The most elementary economy is the production-consumption economy and it consists of the business and the household sector. For a start, the business sector produces and sells one consumption good.
First period: the business sector pays 100 units of wages to the household sector and the household sector spends exactly this amount on the consumption good. There is no saving of the household sector. The business sector's profit is zero and the price of the consumption good is equal to unit wage costs, i.e. P=W/R.
Second period: the household sector saves 10 units (S=10) and spends 90 units. Now, the business sector makes a loss (Q=−10). The market-clearing price is lower than unit wage costs.
Accounting result: saving=loss [Q≡–S]. The complementary notion of saving is not investment but loss. Because of this, I=S never holds. And because of this, the whole discussion of whether the interest rate or the income mechanism establishes the equilibrium/equality of saving and investment is pointless. There is no such thing as equilibrium.
At the Central Bank's balance sheet we have at the end of the 2nd period 10 units of current deposits of the household sector and an equal amount of current overdrafts of the business sector. Without going further into details it should be obvious that the rate of interest on the asset side and the rate of interest on the liability side must be such that their difference covers at least the costs of the central bank under the condition of zero profit.
This is how the accounting identity and the two rates of interest are objectively connected in the most elementary case. There is no need at all for the silly psycho-sociological filibuster about liquidity preference, animal spirits, or ‘comfort and confidence that individuals derive from holding money in the face of an uncertain and unknown future’. No way leads from behavioral storytelling to the understanding of how the monetary economy works. Standard economics — Keynesianism included — is in the wood and will be left there.
For a more detailed depiction of the accounting relationships see The Profit Law.
Preceding Interest and profit.
Related 'End of confusion' and 'I=S: Mark of the Incompetent'.
ICYMI (comment on Henry of Oct 28 on Oct 29)
Total wage income Yw is 100 in period 1, and consumption expenditures C are 100. Saving S≡Yw−C is zero.
Total wage income Yw is 100 in period 2, and consumption expenditures C are 90. Saving S≡Yw−C is 10. Profit Q≡C−Yw is −10.
Accounting check: the balances of both sectors add up to zero S+Q=0.
ICYMI (comment on djb of Oct 29)
Analysis starts with the minimum number of elementary propositions. This is known since the ancient Greeks invented science: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.”#1
When you come clear with saving, investment, and profit then the growth of real and nominal wealth emerges immediately as a result. Wealth cannot be assumed as given but must be derived from the most elementary economic configuration with zero wealth.
Keynes started from faulty premises and because of this, the conclusion I=S is provably false. History from Keynes onwards, though, has shown that proper methodology is beyond the mental capacities of the representative economist. There is no hope for the present generation of economists (in particular for Henry, JKH, djb).
Nevertheless, for the consistent derivation of wealth see the working paper Primary and Secondary Markets
#1 Wikipedia, resume of Aristotle’s Posterior Analytics
ICYMI (comment on MarkanKone of Oct 28)
The introduction of distributed/retained profit and the redefinition of saving cannot rescue I=S. No semantic maneuver can. I have clarified this case in Section 17 of the working paper Keynes’s Missing Axioms.
ICYMI (comment on FedUp of Oct 29)
Keynesian economics is about the monetary production economy: “The entrepreneur economy was one of Keynes’ ways of showing how and why monetary and financial matters must be integrated with real factors from the start of the analysis of a monetary production economy. It is this insight that is missing from virtually all strands of modern mainstream theory.” (Harcourt, 2010, p. 49)
The most elementary monetary production economy consists of the business and the household sector. Your two-person exchange example is obviously no acceptable representation of Keynes’s approach.
Here is a picture of the most elementary monetary production-consumption economy (Wikimedia AXEC31).
Harcourt, G. C. (2010). The Crisis in Mainstream Economics. real-world economics review, (53): 47–51. URL.
ICYMI (comment on Henry of Oct 29, 2:44 pm)
Sales, as seen from the business sector, is the same thing as consumption expenditures, as seen from the household sector.
In period 2 we have 90−100=−10 (not 0).
In the elementary production-consumption economy, the business sector cannot recoup its wage costs if the household sector saves. This is how loss comes into the world.
ICYMI (comment on Henry of Oct 29, 3:29 pm)
This is not a matter of definition but of hard, cold cash. The household sector spends C=90 units as consumption expenditures and the business sector receives exactly this amount but calls it sales. This in no way affects the definition of monetary profit Qm≡C−Yw. Together with the definition for monetary saving Sm≡Yw−C, this gives Qm≡−Sm (or simplified Q=−S if the distinction monetary/nonmonetary is not an issue). Look at the formulas and forget the names. It is the formal proof that counts and nothing else.
ICYMI (comment on Henry of Oct 29, 4:49 pm)
The accounting approach deals with variables that are the product of price and quantity like expenditure or income. Normally, it is not necessary to deal with each component of the product individually. Here it is indeed necessary because you fetch inventory investment out of thin air. Inventory changes occur if the quantity produced and the quantity sold are different.
So let us look closer at consumption expenditures which are given as the product of price and quantity, i.e. C=PX. We start with the case of full market clearing, that is quantity produced and quantity sold are equal and do not change because labor input and productivity do not change either. That is, the real part of the pure consumption economy is frozen.
Now, if consumption expenditures C drop from 100 to 90 in period 2 and the quantity X remains constant the price P must fall in C=PX. The market-clearing price in period 2 is now below the unaltered unit wage costs and this means that the zero profit of period 1 turns into a loss.
Note that the quantities produced and sold are equal in both periods 1 and 2. So there is no change of inventory and therefore inventory investment does not occur. We have I=0 and S=10, so saving and investment are unequal.
Of course, the product market is normally not cleared and there are inventory changes. I have dealt with this case in full generality in Primary and Secondary Markets.
The inclusion of inventory changes, though, does not alter the fact that saving and investment are never equal. And for this simple reason, the familiar story of the interest mechanism cannot be true.
ICYMI comment on Biagio Bossone of Oct 30
You say: “It is not the case that Keynes didn’t have the words to speak about inequality of ex-ante and ex-post saving. Based on his income multiplier process theory, he derived aggregate saving as a pure residual variable, strictly determined by aggregate investment in a way that S = I always and invariably, both ex-ante and ex-post.”
It is not the case that we do not know what Keynes said, but it is the case that Keynesians have not realized since the General Theory that Keynes' formal argument is provably false (2011). This has only been papered over with the ex-ante/ex-post filibuster and this Keynesian verbiage is the very proof of deeper confusion that lasts to this very day.
“Throughout the 1920s and 1930s the focus was increasingly on the role of the equality of saving and investment, but the semantic squabbles that dominated much of the debate (the distinctions between ‘ex-ante,’ and ‘ex-post,’ ‘planned’ and ‘realized’ saving and investment, the discussion of whether the equality of saving and investment was an identity or an equilibrium condition) reflected a deeper confusion.” (Blanchard, 2000, p. 1378)
This includes Keynes “But Keynes, too, sometimes gave the impression of not having fully grasped the logic of his own system.” (Laidler, 1999, p. 281)
Beyond Keynes’ manifest confusion, the correct relationship is ‘always and invariably’ given here.
Keynes, indeed, had the words to speak about the inequality of ex-ante/ex-post saving/ investment. A lack of words had never been the problem of any economist — what has always been in short supply was logic and argumentative consistency.
“The currently prevailing pattern of economic theorizing exhibits the following three characteristics: (1) a syncopated style of argument fluctuating back and forth between literary and symbolic modes of expression, (2) naive translation, or the loose paraphrasing of formulae into sentences, and (3) loose verbal reasoning for certain aspects of theoretical argumentation where explicit symbolic formulation is lacking.” (Dennis, 1982, p. 698)
The ex-ante/ex-post argument squarely falls into the category of loose verbal reasoning, a.k.a. blather. And this carries over to the theory of interest.
Blanchard, O. (2000). What Do We Know about Macroeconomics that Fisher and Wicksell Did Not? Quarterly Journal of Economics, 115(4): 1375–1409. URL
Dennis, K. (1982). Economic Theory and the Problem of Translation (I). Journal of Economic Issues, 16(3): 691–712. URL
Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN Working Paper Series, 1966438: 1–20. URL
Laidler, D. (1999). Fabricating the Keynesian Revolution. Cambridge: Cambridge University Press.
ICYMI (comment on Henry of Oct 30 on Oct 31)
The accounting approach deals always with nominal magnitudes, which carry a monetary dimension like euro/dollar/yen, and never with real magnitudes. Hence, ‘unit’ invariably means ‘monetary unit’ in the given context. By not realizing that the I=S debate runs in nominal terms your whole argumentation has been empty from the outset. Perhaps it is some comfort that you share this sad fate with djb, FedUp, and JKH.
My working paper Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist could be of some help to deconfuse yourself.
ICYMI (comment on Henry of Oct 31 4:22)
Your definition of income (income = household income + enterprise income) is wrong. Total income Y is wage income Yw=WL plus distributed profit Yd=DN. Distributed profit Yd is different from profit Q.
For the complete and consistent set of foundational propositions, which includes the nominal accounting variables as a subset, see this overview,
For details about the difference between profit Q and distributed profit Yd and retained profit Qre (and why Y=Yw+Q is deadly wrong) see Economics for Economists.
It's not so easy, indeed Keynes and many others got the distinction between profit and income wrong, and this is exactly why they all ended in the I=S cul-de-sac.#1 This is the correct relationship: Q≡Yd+I−S. This equation tells you how the profit of the business sector as a whole is generated and how important it is that the business sector’s investment is greater than household sector’s saving, i.e. I>S. This equation tells you also how beneficial the dissaving (S with negative sign) of the American consumer (= growth of private debt) is for the world economy (until it is reversed). But this advanced topic is forever beyond the horizon of those who are stuck with I=S.
#1 I=S: Mark of the Incompetent
Followed by Humpty Dumpty is back again.