Macroeconomics is one of the most embarrassing failures in the history of modern science. The fact is that economists do NOT understand to this day that I=S is provably false since Keynes.
- I is never equal S and even Nick Rowe will eventually grasp it
- How Keynes got macro wrong and Allais got it right
- Kalecki and Keynes: The double macroeconomic false start
- Heterodox economics: When stupidity becomes a public danger
- Keynesians ― terminally stupid or worse?
- For details of the big picture see cross-references Refutation of I=S
Related 'Flawed logic' and 'Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It'.
I is NEVER equal to S. Therefore, it is a futile exercise to ‘explain’ I=S with some silly examples.
Here is the proof.
The elementary production-consumption economy is given with three macroeconomic axioms: (A1) Yw=WL wage income Yw is equal to wage rate W times working hours. L, (A2) O=RL output O is equal to productivity R times working hours L, (A3) C=PX consumption expenditures C is equal to price P times quantity bought/sold X.
In the elementary production-consumption economy, three configurations are logically possible: (i) consumption expenditures are equal to wage income C=Yw, (ii) C is less than Yw, (iii) C is greater than Yw.
- In case (i) the monetary saving of the household sector Sm≡Yw−C is zero and the monetary profit of the business sector Qm≡C−Yw, too, is zero. The product market is cleared, i.e. X=O in all three cases. Accordingly, the market-clearing price as the dependent variable is given by P=C/X=W/R.
- In case (ii) monetary saving Sm is positive and the business sector makes a loss, i.e. Qm is negative. The market-clearing price P is less than W/R.
- In case (iii) monetary saving Sm is negative, i.e. the household sector dissaves, and the business sector makes a profit, i.e. Qm is positive.
It always holds Qm≡−Sm, in other words, the business sector’s profit is equal to the household sector’s dissaving, and the business sector’s loss is equal to the household sector’s saving. In still other words, saving is NOT equal to investment because there is NO investment in the elementary production-consumption economy.
Under the condition that the price remains constant, the market does not clear if saving is greater than zero, i.e. O−X>0 if Sm>0, i.e. the business sector’s inventory increases. The valuation of the inventory is NOT predetermined. For example, if it is valued with zero, then inventory investment is zero and I is NOT equal to Sm. If it is valued higher, then inventory investment is positive but still unequal to Sm.#1
Keynes started macroeconomics with false premises and ended with false conclusions: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (GT, p. 63)
Keynes’ premise income = value of output is false. From the correct macroeconomic axioms follows:
(1) Qm≡−Sm in the elementary production-consumption economy,
(2) Qm≡I−Sm in the elementary investment economy,
(3) Qm≡Yd+I−Sm in the investment economy with profit distribution,
(4) Qm≡Yd+I−Sm+(G−T)+(X−M) in the general case with government in an open economy.
Simple algebra tells everyone that saving is NEVER equal to investment. Both orthodox and heterodox economists are too stupid for the elementary mathematics that underlies macroeconomic accounting.#2
#1 Primary and Secondary Markets
#2 For more details see cross-references Refutation of I=S
Nick Rowe writes: “It’s easy to teach students the arithmetic showing that actual saving must equal actual investment (S=I).” and “S=I is an accounting identity, and accounting identities are true by definition.”
Fact is that “S=I is an accounting identity, and accounting identities are true by definition.” is one of the most stupid statements in the history of the failed/fake science of economics.#1, #2, #3 And the fact that all student generations since Keynes parrot this manifest arithmetic garbage is a metric of the desperately low IQ of economics students.
Take notice that the correct accounting identity for the elementary investment economy reads Qm≡I−Sm, that is, monetary profit Qm is the difference of investment expenditures of the business sector I and monetary saving of the household sector Sm.
Saving has never been nor will ever be equal to investment. So, ‘explaining’ I=S is not easy, just the opposite, it is impossible.
The fact that economists still claim ― 80+ years after Keynes committed the lethal blunder ― that I equals S is due to their utter scientific incompetence. This thread is the very proof that Nick Rowe and Roger Sparks and the rest (except Jamie, who got it: “This makes me want to scream in frustration”) are too stupid for the elementary mathematics that underlies macroeconomic accounting.#4, #5
#1 Wikipedia and the promotion of economists’ idiotism
#2 MMT and the single most stupid physicist
#3 Truth by definition? The Profit Theory is axiomatically false for 200+ years
#4 A crash course in macro accounting
#5 For details see cross-references Accounting
You write: “Here’s the arithmetic of S=I: Define Y as market value of newly-produced final goods (and services). In a closed economy … we divide Y into consumption goods C and investment goods I, so Y=C+I. And we define saving S as S=Y−C. Substitute the first equation into the second to get S=Y−C=C+I−C=I, so S=I.”
This is Keynes’ argument of GT p. 63. It is false because Keynes got macroeconomic profit wrong: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson et al.)
Let this sink in: the economist Keynes NEVER understood the foundational concept of his subject matter. And After-Keynesians NEVER spotted Keynes’ blunder.
In order to get the “arithmetic” right, one has to go back to the most elementary macroeconomic configuration, that is, the elementary production-consumption economy which consists of the household and the business sector.
In this elementary economy, three configurations are logically possible: (i) consumption expenditures are equal to wage income C=Yw, (ii) C is less than Yw, (iii) C is greater than Yw.
- In case (i) the monetary saving of the household sector S≡Yw−C is zero and the monetary profit of the business sector Q≡C−Yw, too, is zero. The product market is cleared, i.e. X=O, i.e. there is NO change of inventory.
- In case (ii) monetary saving S is positive and the business sector makes a loss, i.e. Q is negative.
- In case (iii) monetary saving S is negative, i.e. the household sector dissaves, and the business sector makes a profit, i.e. Q is positive.
It always holds Q≡−S, in other words, at the heart of the monetary economy is an identity: the business sector’s surplus (deficit) equals the household sector’s deficit (surplus). In other words, profit is the counterpart of dissaving and loss is the counterpart of saving. This is the most elementary form of the macroeconomic Profit Law.
For the elementary investment economy the Profit Law reads Q≡I−S. As everyone can see, there is NO such thing as an accounting identity I=S or an equilibrium of saving and investment.
For 80+ years, I=S is a monument of economists’ mathematical incompetence, and “S=I is an accounting identity, and accounting identities are true by definition.” will forever stand out as one of the most idiotic statements in the history of so-called economic thought.
You say: “You can see that business would control the pricing of the products consumed but households would control whether consumption (the second exchange) would occur and when.”
What I indeed see is that you are one of those undereducated blatherers who overpopulate economics. The point at issue is the macroeconomic “arithmetic” and not human behavior/control. More specifically, the point at issue is the refutation of the brain-dead assertion: “S=I is an accounting identity, and accounting identities are true by definition.”
The point at issue is that I=S is mathematically false and by NO means “true by definition” and that economists are too stupid for macroeconomic accounting#1 and that they, after 200+ years, still do not understand what profit is.
Make no mistake, I=S is not only disqualifying for you and Nick Rowe but for the entire profession.#2
In the elementary production-consumption economy, the price is under the condition of market clearing, i.e. X=O, and budget balancing, i.e. C=Yw, the dependent variable, i.e. P=W/R. If the condition of market-clearing is dropped and the firm sets the price then the market is NOT cleared and the change of inventory is given by O−X.
All these cases have been dealt with elsewhere#3 and they are NOT relevant for the point at issue. So, they can be left out for the moment. Again, the point is that investment is NEVER equal to saving and that Nick Rowe’s attempt to explain I=S is 200+ light years beside the point, as usual.#4
This is the state of economics: Walrasian microfoundations are false and Keynesian macrofoundations are false. There is NO economics that satisfies the criteria of science, only senseless blather.
#1 The Common Error of Common Sense: An Essential Rectification of the Accounting Approach
#2 Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It
#3 Primary and Secondary Markets
#4 Cryptoeconomics ― the best of Nick Rowe’s spam folder