"The engine that drives enterprise is not thrift, but profit" - John Maynard Keynes
Last month Naked Capitalism included an interesting article by Philip Pilkington  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:
"(...) 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:
Assets: machines (valued $M); Liabilities: $0. Equity: $M (where $M is an arbitrary dollar amount).
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:
Assets: $M (machines), $B (bakery), $9 (cash); Liabilities: $10 (loan from Bank). Equity: $M + $B - $1 (= $9 cash - $10).
Assets: $10 (loan to Capitalist), $1 (cash); Liabilities: $10. Equity: $1.
Combined equity: $M + $B
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:
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".
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.
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. 
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.
----------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.
----------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.
----------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. 
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.
----------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.
----------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.
 Philip Pilkington. 17-08-2011. Profits in a Capitalist Economy - Where Do They Come From, Where Do They Go?
 Bill Mitchell. 30-08-2011. We Need to Read Marx.
 Michael Hudson. 30-07-2010. From Marx to Goldman Sachs: The Fictions of Fictitious Capital.