Value & Capital, Notes to Chapter XIV -- B. INTEREST AND THE CALCULATION OF INCOME, part 1

This section introduces a discussion that will lead to studying graphically the relationship between the rate of interest and income.  The author begins by noting that for each of the three approximations for income studied earlier, "the calculation of income consists in finding some sort of standard stream of values whose present capitalized value equals the present value of the stream of receipts which is actually in prospect."

In each of the approximations to income, the standard stream "maintains some sort of constancy" instead of fluctuating as could happen in reality.  The three approximations make three different choices for what is assumed to remain constant.  Income No. 2 arithmetically "imputes identically the same sum of money value to each successive week."  Income No. 3 assumes constant purchasing power of each week's receipts, therefore "the money values imputed to successive weeks will vary as the price level is expected to vary."  For Income No. 1, the capitalized money value of all future receipts (in the standard stream) will be held constant from week to week, so the actual money values may vary with both prices and the rate of interest.

The author goes on to note that

...in each case we are broadly doing the same thing.  We are replacing the actual expected stream of receipts by a standard stream, whose distribution over time has some definite standard shape.  We ask, not how much a person actually does receive in the current week, but how much he would be receiving if he were getting a standard stream of the same present value as his actual receipts.  That amount is his income.

If the expected future receipts increase, then the equivalent income will increase by raising the equivalent standard stream of receipts, while maintaining "its old standard shape."

The author also notes that variable interest rates complicate matters.  The present values of both the actual expected stream of receipts and the "old standard stream" will change.  "In order to discover the effect on income we have to find which of these two present values is affected the more."  The succeeding discussion will study this effect in the case where the rate of interest is the same for all durations of loans (which the author asserts is "often or usually legitimate" to assume).