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.