Aggregation in The General Theory
Tyler Cowen is blogging his way through Keynes's The General Theory of Employment, Interest, and Money, and he's just done Chapter 7. (Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Chapter 6). One of his conclusions about Chapter 7 is this: "The last two paragraphs of this chapter are a nice statement of what macroeconomics is all about." So what are the last two paragraphs of Chapter 7, and why are they so important? (Actually, I think it's the last three paragraphs, so I'll add that one.)
"The reconciliation of the identify between savings and investment with the apparent "free-will" of the individual to save what he chooses irrespective of what he or others may be investing, essentially depends on saving being, like spending, a two-sided affair. For although the amount of his own saving is unlikely to have any significant influence on his own income, the reactions of the amount of his consumption on the incomes of others makes it impossible for all individuals to save any given sums. Every such attempt to save more by reducing consumption will so affect incomes that the attempt necessarily defeats itself. It is, of course, just as impossible for the community as a whole to save less than the amount of current investment, since the attempt to do so will necessarily raise incomes to a level at which the sums which individuals choose to save add up to a figure exactly equal to the amount of investment.
"The above is closely analogous with the proposition which harmonizes the liberty, which every individual possesses, to change, whenever he chooses, the amount of money he holds, with the necessity for the total amount of money, which individual balances add up to, to be exactly equal to the amount of cash which the banking system has created. In this latter case the equality is brought about by the fact that the amount of money which people choose to hold is not independent of their incomes or of the prices of the things (primarily securities), the purchase of which is the natural alternative to holding money. Thus incomes and such prices change until the aggregate amounts of money which individuals choose to hold at the new levels of incomes and prices thus brought about has come to equality with the amount of money created by the banking system. This, indeed, is the fundamental proposition of monetary theory.
"Both these propositions follow merely from the fact that there cannot be a buyer without a seller, or a seller without a buyer. Though an individual whose transactions are small in relation to the market can safely neglect the fact that demand is not a one-sided transaction, it makes nonsense to neglect it when it comes to aggregate demand. This is the vital difference between the theory of the economic behaviour of the aggregate and the theory of the behaviour of the individual unit, in which we assume that changes in the individual's own demand do not affect his income."
The first of these three paragraphs is a statement of the paradox of thrift. The second notes the interdenpedence of actions. And the third invokes the aggregation problem, arguing that aggregation of individual actions can lead to outcomes that are not the same as simply the individual actions writ large. We teach this, in introductory economics, by invoking the Fallacy of Composition; Keynes's insight here, in Chapter 7, was to recogninze the importance of the Fallacy of Composition for the operation of the aggregate economy, and to propose a theoretical structure that took it into account