than the old.  A fall in the rate of interest lengthens the average period.

Value & Capital, CHAPTER XVII, Section 3

In this section, the author generalizes the effect of a change in interest rate, which was discussed in the previous section for a specific case.  The previous section considered the interest rate for loans of a given duration, with all other rates of interest assumed to be unchanged.  The current section generalizes this analysis "so as to give the effect of a general shift in interest rates."  In general the effect is as follows:

If rates of interest per week fall for loans of all periods ... this in itself induces a direct tendency for substitution in favour of future surpluses, against the current surplus.

For example, in the context of production planning, a fall in interest rates would (other things being equal) make it more favorable to borrow today to make investments that would lead to a given increase in production at some future date.  The author explains that the effect is not proportional for all future time periods;  instead the effect would be compounded over time.  "Thus we should expect to find the greatest expansion in those surpluses which are farthest away in time."   He also notes that the effects of other surpluses may exhibit a negative effect ("a pull making for contraction") on a given surplus.

He summarizes the effect on surpluses as follows:

The whole effect on the stream of surpluses may be expressed by saying that it is given a tilt;  it is lowered at one end and raised at the other;  it is rotated, as it were, about some point in the middle. 

He includes the following illustration to show the effect on output streams over time (starting with the current period):

Input streams, conversely, are affected in the opposite way, hence the following illustration:

The relative strengths of these tilting effects would depend on technical conditions present in each specific case.

The author mentions that a similar tilting effect on output streams was encountered in an earlier section.  But the effect there (which arose in the context of a price rise assumed to be permanent) was one that was "owing to technical rigidities and the specificity of initial equipment."  In the present setting the tilting effect arises instead from "the very nature of interest itself."

Although technical rigidities and other factors will have an effect here, any stimulus to current production will likely not be very significant.  Therefore the author concludes the following:

The precise distribution over time of the new production plan depends upon technical conditions, for they decide when it will be possible to increase the futurity of output, and diminish the futurity of input.  It is not possible to lay down any hard and fast rule about the output or input of any given date (or even the surplus of any given date);  all we can say is that there must be an upward tilt to the stream of surpluses, in some broad sense or other.

In the next section, the author will begin to give an exact definition to this "broad sense."

Value & Capital, CHAPTER XVII, Section 2

In this section, the author examines the effect of a supposed change in the interest rate for loans of a given duration, assuming that the interest rates for loans of all other durations remain unchanged.  (In the next section, he will generalize from this particular case, to look at "the effect of a general shift in interest rates.")

As a helpful illustration of the effect of interest rate changes, suppose that one's goal is to save up, so as to have a certain quantity of money accumulated at some certain future date.  If interest rates fall, then this means that one must set aside more money now to achieve the planned savings goal.

In the author's discussion, the effect on prices of a fall in the interest rate for loans of t weeks will be to raise the discounted prices of "outputs and inputs planned for the week starting t weeks ahead."  The production planner would also find it profitable to increase the planned outputs for that week and decrease the planned inputs.  The author notes that "This would involve, as a counterpart, either an increase in the inputs planned for other weeks, or a decrease in the outputs, or both."

In general, because of indirect effects of increased demands for some inputs or outputs on the demands for other inputs or outputs, "it is not absolutely certain that any particular output of the date in question will be increased, nor that any particular input will be diminished."  But because the affected inputs and outputs are those of a given week (i.e. contemporaneous), "a change in the rate of interest will change all their discounted prices in the same proportion."

The author thus argues that we can "lump" these contemporaneous commodities into a single commodity that he calls the surplus, which is the value of the outputs minus the value of the inputs.  He then arrives at the central conclusion of his example, which is the following:

The absolutely definite rule, which gives without any exception the effect of a fall in the rate of interest for loans of t weeks, is simply this:  the surplus planned for the (t + 1)th week must be increased.

From this conclusion he goes on to argue that

We can simplify down the problem of the production plan, and regard it merely as the problem of choosing the most profitable stream out of a set of possible streams of surpluses; the list of possible streams being given by technical conditions, and converted into value terms by the assumption of given prices and given price-expectations.  The effect of interest-changes can then be regarded as consisting in substitution among surpluses, using this as a shorthand expression for substitution and transformation among the outputs and inputs, from which the surpluses are built up.

The author closes the section by noting that an increase in one surplus must come about "by substitution at the expense of  other surpluses (it is only possible for one surplus to be expanded if others are contracted)."  It may be possible, however, for a limited number of complementary surpluses to increase at the same time.

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'.