Or, "Profits = Expenditure - Income". Those are just alternative ways of saying the same thing, for a closed economy, if investment and saving include government investment and saving.
Most economists will say that's wrong. And it is wrong by standard definitions, where aggregate expenditure and income are the same thing, and investment and saving are also the same thing (for a closed economy, including government investment and saving).
But let me tell you a story:
There are firms and households (ignore government and foreigners). Firms rent land and labour from households, and use it to produce food which they sell to households (ignore capital). There is a fixed stock of currency that is used to buy and sell everything. Food cannot be stored. No other assets.
In any given year, if households spend $100 more buying food than the income they earn from rent and wages, then at the end of the year households own $100 less currency and firms own $100 more currency than at the beginning of the year. Firms have made a profit exactly equal to the $100 difference between households' expenditure and income. Or, firms' $100 profits are equal to households' negative saving (there is no capital and no investment in this story).
But who owns the firms?
If households own the firms, we can say that firms' assets are owned by households, and firms' profits are included in households' income. And if we do that, then we are back at the standard definitions where Expenditure = Income, and Investment = Saving, must always be true.
Or we could adopt an intermediate position: we could say that firms' profits are part of household income only if firms actually distribute those profits to the households that own them. In which case we get: Undistributed Profits = Expenditure - Income = investment - Saving.
There's a number of different ways we could add things up. Which is the best way? It depends.
Suppose firms were like a strange religious cult; they save all their profits for six years, then on the seventh year they blow the lot by spending it all on food which they burn as a sacrifice to the gods. None of the households want firms to do that; it's just what firms do, following some weird internal logic of their organisational structure. If so, you had better build that fact about firms' behaviour into your macroeconomic model. And it would not make sense to include firms' profits as part of households' income, because households know they will never be able to consume firms' profits. (And a corporate profit tax might really be a tax on corporations, and not on the households who own them, work for them, or buy from them.) So Profits = Expenditure - Income = Investment - Saving.
There is no one right way to do the accounting (though there are conventional ways, and it's easier to understand what others are saying if we all follow the same conventions). The accounting can't tell you what the world looks like (though it can help you keep your head straight when you are looking at the world). First decide what the world looks like; then do your accounting accordingly.
[An economist will probably make a comment on this post, and that comment will go automatically into the spam folder. Because Typepad, and history, across this and other macro blogs. But if it's a reasonable comment I will fish it out, after a short delay.]
MMTers like to bypass the saving=investment identity with impunity by using exactly this sort of distortion of definitions. I say stick with conventional meanings and state that firms destroy household saving/income every 7 years. Don't let MMTers confuse everyone with these tricks.
Posted by: Benoit Essiambre | January 24, 2018 at 09:50 PM
Benoit: from my experience, MMTers *insist* in the I=S identity.
" I say stick with conventional meanings and state that firms destroy household saving/income every 7 years."
We could do it that way. Be trickier to keep track of things though.
Posted by: Nick Rowe | January 24, 2018 at 10:19 PM
How does the story continue if run through multiple pay cycles? Can investment continue to exceed saving if firms do not in some way transfer that investment to households? This seems like a good way to begin an explanation of the loanable funds fallacy, though I'm sure that's not the goal.
Posted by: DZ | January 24, 2018 at 11:16 PM
DZ: In my story, if we aggregate over 7 years, Investment = Saving. But I could change the story a bit, so that wouldn't happen. Suppose they only blow half their accumulated profits, and it's a growing economy.
Posted by: Nick Rowe | January 24, 2018 at 11:36 PM
I somewhat disagree with 'First decide what the world looks like; then do your accounting accordingly.'. If you decided the world looks like your model and you defined 'Profits = Expenditure - Income' for accounting purposes, then if you came across another different world (like our one) where this didn't hold then this definition is useless and you have to redo accounting to match this other world..
Shouldn't accounting be universal and be able to define terms and identities so they can describe all possible worlds ?
Posted by: Market Fiscalist | January 25, 2018 at 12:07 AM
Under standard national accounts definitions, national saving includes household saving and undistributed profits (as well as government saving if there's a government sector). So in a closed economy, national saving = investment. But you know that, so I'm unclear what you're trying to accomplish by introducing alternative definitions. In what sense would undistributed profits *not* be considered a type of saving? Or is your point just that we need to think about business saving separately from household saving? Though I think a lot of macroeconomists already do talk about national saving as consisting of household, business, and government saving.
Posted by: Brent Moulton | January 25, 2018 at 01:09 AM
Isn't it all supply and demand? Economists have always assumed the profit stream is subsequently broken into a series of supply and demand trades. Easy to prove.
Posted by: Matthew Young | January 25, 2018 at 03:13 AM
Nick: “Most economists will say that's wrong. And it is wrong by standard definitions”
Non-economist here. I started reading about economics nearly a decade ago after spending many years in business and government. Accounting is a standard tool in business and government, so I imagined that an obvious way in to economics would be via accounting identities. However, for some reason economists’ accounting identities didn’t make sense to me. Also, economists seem to have been arguing about them since WWII, so it was clear that there was something about these identities which wasn’t right.
I eventually realised that there were no “standard definitions” for the terms in the identity. However, this is obscured by the fact that no-one ever makes it clear what the terms mean, and everyone assumes that everyone else means the same thing.
I like the identity in the form:
I + C = C + S
as it’s the form that is most approachable for someone with a business background.
I realised that the first (of THREE) main causes of confusion is that economists use two different interpretations of the identity. This arises because no-one ever clarifies which sectors are associated with each term.
The first interpretation is:
I(B) + C(B) = C(H) + S(H).
The second interpretation is:
I(B) + C(B) = C(H) + S(B + H).
It is the fourth term which causes this confusion.
Many economists appear to use the first interpretation and claim that it represents the “standard definition”. However, after much thought, the second interpretation is correct.
Even if I am wrong, economists could fix this easily by writing the identity in a way that includes the sectors EXPLICITLY. Alternatively, if I am right, they could separate the S term into two. Business saving is retained profit so:
I(B) + C(B) = C(H) + S(B + H)
Or
I(B) + C(B) = C(H) + S(B) + S(H)
Moving the S(B) terms to the LHS
I(B) – S(B) + C(B) = C(H) + S(H)
As business saving is retained profit, we can rename the S(B) term as RP(B):
I(B) – RP(B) + C(B) = C(H) + S(H)
which is consistent with the title of your post.
I will stop there. However, if you are interested, I can explain what I think are the other two main causes of confusion with these identities for non-economists with a business background. I suspect that these confusions are at the heart of what makes these identities so difficult to understand for many students as well.
Posted by: Jamie | January 25, 2018 at 05:14 AM
Brent: "Or is your point just that we need to think about business saving separately from household saving?"
My point is it depends. If firms act in the interests of the households who own them, we should add them together. It makes no difference whether your agent retains part of your income and saves it for you, or hands it over for you to save. But if firms have their own ends (like in my religious cult example) we should keep them separate.
But someone will eventually read this post and leave a comment; then you will see where I'm coming from.
Posted by: Nick Rowe | January 25, 2018 at 06:28 AM
Is Nick Rowe stupid or corrupt or both?
Comment on Nick Rowe on ‘”Profits = Investment − Saving”’
“Since every act of spending results in income for somebody else, total spending for the economy as a whole equals total income. This is true by definition and is a basic building block in macroeconomics.” (Cooper) Both, orthodox and heterodox economists subscribe to this statement as the self-evident rock-bottom truth of all of economics.
The foundational methodological error/mistake/blunder of economics is that the pivotal concepts — profit and income — are ill-defined and not at all understood. This explains why economics is a failed science or what Feynman called a cargo cult science. Actually, economics is at the stage of medieval physics before the pivotal concept of energy was properly defined and understood.
The proof of the utter scientific incompetence of economists is given with the fact that the profit theory is false since Adam Smith.#1, #2, #3
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)#4
That Keynes was too stupid for the elementary mathematics of macro accounting was proven by Allais.#5
According to well-established scientific standards, profit theory, Keynesian economics, and all I=S/IS-LM models are definitively refuted. However, economists NEVER lived up to any standards “In economics we should strive to proceed, wherever we can, exactly according to the standards of the other, more advanced, sciences, where it is not possible, once an issue has been decided, to continue to write about it as if nothing had happened.” (Morgenstern, 1941)
Nick Rowe stands firmly in this corrupt methodological tradition “If households own the firms, we can say that firms’ assets are owned by households, and firms’ profits are included in households’ income. And if we do that, then we are back at the standard definitions where Expenditure = Income, and Investment = Saving, must always be true. … There’s a number of different ways we could add things up. Which is the best way? It depends.”#6
See part 2
Posted by: Egmont Kakarot-Handtke | January 25, 2018 at 08:21 AM
Part 2
This is the classical argument since Alice’s and Humpty Dumpty’s memorable methodological dialogue “’When I use a word,’ Humpty Dumpty said in rather a scornful tone, ‘it means just what I choose it to mean — neither more nor less.’ ‘The question is,’ said Alice, ‘whether you can make words mean so many different things.’ ‘The question is,’ said Humpty Dumpty, ‘which is to be master — that’s all’.”
Science, of course, is different “The only way to arrive at coherent languages is to set up axiomatic systems implicitly defining the basic concepts.” (Schmiechen) Science is defined by material and formal consistency and this is known since 2000+ years ― except among economists “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.” (Aristotle)
Keynes’ premise Income = Value of Output is axiomatically false and because of this, the whole analytical superstructure of Keynesianism up to MMT is scientifically worthless. Worse, with MMT the toxic combination of stupidity and corruption has reached a new quality and mutated to political fraud.#7
Since Keynes, macro is proto-scientific garbage but Nick Rowe and his Trump University colleagues have not realized it.#8
Egmont Kakarot-Handtke
#1 The profit theory is false since Adam Smith
https://axecorg.blogspot.de/2017/11/the-profit-theory-is-false-since-adam.html
#2 “A satisfactory theory of profits is still elusive.” (Palgrave Dictionary, Desai, 2008)
#3 “... one of the most convoluted and muddled areas in economic theory: the theory of profit.” (Mirowski, 1986)
#4 I is never equal S and even Nick Rowe will eventually grasp it
https://axecorg.blogspot.de/2018/01/i-is-never-equal-s-and-even-nick-rowe.html
#5 How Keynes got macro wrong and Allais got it right
https://axecorg.blogspot.de/2016/09/how-keynes-got-macro-wrong-and-allais.html
#6 No accountant worth his salt adds wage income (= flow) and profit (= balance of the flows consumption expenditures and wage income) together. Only brain-dead economists do this. For more details about flow―balance consistency see cross-references Accounting
http://axecorg.blogspot.de/2016/12/accounting-cross-references.html
#7 Down with idiocy!
http://axecorg.blogspot.de/2017/12/down-with-idiocy.html
#8 Rethinking macro
https://axecorg.blogspot.de/2018/01/rethinking-macro.html
Posted by: Egmont Kakarot-Handtke | January 25, 2018 at 08:22 AM
"An economist will probably make a comment on this post, and that comment will go automatically into the spam folder. Because Typepad, and history, across this and other macro blogs. But if it's a reasonable comment I will fish it out, after a short delay."
This might be a rare example of where I'm not entirely sure if someone in the real world is speaking "de re" or "de dicto", as we say in philosophy. (Do you mean any old economist or one in particular? I suspect the latter! ;) )
I agree with the point of this post, Nick, and I think that it helps reconcile two methodological truths: good account matters in economics AND no economic knowledge is ultimately purely an accounting truth. It might be helpful to try to put your point in terms of the distinction in logic and the foundations of mathematics between (a) a calculus and (b) the interpretation of that calculus.
By the way, I recently graduated with my PhD. Thanks for all of your blogposts that opened up much of macro to me!
Posted by: William Peden | January 25, 2018 at 10:57 AM
William (Dr Peden!): Congratulations on the PhD!
"(Do you mean any old economist or one in particular? I suspect the latter! ;) )"
Yep. See just above your comment.
Posted by: Nick Rowe | January 25, 2018 at 12:15 PM
Let me riff on the initial post a bit.
Let's say you have an economy where all the firms are owned by foreigners. Because colonialism or something like that.
Households sell their labor/land to the firms, and the firms produce food which the households buy.
If the firms earn a profit, it is remitted offshore.
It seems that what "profit" means in this example is just that the foreigners are entitled to some % of the food each year (they could lend currency to, or buy land from, the households -- but that just entitles the foreigners to a larger cut of the food in future years).
This just would be an example of GNP < GDP in conventional accounting, and it would be important to focus on both for this type of economy; "profit" being the delta between the two metrics.
Alternatively, you have a class of domestic people who run the firms (because they are genetically, culturally, or fortunately endowed with those roles) and profits just represent a return to a class of labor and/or capital.
Posted by: louis | January 25, 2018 at 01:22 PM
louis: "This just would be an example of GNP < GDP in conventional accounting, and it would be important to focus on both for this type of economy; "profit" being the delta between the two metrics."
Yep. And it will matter whether foreigners spend their income differently from domestics.
Posted by: Nick Rowe | January 25, 2018 at 04:00 PM
I see a couple of unexplained omissions...
In para 4, you state that the firms have $100 more 'profit' than households, but you have omitted that the household's therefore hold the REAL surplus of the $100 of food that they bought. Yes the firms are up $100 in currency but they are down $100 in food. The households have the food and the firms don't. The $100 isn't a 'thing' that the firms hold instead, rather it's a future claim on things which don't exist yet. (consider that if the firms bought back some of the food with the Dollars, now the households hold that future claim on things which don't exist yet).
In para 8, the firms suddenly blow 6 years of profits on buying food and destroying it. But where did that food come from??? If this is a closed system then that MUST be the food the firms themselves produced. Which means the firms have simply bought back their own food from their customers and now the customers have their Dollars back. So we're just back in the same position as 6 years ago – the point before the firms paid their workers to produce the food. On the other hand, if it's not a closed system all of a sudden and the food came from outside this system, then someone outside this system now holds the currency that the firms bought all that food with. The firms destroyed the food, but the currency still sits in someone's account or belongs to someone.
The currency is just an accounting loop which manages the linear throughput of real production, and you have taken a tiny time slice in that ongoing infinite process, left some things out but then claim to have identified something? If you put those omitted missing pieces back into your examples, then I'm not seeing any huge proof of anything. What have I missed..?
Posted by: Economuse | January 25, 2018 at 04:09 PM
PS you also failed to say where the $100 and other currency came from? For example if the firms took out $100 in loans, then their profit cancels that and they can now pay their loans back.
Or if not the firms, then someone in your system took out that $100 and owes that credit back out of the system and back out of existence.
I'm really not sure that you're seeing all the balls that are in the air here...?
Posted by: Economuse | January 25, 2018 at 04:15 PM
"#5 How Keynes got macro wrong and Allais got it right
https://axecorg.blogspot.de/2016/09/how-keynes-got-macro-wrong-and-allais.html"
Qre = I - S arises because of EKH's narrow definition of income. Change the definition to the usually accepted definition and the usual Keynesian identity reappears. This is easily demonstrated.
Posted by: Henry Rech | January 25, 2018 at 06:10 PM
Nick,
Did you delete my comment?
Posted by: Henry Rech | January 25, 2018 at 06:20 PM
The comments boil down to one question, Do profits flow into economic conditions.
Do profits keep the money system closed (we always move to even balances) and dense (we can always find the best path). Economists assume their is a retained earnings and distributed earnings that insures this condition is true, and we retain that naturally. It may not be true, I dunno.
What happens if the profits are non-economic? For example, huge pension funds that know they are not a complete market and are subject to regulatory arbitrage. This condition results in secret collusion (change the names to suit the politics here). And labor markets during transition tend to be uneconomic in the money sense.
Government catastrophe insurance?
Posted by: Matthew Young | January 25, 2018 at 07:02 PM
>MMTers *insist* in the I=S identity.
I only have a small sample but some MMTers were arguing in favor of government spending money and going into debt to boost people's perceived savings and to boost aggregate demand. I countered that this would depress aggregate investment, at least long term aggregate investment (by redirect resources towards consumption or short term investment) and leave us worst off in the long run. They argued that people's savings don't matter because they are purely financial and net to zero on the aggregate anyways. I said that no, savings net to investment, and investment matters for future production. But they wouldn't buy that. I've had multiple MMTers insist that savings, except for some financial promises net to zero, that they are just the other side of government debt (and on top of that these people conflate government debt and central bank liabilities) and they think we need the high government debt to allow people to save. And I'm always like no, savings can also be supported by private investment and if you use too much government debt, if a cohort of people retire and try to spend their savings at the same time, the government might be forced to tax them away or confiscate them through high inflation.
I'm no expert though so I may have gotten something wrong.
Posted by: Benoit Essiambre | January 25, 2018 at 07:17 PM
Nick Rowe
You say it depends, and this a not so smart answer from the handbook of lame excuses.#1 Science is about proof, so here is the unassailable proof of Nick Rowe’s incompetence.
1. Premises
The elementary production-consumption economy is given by three macro 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.#2
2. Logical implications
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. For a start, the market clearing price as 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.
It always holds Qm+Sm=0 or Qm=−Sm, in other words, 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) but saving is equal to loss. There is NO such thing as an IS-curve but there is an SL-line = Saving/Loss-line which runs with minus 45 degrees through the origin.#3
3. Conclusion
Simple algebra tells everybody that saving is NEVER equal to investment and that, by consequence, there is NO such thing as an IS-curve. All IS-LM models are a priori false. Nick Rowe’s model is wackadoodle.
4. Generalization
The axiomatically correct Profit Law says for the general case Qm=Yd+I−Sm+(G−T)+(X−M). Legend: Qm monetary profit, Yd distributed profit, I investment expenditures, Sm monetary saving, G government expenditures, T taxes, X exports, M imports. Again, there is NO such thing as an equality/identity/equilibrium of investment and saving. Both variables are entirely independent.#4
Egmont Kakarot-Handtke
#1 Failed economics: The losers’ long list of lame excuses
https://axecorg.blogspot.de/2017/01/failed-economics-losers-long-list-of.html
#2 For more details see Economics for Economists
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2517242
#3 See on Wikimedia
https://commons.wikimedia.org/wiki/File:AXEC124.png
#4 For details of the big picture see cross-references Refutation of I=S
http://axecorg.blogspot.de/2015/01/is-cross-references.html
Posted by: Egmont Kakarot-Handtke | January 25, 2018 at 07:22 PM
Henry: It got caught in the spam filter. I just fished it out.
Posted by: Nick Rowe | January 25, 2018 at 07:51 PM
Economuse:
That's exactly what I spotted, and since food cannot be stored the price of food during the sacrifice year would skyrocket and households would starve. I think they would quickly refuse to rent any land to such firms and just grow their own food instead.
Also, starting out with "there is no capital and no investment in this story" would appear to make statements like "Investment = Saving" kind of meaningless.
Posted by: Tel | January 26, 2018 at 02:16 AM
Benoit Essiambre
You say “MMTers *insist* in the I=S identity.”
The MMT balances equation reads (I−S)+(G−T)+(X−M)=0. This boils down to I=S if the government balance and the foreign trade balance is set to zero. The MMT balances equation is provably false.#1
The axiomatically correct balances equation reads (I−S)+(G−T)+(X−M)−(Qm−Yd)=0. The correct equation contains profit Qm and distributed profit Yd while these pivotal economic magnitudes are MISSING in the MMT equation.
Conclusion: Keynes’ I=S was false because Keynes NEVER understood what profit is which is the defining mental defect of the representative economist. The Post Keynesians realized nothing.#2 The MMTers, too, realized nothing and built their whole approach on the false macroeconomic balances equation. Because of this, the whole analytical superstructure of MMT is scientific garbage. MMT policy lacks sound scientific foundations and is nothing more than ordinary political fraud.
Economuse
You say “Qre=I−S arises because of EKH’s narrow definition of income. Change the definition to the usually accepted definition and the usual Keynesian identity reappears. This is easily demonstrated.”
Yes, indeed. The point is, though, that what you call “narrow definition of income” is the correct definition and what you call the “usually accepted definition” is provably false. Here is the proof.
It holds
(i) Qm=−Sm in the elementary production-consumption economy,
(ii) Qm=I−Sm in the elementary investment economy,
(iii) Qm=Yd+I−Sm in the elementary investment economy with profit distribution.
Let us now take equation (ii) and play the Humpty Dumpty shell game.
We introduce a new definition by saying that profit may be called “saving of the business sector” and that this “saving” can be added up with saving of the household sector to “total saving” Σ thus
(a) Σ≡Qm+Sm and now (ii) is rewritten
(b) Qm+Sm=I and then, bingo,
(c) Σ≡I that is, “total saving” is “by definition” identical to investment or in the usual sloppy parlance saving equals investment.
Let us call this the Humpty Dumpty Fallacy. It is at the bottom of all IS-LM models. Note that “total saving” Σ is different from “household sector saving” Sm and that this crucial difference simply vanishes in the brain-dead slogan “saving equals investment”.
The methodological blunder consists in the introduction of the redundant definition (a).
The parallel blunder consists in the introduction of the redundant definition of “total income” as the sum of wages and profits, i.e. Ψ≡Yw+Qm. Note in particular that here a flow Yw and a difference of flows Qm is added together which is a plain flow-balance inconsistency.#3
Needless to emphasize that economists never feel any irritations about logical inconsistencies, just the opposite, this is the air that they breathe from their student days to the grave. This is why economics is a failed science.
Conclusion: All of economics is proto-scientific garbage because the foundational concepts profit and income are ill-defined since Adam Smith.
Egmont Kakarot-Handtke
#1 For the full-spectrum refutation of MMT see cross-references.
http://axecorg.blogspot.de/2017/07/mmt-cross-references.html
#2 Why Post Keynesianism Is Not Yet a Science
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1966438
#3 A tale of three accountants
https://axecorg.blogspot.de/2017/07/a-tale-of-three-accountants.html
Posted by: Egmont Kakarot-Handtke | January 26, 2018 at 06:02 AM
Tel - let's say the profit margin is 2% a year, and accumulated profits approximate 12% by the 7th year, the households wouldn't necessarily starve.
I think a fun Nick Rowe post would analyze what the interest rate looks like in this toy economy, where everyone knows that every 7th year effective supply is ~88% of the other 6 yrs. I don't have formal economic training so I can't do the math, but I've read a lot of Nick's posts so I'll try.
1) You assume there's diminishing marginal utility to consumption, and so households try to smooth consumption. Don't take into account time preference for now.
2) You take wages as defining the unit of currency (i.e. everyone gets paid a fixed 10 tokens for their labor every year, but the price of food in tokens can change based on market forces)
3) There are 100 households being paid 1,000 tokens total per year. The firm produces 10,000 apples a year.
4) To make it easier on my brain, I will use a 2 yr cycle instead of 7. Y1 = all production consumed by households and the firm lends to households; Y2 = the firm has demand to consume what it can
Price: In the first year of the cycle, the firm offers 10,000 apples for sale and lends out 100 tokens on 1 year term. 1100 tokens chasing 10,000 apples = $11/apple price. In the 2nd year, the firm pays 1,000 tokens in wages, and some portion of those is returned as principal + interest on the loans. Still, the firm spends whatever cash flows back on the loans, so there are 1,000 tokens in total to be spent, and a $10/apple price in Y2.
Interest rate: if a household does not borrow from the firm, it can consume 100 / 11 = 9.1 apples in Y1 and 100 / 10 = 10 apples in Y2. To smooth consumption, it seems the household would be willing to borrow at some rate to shift consumption from Y2 to Y1. For example, it would likely be willing to borrow 4.5 tokens at a 11% interest rate to consume 9.5 apples each year, even though in total it ends up w/ slightly less food.
But the firm needs to induce each household to borrow 100 tokens. So the rate must be lower. In fact, it must be below zero, because there is 10% deflation from Y1 to Y2, and borrowing 10 tokens at 0% likely leaves you worse off than not borrowing at all, and certainly worse off than borrowing 9 tokens at 0%. At a -15% rate, for example, you end up with 19.25 total apples borrowing 10 tokens, and 19.23 borrowing 9 tokens, but consumption is slightly smoother in borrowing 9, so it is possible households may demand a more negative rate depending on how quickly marginal utility sloughs off.
Lets say the market clearing rate is -50%. Each household borrows 10 tokens, spends 110, and eats 10 apples in Y1, and pays back 5 tokens, spends 95, and eats 9.5 apples in Y2. The firm consumes 0 in Y1, and spends its 50 of Y2 cash flow on 5 apples. So while the accounting profit margin may look to be 9.1% in Y1 (1100 in income, 1000 in wages), the firm only ends up consuming 5% of production in Y2 in this little model.
I'm sure I messed something up here (profit margin being determined by amt of tokens lent, and the fact that there's zero profit in Y2 both seem like loose threads to me) but I'd be interested in how Nick sees this.
Posted by: louis | January 26, 2018 at 10:36 AM
Are the firms in this model missing a trick? For each of the first 6 years they could be buying food off each other with the profits and still keeping all the money within the firm sector. In the seventh year even after they have bought (and burned) the food (off each other) they still retain the $700 transferred to them from households. They will get richer every year until households run out of cash holding or get to a point where they are happy with their cash balances. An interesting feature is that the more firms buy from each other the bugger total profits are !
Posted by: Market Fiscalist | January 26, 2018 at 12:36 PM
EKH defines household income:
Household Income = Wage Income + Distributed Firm Profits
=> Y = Yw + Yd
However, conventional Keynesian macro defines total economy income:
Total Eco. Income = Wages Income + Dist Firm Profs + Retained Firm Profs
Using Yt for total income and Qre for retained firm profits:
=> Yt = Yw + Yd + Qre
Similarly, EKH deals with household savings not total economy savings viz.:
Household Savings = Household Income – Consumption
=> Sm = Y – C
However, conventional Keynesian macro defines total economy saving:
Total Eco. Saving = Household Income + Retained Firm Profs – Consump.
Using St for total savings:
=> St = Y + Qre – C
Rearranging:
=> St = Y – C + Qre
and given Sm = Y – C
=> St = Sm + Qre
Rearranging:
=> Sm = St – Qre
Taking EKH's equation
=> Qre = I – Sm (EKH I defines as investment)
and substituting into this equation for Sm as above:
=> Qre = I – (St – Qre)
=> I = St
That is, removing the definitional impediments EKH imposes, EKH's equations reduce to the Keynesian relationship of equality between investment and savings.
When EKH says investment is never equal to savings and hence Keynes’ relationship does not hold, EKH is comparing apples to oranges. EKH's definitional schema (based on the household perspective) precludes EKH from comparing its results from those of the schema used by Keynes (that is, the conventional macro accounting one).
Posted by: Henry Rech | January 26, 2018 at 05:02 PM
Qre = I – Sm (EKH I defines as investment)
Should be
Qre = I – Sm (EKH defines I as investment)
Posted by: Henry Rech | January 26, 2018 at 05:07 PM
Take a closed economy w.o. gov. activity.
By definition we have Wages + Profits = Investment + Consumption.
Assume the classical saving hypothesis such that Wages = Consumption.
Then you have that Investment = Profits.
Michael Kalecki once interpreted it such that capitalist determine their own profits by their own investments.
Posted by: A.T. | January 26, 2018 at 05:17 PM
Reply to Benoit Essiambre
You say “MMTers *insist* in the I=S identity.”
The MMT balances equation reads (I−S)+(G−T)+(X−M)=0. This boils down to I=S if the government balance and the foreign trade balance is set to zero. The MMT balances equation is provably false.#1
The axiomatically correct balances equation reads (I−S)+(G−T)+(X−M)−(Qm−Yd)=0. The correct equation contains profit Qm and distributed profit Yd while these pivotal economic magnitudes are MISSING in the MMT equation.
Conclusion: Keynes’ I=S was false because Keynes NEVER understood what profit is which is the defining mental defect of the representative economist. The Post Keynesians realized nothing.#2 The MMTers, too, realized nothing and built their whole approach on the false macroeconomic balances equation. Because of this, the whole analytical superstructure of MMT is proto-scientific garbage. MMT policy lacks sound scientific foundations and is nothing more than ordinary political fraud.
Reply to Economuse
You say “Qre=I−S arises because of EKH’s narrow definition of income. Change the definition to the usually accepted definition and the usual Keynesian identity reappears. This is easily demonstrated.”
Yes, indeed. The point is, though, that what you call “narrow definition of income” is the correct definition and what you call the “usually accepted definition” is provably false. Here is the proof.
It holds
(i) Qm=−Sm in the elementary production-consumption economy,
(ii) Qm=I−Sm in the elementary investment economy,
(iii) Qm=Yd+I−Sm in the investment economy with profit distribution.
Let us now take equation (ii) and play the Humpty Dumpty shell game.
We introduce a new definition by saying that profit may be called “saving of the business sector” and that this “saving” can be added up with saving of the household sector to “total saving” Σ thus
(a) Σ≡Qm+Sm and now (ii) is rewritten
(b) Qm+Sm=I and then, bingo,
(c) Σ≡I that is, “total saving” is “by definition” identical to investment or in the usual sloppy parlance saving equals investment.
Let us call this the Humpty Dumpty Fallacy. It is at the bottom of all IS-LM models. Note that “total saving” Σ is different from “household sector saving” Sm and that this crucial difference simply vanishes in the brain-dead slogan “saving equals investment”.
The methodological blunder consists in the introduction of the redundant definition (a).
The parallel blunder consists in the introduction of the redundant definition of “total income” as the sum of wages and profits, i.e. Ψ≡Yw+Qm. Note in particular that here a flow Yw and a difference of flows Qm is added together which is a plain flow-balance inconsistency.#3
Needless to emphasize that economists never feel any irritations about logical inconsistencies, just the opposite, this is the air that they breathe from their student days to the grave. And this is why economics is a failed science.
Conclusion: All of economics is proto-scientific garbage because the foundational concepts profit and income are ill-defined since Adam Smith.
Egmont Kakarot-Handtke
#1 For the full-spectrum refutation of MMT see cross-references.
http://axecorg.blogspot.de/2017/07/mmt-cross-references.html
#2 Why Post Keynesianism Is Not Yet a Science
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1966438
#3 A tale of three accountants
https://axecorg.blogspot.de/2017/07/a-tale-of-three-accountants.html
Posted by: Egmont Kakarot-Handtke | January 27, 2018 at 03:55 AM
Henry Rech
You say “EKH defines household income: Household Income = Wage Income + Distributed Firm Profits => Y = Yw + Yd. However, conventional Keynesian macro defines total economy income: Total Eco. Income = Wages Income + Dist Firm Profs + Retained Firm Profs.” Then you rearrange the equations and conclude: “That is, removing the definitional impediments EKH imposes, EKH’s equations reduce to the Keynesian relationship of equality between investment and savings.”
In fact, I have proven this:
(i) Loss/profit is equal to saving/dissaving in the elementary case of a production-consumption economy, i.e. Qm=−Sm (1), and equal to the difference between investment and saving, i.e. Qm=I−Sm (2), in the case of an investment economy without profit distribution. Conclusion: household sector saving is NEVER equal to business sector investment.
(ii) Keynes’ slogan saving-equals-investment is axiomatically false and is definitively refuted. By implication, the whole General Theory is refuted.
(iii) It is, however, quite easy to regress to Keynes’ false formula by introducing redundant definitions. So, by introducing the definition of “total saving” Σ, thus that Σ≡Qm+Sm, equation (2) turns to Σ≡I that is, “total saving” is “by definition” identical to investment. This, of course, is a methodologically inadmissible semantic shell game.
(iv) The same shell game is performed with the introduction of the redundant definition of “total income” as the sum of wage income and profits, i.e. Ψ≡Yw+Qm. This definition is methodologically inadmissible because a flow Yw and a difference of flows Qm is added together which is a plain flow-balance inconsistency.
So, yes, Keynes’ slogan saving-equals-investment can at any time be reestablished with the Humpty Dumpty Fallacy. The students of economics simply swallow and parrot every crap as the history of economic thought shows.#1 History shows also that heterodox profit theory has not been one iota better and falls flat as an alternative.#2
In order to end the 200+ years old predominance of utter incompetence in economics, it is necessary to get rid of the whole bunch of blatherers, shell game artists, morons, and agenda pushers. Those who still parrot saving-equals-investment and those who present I=S/IS-LM models on their blogs and those who peer-review and publish this proto-scientific garbage have to go first.
Egmont Kakarot-Handtke
#1 For details of the big picture see Refutation of I=S
http://axecorg.blogspot.de/2015/01/is-cross-references.html
#2 Heterodoxy, too, is scientific junk
http://axecorg.blogspot.de/2015/09/heterodoxy-too-is-scientific-junk_85.html
Posted by: Egmont Kakarot-Handtke | January 27, 2018 at 06:12 AM
"investment and savings"
"investment is never equal to savings'
I should have course said "saving" instead of "savings".
Posted by: Henry Rech | January 27, 2018 at 06:35 AM
EKH,
"...in the case of an investment economy without profit distribution"
It's all about definition and initial assumptions.
Your formulation might apply to such an economy but it seems to me that your assumption is heroic.
Posted by: Henry Rech | January 28, 2018 at 12:19 AM
"....household sector saving is NEVER equal to business sector investment"
OK, however, the Keynesian formulation specifies total investment, not just household investment.
It's apples and oranges.
Posted by: Henry Rech | January 28, 2018 at 12:30 AM
Henry Rech
I said “Conclusion: household sector saving is NEVER equal to business sector investment.”
You say: “OK, however, the Keynesian formulation specifies total investment, not just household investment.”
Keynes said “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.”
There is NO such thing as household investment. The household sector either saves (consumption is less than income) or dissaves (consumption is greater than income) in the elementary cases under discussion and NOTHING else.
Egmont Kakarot-Handtke
Posted by: Egmont Kakarot-Handtke | January 28, 2018 at 04:13 AM
Henry Rech
Keynes always believed that ‘a little clear thinking’ or ’more lucidity’ could solve almost any problem. (Moggridge, 1976, p. 39)
Egmont Kakarot-Handtke
Posted by: Egmont Kakarot-Handtke | January 28, 2018 at 04:17 AM
OK. Apologies.
Should have said the Keynesian formulation specifies total saving, not just household saving.
Posted by: Henry Rech | January 28, 2018 at 04:54 AM
Cryptoeconomics ― the best of Nick Rowe’s spam folder
Comment on Nick Rowe on ‘”Profits = Investment − Saving”’
Nick Rowe concluded his post with this cryptic remark “[An economist will probably make a comment on this post, and that comment will go automatically into the spam folder. Because Typepad, and history, across this and other macro blogs. But if it’s a reasonable comment I will fish it out, after a short delay.]”
Nick Rowe, though, gladly publishes comments like this: “I agree with the point of this post, Nick, and I think that it helps reconcile two methodological truths: good account matters in economics AND no economic knowledge is ultimately purely an accounting truth. It might be helpful to try to put your point in terms of the distinction in logic and the foundations of mathematics between (a) a calculus and (b) the interpretation of that calculus. By the way, I recently graduated with my PhD. Thanks for all of your blogposts that opened up much of macro to me!”
In the topsy-turvy econoblogosphere the best stuff is in the spam folders, and what is tirelessly recycled is soft soap, blather, gossip, propaganda, disinformation, and proto-scientific crap.
It is at anybody’s guess to which extend the econoblogosphere is corrupted. The problem, of course, is that spam folders are invisible to the general public. Private censorship is built into the blogging software and works without any traces.
Occasionally, there are exceptions. For those who appreciate the privilege of casting a glance into Nick Rowe’s spam folder, here is a sample of comments he suppressed over the last two years.
I is never equal S and even Nick Rowe will eventually grasp it
https://axecorg.blogspot.de/2018/01/i-is-never-equal-s-and-even-nick-rowe.html
The Law of Interdependent Budgets
https://axecorg.blogspot.de/2017/11/the-law-of-interdependent-budgets.html
Laying the bastard Phillips curve to rest
https://axecorg.blogspot.de/2017/07/laying-bastard-phillips-curve-to-rest.html
Macro poultry entrails reading
https://axecorg.blogspot.de/2017/01/macro-poultry-entrails-reading.html
Nick Rowe: Bury me at the end of coal-pit
https://axecorg.blogspot.de/2016/12/nick-rowe-bury-me-at-end-of-coal-pit.html
Getting out of IS-LM = Getting out of despair
https://axecorg.blogspot.de/2016/06/getting-out-of-is-lm-getting-out-of.html
IS-LM is dead and waiting to be buried
https://axecorg.blogspot.de/2016/02/islm-is-dead-and-waiting-to-be-buried.html
Worthless Canadian model bricolage
https://axecorg.blogspot.de/2015/12/worthless-canadian-model-bricolage.html
Since the agenda pushers Adam Smith/Karl Marx, fake news is standard communication procedure in political economics. Thus, any idea of what scientific ethics means got entirely lost. Economics has to be rebuilt up from scratch, or as Joan Robinson had it: Scrap the lot and start again.#1
Egmont Kakarot-Handtke
#1 How to restart economics
https://axecorg.blogspot.de/2016/01/how-to-restart-economics.html
Posted by: Egmont Kakarot-Handtke | January 28, 2018 at 02:43 PM
From whom to the companies buy food to sacrifice on the 7th year? Other companies? Individuals? Food exporting foreigners?
It's like electromagnetism. Change in the electric field induces magnetism. Change in the magnetic field induces electric flow. When everything is in a cycle, what matters is velocity, not residual quantities.
Posted by: Kaleberg | January 29, 2018 at 09:30 PM