"The engine that drives enterprise is not thrift, but profit" - John Maynard Keynes
Last month Naked Capitalism included an interesting article by Philip Pilkington [1] on the origin of profits. Mr. Pilkington's "key point here [was] that investment creates profit", as opposed to the Marxian view that, in a capitalist mode of production, labour creates profits in the guise of surplus value.
To make his point Mr. Pilkington described and used a simple but clever model.
These are the key "ingredients" of his model:
- One island (i.e. a national economy with no exports or imports, with a government but without taxes or government expenditure: GDP = C + I , see below about depreciation and other inputs/intermediate consumption)
- One capitalist (who owns fixed capital: everything but labour power and money)
- One bank ($10 in $1 coins)
- Ten workers (5 builders, 5 bakers)
And these are the basic assumptions:
- Only workers consume (they don't save anything);
- There is a minimum wage ($1 a day);
- The Capitalist and the Bank do not consume;
- "No input costs apart from the cost of labour" and "capital goods (machines etc.) do not depreciate" (labour is the only production input: no intermediate consumption).
- The income tax rate is nil.
For the full motivation, read its description, under the heading "A Capitalist, A Bank, Ten Workers, Two Presidents and a Giant Loaf of Bread" (Mr. Pilkington is a writer, and, it seems, a good one, too!).
The model, as I intend to show, does not achieve its goal and tends to obscure things unnecessarily. However, unexpectedly, this has a positive effect.
Readers familiar with the article under scrutiny, may skip the following and jump directly to Discussion.
Otherwise, let's follow Mr. Pilkington's own exposition:
Day 1
"(...) The capitalist hires 5 workers (the builders) to build a bread factory - spending $5. He then hires the other 5 workers (bakers) to make bread in the factory - spending an additional $5. All of this money is raised from the local bank which charges him a rate of $1 interest a day. The capitalist ends up with a giant loaf of bread which he sells to the workers for all their wages - the bread thus sells for $10 and each worker gets a 10% share.
"(...) At the end of the working day, the builders once more join the bakers at the factory door and, since everyone has received their wages, the bread sells at its previous rate - the capitalist gets $10 (after interest payments he has $9), the workers all get a 10% share of the giant loaf and there is no deflation."
Let's pause here and think about what just happened.
Before the first day, these were the balance sheets of Capitalist and Bank:
Capitalist:
Assets: machines (valued $M); Liabilities: $0. Equity: $M (where $M is an arbitrary dollar amount).
Bank:
Assets: $10 (cash); Liabilities: $10 (presumably). No equity.
Bank's and Capitalist's combined equities: $M
During the first day:
Capitalist invested $5 to build a bakery and used the $5 remaining to pay wages.
A loaf of bread, costing $5 in wages, was sold for $10 (10 workers' combined wages), for a profit of $5. The price of bread was $10/loaf.
GDP: $B (brand new bakery's market value; more on this on Discussion) plus $10 (big loaf of bread). GDP = $B + $10.
At the end of the first day, these are the balance sheets of Capitalist and Bank:
Capitalist:
Assets: $M (machines), $B (bakery), $9 (cash); Liabilities: $10 (loan from Bank). Equity: $M + $B - $1 (= $9 cash - $10).
Bank:
Assets: $10 (loan to Capitalist), $1 (cash); Liabilities: $10. Equity: $1.
Combined equity: $M + $B
Day 2
Capitalist already has a bakery. Turning to the builders, he says: "Smell you later".
A depression resulted: unemployment appears (5 builders), GDP falls in both real and nominal terms; prices fall. In real terms, only one loaf of bread was produced: real GDP = $10 (Day 1 prices). The price of bread plummeted (from $10/loaf to $5): nominal GDP = $5 (Day 2 prices). CPI = -50%.
Observe that Capitalist is a peculiar beast indeed: bread demand and prices have fallen, but he refuses to adjust output (still produces one loaf of bread); by assumption 2, he is not a wage-setter, either (even though unemployment increases labour supply); and doesn't even think about asking Government to cut the minimum wage. Further: he can't really sack any baker or increase productivity (more on this below in Discussion). A magical island indeed! As a consequence, although nominal wages remain unchanged ($1/day), real wages doubled.
Faced with falling bread prices and higher real wages, it's no wonder that Capitalist barely managed to match costs and receipts: $5 wage bill, $5 receipts.
But Capitalist is not much weirder than Bank, who remains mute and does nothing at all.
At the end of the Day 2, these are the balance sheets of Capitalist and Bank:
Capitalist:
Assets: $M (machines), $B (bakery), $8 (cash); Liabilities: $10 (loan from Bank). Equity: $M + $B - $2. Capitalist, all panicky, barely manages to mutter: "I'm in deep shit".
Bank:
Assets: $10 (loan to Capitalist), $1 (cash); Liabilities: $10. Equity: $2. Bank exclaims: "Ye-haw! Crisis? What crisis?"
Combined Bank and Capitalist equity: $M + $B (unchanged since Day 1).
The other big surprise is that the 5 bakers are also winners: those guys are lucky that Capitalist is their boss. A really magical island!
From Day 2 on, little changes: GDP and prices fall no further, unemployment does not increase. A sort of equilibrium is reached where Capitalist loses $1 a day. Eventually (Day 5), before running out of money to pay wages and interests, Capitalist leaves the key to the bakery with Bank. Bank may or may not continue producing bread. If it decides to produce bread, the one loaf of bread GDP does not change.
Discussion
To argue his point, Mr. Pilkington set a one-off investment pulse, which, given assumptions 4 and 5, translated entirely into workers' income. This affects effective demand.
Prof. Bill Mitchell, a top exponent of MMT, has treated recently the topic of effective demand, saving me the effort of explaining it here. [2]
To put things simply: construction (private investment) provided jobs to 5 builders, baking, to 5. The demand by 10 cashed-up workers drove the price of the only loaf of bread up, to $10, well beyond the point where its price exceeded its cost ($5). This translated into profits.
Note as well, that every day, the physical product of the physical input of labour was enough to adequately sustain the workers and create a surplus.
For example, on Day 1: a 10 worker-day input (current market price: $10) originated an output consisting of a loaf of bread (current market price: $10) plus a bakery (current market price: $B). The 10 workers ate the loaf (1/10 each); Capitalist kept the bakery. In monetary terms: the workers were paid $10 and Capitalist kept the $5 profit (logically $B = $5, although it was not the product of a sale, as required by the GDP calculation!), from which he paid $1 to Bank later.
Day 2: a 5 worker-day input (current market price: $5) originated an output consisting of a loaf of bread (current market price: $5). The 5 workers ate the whole loaf, which the previous day was enough for them and the builders (each baker is getting 2/10 of the loaf), but no additional profit was left for Capitalist. Because real wages increased, it is the bakers who are getting the surplus now! That's another reason why I keep insisting that this is a magical island: the assumptions on price formation and the assumptions on he behaviour of Capitalist are producing strange effects.
Anyway, the conclusion, to me, seems inescapable: value was added to the product in excess of its inputs. Given that only labour was used as input, in this case I can't imagine how it can be argued that labour isn't solely responsible for the value added. When Capitalist appropriated the excess, this excess was called profit. But if labour is solely responsible for the value added, what role played Capitalist to justify his getting a profit? I'll leave the reader to ponder that question.
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In any case, all this was overlooked and seemed to have reasoned: there was an investment then and there is a profit, now; investment stops, profit stops. Gotcha Karl Marx! (More on this when discussing Kalecki's profit equation).Not so quick. As hinted above, here assumptions 1 and 2 play a crucial role. Let Nc be the number of builders and Nb that of bakers. Once the investment stream ceased, effective demand declined (from Nb + Nc to Nb). Production cost equals w.Nb (w is the daily wage in dollars), while sale revenue is (1-t).w.N (N = Nb + Nc if date = Day 1, Nb otherwise; t is the income tax rate). As by assumption 5, t = 0, profits ((1-t).w.N - w.Nb) had to cease with the investment stream (N fell to Nb).
Incidentally, this means that in the island it doesn't help sacking bakers: other things remaining the same, saving 1 dollar in the wage bill means a loss of 1 dollar in
If length of journey had been included, perhaps a different result would obtain. Alas, it wasn't included.
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What about Kalecki's profit equation, presented thus:Pn = I + (G - T) + NX + Cp - Sw?
("Pn = total profits after tax. I = gross investment. G = government spending. T = total taxes. (So, G - T = the total government budget deficit). NX = net exports (total exports minus total imports). Cp = capitalists' consumption. And Sw = total workers' saving.")
By design, all terms in the RHS of the equation are nil, except investment (Day 1, only!). Therefore, the equation becomes:
Pn = I.
Mr. Pilkington's conclusion still holds partially: investment, in this case, did create a profit, as expected using the equation (i.e. it was a sufficient condition for profit in the magical island). I have already argued why it did not, however, invalidate Marx's conclusion, as apparently intended.
Moreover, other variables (a fiscal deficit, for instance) would have created a profit, as well, as the non-trivial version of the equation shows. Thus investment is one among other possible "causes" of profit (i.e. investment is not a necessary condition for profit).
Further, let's consider now an income tax rate of 50% and see what happens with Capitalist's profit even in Day 1! ((1-t).5.w.N - w.Nb, with t = 0.5, N = 10, Nb = 5). Investment in this case does not "cause" a profit!
So, is the Kalecki equation wrong? On the basis of what little I know about it, I have no elements to say that. What I would say is that Mr. Pilkington's interpretation of the equation is incorrect: Marx is speaking of profits at an individual enterprise level; Kalecki's equation speaks of profits at the macroeconomic level.
Further, with the already expressed reservation that I don't really know much about it and pending further tinkering with the model, I would say that the Kalecki profit equation and the LTV seem fully compatible.
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Moving to another subject. Note that the way the agents were named in this model (Capitalist and Bank) obscures a fact: in reality, both are capitalists! A Bank/Capitalist separation might have been essential for Mr. Pilkington's purposes (to argue that investment causes profit), but it obscured his analyses and might have contributed to his confusion; but for my purposes here, it is useful, nonetheless. Capitalist is certainly losing money, and this is correctly noted, but his loss is caused by the need to share his money with Bank. That's why the combined Bank and Capitalist equity remains constant: $M + $B.
This may or may not surprise Mr. Pilkington, but it certainly does not surprise a Marxist: banking does not produce surplus value, but it still makes a profit. Where does this profit come from? It comes from someone else's surplus value!
Capitalist is contractually obliged to share with Bank the surplus value obtained during Day 1 in the form of interests payments, at the rate of $1 a day. In other words: Capitalist, in reality, is exploited by Bank.
Prof. Michael Hudson has written extensively about this. [3]
This shows that there's a value added in Marxian economics which is not provided by the model under scrutiny or even by Kalecki's profit equation.
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Finally, there is at least one other issue that remains to be treated. But that issue requires a separate treatment, because Kalecki's equation would seem to offer a macroeconomic way to understand how an economy, where workers are paid less than the value they create, can operate, when the so-called Say's Law supposedly proves it impossible.And, quite significantly, the equation purports to explain capitalists' profits, which since at least Sismonde di Sismondi and especially Karl Marx is seen as the source of accumulation and recurrent crisis.
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A last word: I have criticized Mr. Pilkington's article heavily. This doesn't mean that his effort was without merit. Quite to the contrary. I'd encourage him to persevere in his endeavour. Maybe one way would be to relax the constrains on the Capitalist/Bank's behaviours. Perhaps another way would be changing how prices are formed: the way chosen ensures that markets clear, which is rather ironic for someone who often attacks Say's Law.And I thank the readers for their patience.
Articles referenced:
[1] Philip Pilkington. 17-08-2011. Profits in a Capitalist Economy - Where Do They Come From, Where Do They Go?
[2] Bill Mitchell. 30-08-2011. We Need to Read Marx.
[3] Michael Hudson. 30-07-2010. From Marx to Goldman Sachs: The Fictions of Fictitious Capital.
I think you are attacking this article unfairly. kaleckian algebra is not making any claim about where the "value" or energy involved in production comes from. it is tracing the nominal flows to see how it is possible for capitalists receipts to be an excess of their outlays within a certain period. this is like scolding a string theorist looking at the origin of the universe for not explaining crocodile migration patterns. the model is aimed at something else. further, it should be obvious that the model is purely expositional, but you attack it as if he's predicting the unemployment rate based on it.
ReplyDeleteHi Nathan
ReplyDeleteThat came in real quick!
Allow me to quote myself regarding Kaleckian algebra:
"So, is the Kalecki equation wrong? On the basis of what little I know about it, I have no elements to say that. What I would say is that Mr. Pilkington's interpretation of the equation is incorrect: Marx is speaking of profits at an individual enterprise level; Kalecki's equation speaks of profits at the macroeconomic level."
In other words, exactly the opposite to what you object and pretty much the same thing you say is the correct interpretation: "it is tracing the nominal flows to see how it is possible for capitalists receipts to be an excess of their outlays within a certain period."
You also said: "further, it should be obvious that the model is purely expositional, but you attack it as if he's predicting the unemployment rate based on it."
I don't see Mr. Pilkington's model (although not clear in your reply, I'll assume here you are referring to it, not to Kalecki's equation) as purely expositional.
The quote below suggests Mr. Pilkington himself did not see his model as purely expositional, but as an argument "about where the 'value' or energy involved in production comes from":
"The key point here is that investment creates profit."
So, three questions for you:
Why is it obvious that the model is "purely expositional"? What exactly do you mean with "expositional"?
What do you mean with "you attack it as if he's predicting the unemployment rate based on it"? I ask this because I don't think I attacked it for that reason at all.
Quite to the contrary: it's obvious that the end of the bakery construction has to leave builders unemployed. That's the point with effective demand: people still have wants and needs, what they don't have is money to buy stuff. And they don't have money because they are unemployed.
Take your time. No need to rush to reply.
that came in quick because college is boring. reading this piece and responding has been the most intellectually stimulating thing I've done in the 16 days I've been here.
ReplyDeleteex·po·si·tion-A setting forth of meaning or intent.
"The key point here is that investment creates profit."
to me he is explaining the concept that investment (among other fiscal sources as you astutely point out) create profit. the quote you pick out seems like precisely that. no part of this model or it's explanation seems to me to have done any more then explain the logic behind the kalecki (and levy) profit equation.
"to me he is explaining the concept that investment (among other fiscal sources as you astutely point out) create profit. the quote you pick out seems like precisely that. no part of this model or it's explanation seems to me to have done any more then explain the logic behind the kalecki (and levy) profit equation."
ReplyDeleteI've reviewed the Pilkington article I am commenting, and now I understand your position. The quote I offered is more ambiguous than it seemed to me: you probably have not read his other pieces.
The article I am focusing on is part of a series. A subsequent piece in that series, entitled "Dynamism and Instability – The Search for Profits and Disequilibrium" (31-08-2011) makes Mr. Pilkington's position much clearer:
"Marx asked himself wherefrom the capitalist derived his profit and came to the conclusion that it must be from the worker. Marx, like Ricardo before him, believed that all value came from labour; that is, the blood, sweat and tears of workers. We might find this a convincing argument from a moral perspective – after all, doesn’t the worker do all the work? Or we may not find it a convincing moral argument at all – is that to say that the capitalist literally does nothing? But whether this is morally convincing or not it is, in essence, irrelevant to understanding the processes of a capitalist economy.
"Michal Kalecki – whose theory of profit we studied in the last piece – called the idea that profit somehow came from the labourer ‘metaphysical’, and he was right. Marx should have forgotten for a moment abstract questions about where so-called ‘value’ came from and instead looked a little harder at his equation:
" M—C—M’
"If he had he might have noticed that at a macro-level the profit (M’) in fact must have come in some sense from the original outlay – that is, the investment (M).
"In the last piece we saw that this is precisely the conclusion that Kalecki came to. He showed how all profit comes from investment."
In other words, Mr. Pilkington believes that Ricardo and Marx argued that labour was the origin of value on moral grounds. (That's why I insist that this is particularly ironic in his model, based as it is on the assumption that only labour inputs intervene: see assumption 5)
Similarly, in Mr. Pilkington's view, the idea that profits were in reality simply output in excess of inputs appropriated by the capitalists was a product of metaphysical thinking from Marx, and perhaps from Ricardo. (That explains why I emphasize how output in monetary and physical terms was actually distributed among workers and Capitalist)
Further, he believes that Kalecki's profit equation provides an alternative explanation of profits based exclusively on investment (or at least mainly on investment). And the Kalecki and Marx/Ricardo explanations would be, in Mr. Pilkington's account, mutually exclusive. I repeat here the specific sentence where Mr. Pilkington says this explicitly:
"If he [Marx, that is] had he might have noticed that at a macro-level the profit (M’) in fact must have come in some sense from the original outlay – that is, the investment (M). In the last piece [the one I am commenting on] we saw that this is precisely the conclusion that Kalecki came to. He showed how ALL profit comes from investment."
You'll observe that this is not what Kalecki's equation says, as it clearly includes fiscal deficit, NX, Cp and Sw.
You'll notice as well the irony in accusing Marx of losing sight of the larger picture by focusing too much on abstract questions, when Mr. Pilkington himself loses sight of the whole of the Kalecki equation, by focusing exclusively in the first term in a sum (i.e. I).
Nathan,
ReplyDeleteSorry, I made a mistake above: where it says "see assumption 5" it should say "see assumption 4".
I'll be honest i saw but didn't really read that piece. this writing seemed unfair since the referenced article didn't include any reference to marx. now i think you have a fair point and that was sloppy (like most dismissals of marx are) on philip's part. however, i think you may want to edit the post to include those quotes.
ReplyDeleteNot to worry!
ReplyDeleteYou seem to be much more knowledgeable about the Kalecki equation than me.
Can you point me to some web FREE resources about it? I'm afraid my financial situation is not really that great. :-)
Another thing, Nathan,
ReplyDelete"however, i think you may want to edit the post to include those quotes."
Maybe I should do that: it would make things easier for other readers. But somehow I feel that wouldn't be very honest. Sort of like am cheating? What do you think?
I don't think you get what I'm saying.
ReplyDeleteMagpie: "What I would say is that Mr. Pilkington's interpretation of the equation is incorrect: Marx is speaking of profits at an individual enterprise level; Kalecki's equation speaks of profits at the macroeconomic level."
In the article linked to below I deal with this and recognise it:
http://www.nakedcapitalism.com/2011/08/philip-pilkington-dynamism-and-instability-%E2%80%93-the-search-for-profits-and-disequilibrium.html
"Michal Kalecki – whose theory of profit we studied in the last piece – called the idea that profit somehow came from the labourer ‘metaphysical’, and he was right. Marx should have forgotten for a moment abstract questions about where so-called ‘value’ came from and instead looked a little harder at his equation:
M—C—M’
If he had he might have noticed that at a macro-level the profit (M’) in fact must have come in some sense from the original outlay – that is, the investment (M)."
The key move there is from Marx's circuit -- which is micro-level -- to Kalecki -- which is macro level. I go into this in one of the comments. See here:
http://www.nakedcapitalism.com/2011/08/philip-pilkington-dynamism-and-instability-%E2%80%93-the-search-for-profits-and-disequilibrium.html#comment-456430
The key here is that Marx is pursuing a sort of metaphysical substance called 'value'. I don't believe such a 'substance' exists. For me -- and, I believe, for Kalecki -- value is simply a nominal entity placed on a thing. There is no inherent 'value'; just a number we stick on it -- dollars or whatever.
So, you can say that my piece is 'compatible' with the LTV -- and you can say the same about Kalecki's equation. But it's equivalent to saying that it's 'compatible' with, I dunno, the theory of gravity, or the big bang theory. Sure they're compatible insofar as they don't rule each other out. But they have nothing to do with one another.
Similarly you can say that my piece 'misses' the LTV. But it doesn't. It rules it out as a metaphysical presupposition from the outset. Why? LTV cannot really tell us anything about how an economy operates. We can make predictions about profits and growth from the Kalecki equation. We cannot make any predictions from the LTV (Marx tried with his 'organic composition of capital' arguments -- he failed).
The only thing LTV can do is make a moral case indicting capitalism for operating in an inherently unequal way. If you want to do that that's fine. But it's just an opinion. I can use another system (say, 'oxygen theory of value') to argue another moral-economic argument (say, that capitalism extracts value from oxygen by polluting it). That's fine if you want to do it -- and you're free to do it -- but from a purely economic point of view it's superfluous.
If you look at the comments I critique the Marxist -- or 'metaphysical' -- perspective in depth. People really went to town so you get a good overview of the whole argument.
Best,
Phil
Hi TheIllusionist
ReplyDeleteWelcome to my blog and thanks for your comment.
Before jumping to the matters at hand, I would like to make clear that I found your effort meritorious and interesting, although I am indeed very critical of it and I believe it ultimately failed to make your case.
Well, let's get to business. You say: "I don't think you get what I'm saying."
That's possible, although I find it extremely unlikely, in relation to your two Naked Capitalism articles. However, it is entirely accurate with your present comment.
In any case, from what little I could understand, you seem to consider the key to Marx's alleged mistake (and, for the moment at least, I trust you'll allow me to use the "alleged" qualification) lies in his conception of value.
I believe that value seems to be the key to our difference of opinion; thus, perhaps a good starting point would be to define precisely what value is. After that perhaps we could proceed with the rest of your comment.
The only place in your reply where you describe what value means to you is in the following paragraph:
"The key here is that Marx is pursuing a sort of metaphysical substance called 'value'. I don't believe such a 'substance' exists. For me -- and, I believe, for Kalecki -- value is simply a nominal entity placed on a thing. There is no inherent 'value'; just a number we stick on it -- dollars or whatever."
Could you please elaborate this? More specifically: in what sense is value "a sort of metaphysical substance"? And why you don't believe value exists?
I am not asking this out of fastidiousness, but because your meaning is far from obvious to me.
It goes without saying that you are free to take your time to respond. We are all busy and the idea is not to burden anyone.
Again, thanks for the reply.
I am very late to this discussion. Sorry about that.
ReplyDeleteMy understanding is that Kalecki's profit equation relates to the realization of surplus value. Marx argued that surplus value is created in production on the basis of surplus labor. However, surplus value is only realized (converted into money) in exchange. Kalecki's contribution shows how - and to what extent - surplus value is realized.
Consider production. Some stuff is produced. Marx is arguing that this stuff has a value (in terms of money or labor) that cannot be altered by the act of exchange. If the buyer gains by getting something cheap, the seller loses by the same amount. All such exchanges above or below value will cancel, and the overall value of the stuff exchanged will not change as a result of the process. (There may be nominal changes in the value of money, but in real terms Marx is saying no value can be lost or gained in exchange.)
However, this does not mean that all the value created in production will be realized (i.e. converted into money). Some of the stuff may stay as stuff - i.e. unsold inventories. In that case, the surplus value of the affected capitalist remains in the form of stuff rather than money. It is still of the same value, but it has not been realized. (It is also likely that this build up in inventories will impact negatively on production levels and result in less value creation in the next period.)
In the simplest closed two-sector model without worker saving or capitalist consumption, Kalecki's analysis shows that capitalists will only succeed in realizing the surplus value produced in money terms to the extent that they invest. It is only through investment expenditure that total price (sum of all prices) will exceed the aggregate wage bill.
In a four-sector model with capitalist consumption and worker saving, the amount of surplus value realized is equal to capitalist expenditures (capitalist consumption and investment) plus the budget deficit plus net exports minus worker saving.
Note, though, that agreeing or disagreeing with Marx's theory of value creation does not dictate a position on Kalecki's analysis. It is therefore conceivable that, on the basis of Kalecki's analysis, somebody might interpret the monetary expenditures as the creator of surplus value, not labor. This may well have been Kalecki's own interpretation. I understand he was dismissive of Marx's theory of value.
Personally, I think Kalecki's analysis is very valuable, but I disagree with his dismissal of Marx's theory of value.
By the way, Pilkington's dismissal of Marx's theory of value is predictable. Many have given the same set of pat phrases for a century or so, but they are not really entitled to do so anymore in view of the TSSI literature, which at the very least establishes that Marx's theory can be interpreted in a way that is internally consistent. Nor is his theory "metaphysical". As for Marx's theory of value not helping to explain capitalism, personally I can't think of another insight in economics or political economy that has as far-reaching implications. Oh well.
ReplyDelete"I am very late to this discussion. Sorry about that."
ReplyDeleteNot at all, thanks for contributing. And welcome.
Well, the discussion with Pilkington, however frustrating, had a positive effect: it forced me to read about this subject.
As you, I also understand Kalecki's profit equation has to do with value realization and effective demand. And I fully concur with this: "Marx is arguing that this stuff has a value (in terms of money or labor) that cannot be altered by the act of exchange."
I'll admit I am not familiar with what Kalecki himself wrote, but thanks to Prof. Mitchell's hints in his blog, I am forming a picture about where the profit equation comes from and what exactly it means.
One of the texts Mitchell recommended (Levy, Farnham and Rajan, Where Profits Come From?) may provide an additional clue to the puzzle posed by this equation.
If the authors presented it faithfully to Kalecki, the Kalecki algebraic derivation of the profit equation seems to me logically rather dubious. I hasten to add that this does not imply the equation is no good: according to the authors, Jerome Levy independently derived the equation from a flow of funds perspective, not easily dismissed. In fact, I have not found any grounds to reject the Levy Sr. derivation.
In my opinion, the problem arises when one accepts both derivations as equally valid. In fact, this would go a long way into explaining why so much effort is put into the Jerome Sr. derivation, in the first place.
Any way, in the analysis of the second flow-of-funds model considered in the Jerome Sr. derivation (household, business and banking sectors), this is stated:
"We now can see the causal relationship between personal saving and profits. The decision by households to save some of their income is responsible for reducing profits. (...) Figures 2 and 3 illustrate an interesting point: total saving in our simple economy is always zero. When personal saving is zero, profits are also zero (profits exactly equal business saving since there are no profits taxes or dividends). In the case where personal saving is $60, business saving is -$60. Total saving must be zero because there is no investment. No new wealth is accumulated in this economy for the simple reason that no new wealth is created. Our simple economy produces only consumer goods and services, and no inventories are built for future consumption." (Pages 9 and 10).
I trust from this passage you will see why the Pilkington model, which closely resembles this situation, is so peculiar: without investment the bakers get all the value they produce (twice the normal bread daily quantity, when the necessary time only produces a single portion) and the rate of surplus value with no investment is zero!!!
I have got a copy of Rosa Luxembourg's "The Accumulation of Capital" (intro by Joan Robinson) and I am painfully going through it, as it seems to me it may have something relevant to say.
In any case, I find that to state that Kalecki's profit equation establishes that investment causes profit, with no role for value (as Pilkington does) is entirely similar to state that statistical thermodynamics (speed and mass of molecules) does not play a role in Boyle-Mariotte Law: given a fixed volume of gas, at constant temperature, volume and pressure are inversely related.
Any way, those are my two cents.
Cheers.