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.
