Value & Capital, Notes to Chapter XIV -- A. SAVING AND INVESTMENT

Regarding saving and investment, the author states in the preliminary paragraph of his notes on Chapter XIV that "I think the reader has a right to demand some expression of opinion on that controversial topic."  He then begins his note on the topic by explaining that the principal difficulty "evidently arises from the multiplicity of ways in which the terms can be defined."  He observes that saving can be defined in a way that corresponds to each of the definitions of income discussed in the preceding chapter (each of which would, in turn, give rise to a corresponding definition of investment).  He also states that saving can be defined ex ante or ex post.  He argues that the choice of which definition of income to use is not important to the analysis, but he states that "the ex ante - ex post distinction is of course very important."  (One wonders whether the author thought this should be obvious.)

For his explanation the author chooses to use Income No. 1 as his basis for defining saving and investment;  he notes that if he chose another definition of income, "the whole argurment would be exactly duplicated."  Using this definition of income (and the same kind of one-week model he has used in earlier analyses) he defines a person's savings ex ante to be "the difference between his actual consumption during the week and that level of consumption which would leave the money value of the prospect he can expect to have at the end of the week the same as it actually was at the beginning."  If the week is assumed to be a short enough time that "the accretion of interest" is negligible , then saving can also be said to be "the increment in the money value of his prospect planned to accrue during the week."  If any changes in his earning power are ruled out, then "his saving may also be written as the planed increment in the value of his property.  All this is saving ex ante; saving ex post will be the realized increment in the value of his property."

Regarding saving and investment ex post, the author gives an argument for the equality of their aggregate amounts that is so straightforward that I prefer to reproduce it in full:

Savings ex post may be aggregated for all members of the community.  Their sum total will equal the total increment in the money value of all persons' property which accrues during the week.  Now property has three forms:  it may consist of physical goods (real capital), or securities, or money.  But money, as we have seen, is either a physical good, like gold, or a security, like notes or bank deposits.  Our three categories thus reduce to two.  Further, securities are simply debts of various sorts from one person (or concern) to another; and therefore, when all property is aggregated, they cancel out.  Total savings ex post therefore reduce to nothing else but the increment in the value of physical capital; which is what seems to be meant by investment -- of course investment ex post.

While the author notes that this equality is a "mere truism," indicating only that "all the capital goods in the economy belong to somebody," the relationship between saving and investment ex ante is more interesting.  For the simple one-week model that the author uses, in which all demands and corresponding supplies are assumed to be equal during the week, it is indeed true that savings equal investment ex ante, but this is a property of the one-week model, and it will not hold for a longer time period.  As the author explains, "The ex post magnitudes will be equal whatever period we take, but the ex ante magnitudes will only be necessarily equal if plans are consistent."  Over a longer time period, planned saving could exceed planned investment.  "If an attempt is made to carry through the plans without readjustment, supplies of commodities will begin to exceed demands, and (so far as we can see at present) prices will tend to fall.  Similarly, if planned investment exceeds planned saving, there will be a tendency for prices to rise."

Toward the end of this note, the author exclaims "What a tricky business this all is!"  He then goes on to note four statements that John Maynard Keynes made regarding savings and investment:
(1) In his Treatise on Money, that they are only equal in conditions of equilibrium, and
(2) that an excess of investment over saving means rising prices, and vice versa;
(3) in the General Theory, that savings and investment are always equal, and
(4) that this is a mere identity or truism, without significance for the determination of prices.

"As far as I can make out," Hicks notes, "there are relevant and important senses in which all four of these statements are each of them right and each of them wrong."