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.