Blog-Reference and Blog-Reference
Your treatment of profit is partial and marginalistic. Marginalism is defined by the Walrasian axiom set = microfoundations. Because the Walrasian axioms are provable false your treatment of profit is false. Marginalism has already been dead in the cradle 140+ years ago.#1
For the determination of monetary profit of the economy as a whole one has to start with the most elementary case of a pure production-consumption economy without investment, government, and foreign trade.#2 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 Sm≡Yw-C is zero and the monetary profit of the business sector Qm≡C-Yw, too, is zero.
In case (ii) monetary saving Sm is positive and the business sector makes a loss, i.e. Qm is negative.
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=0 or Qm=-Sm, in other words, loss is the counterpart of saving and profit is the counterpart of dissaving. This is the most elementary form of the Profit Law. Total profit is distributed among the firms that comprise the business sector.
Profit for the economy as a WHOLE has NOTHING to do with productivity, the wage rate, the working hours, exploitation, competition, capital, power, monopoly, waiting, risk, greed, the smartness of capitalists, or any other subjective factors. Total profit/loss is objectively determined in the most elementary case by the change of the household sector’s debt.#3
#1 For details see ‘First Lecture in New Economic Thinking’
#2 The macrofoundations approach starts with three objective-systemic (= behavior-free) axioms: (A0) The objectively given and most elementary configuration of the economy consists of the household and the business sector which in turn consists initially of one giant fully integrated firm. (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 expenditure C is equal to price P times quantity bought/sold X. For a start it holds X=O.
#3 For more details see cross-references Profit
You say: “Capitalists may consume too. Workers may save too.”
True. In this case, the Profit Law reads Qm≡Yd-Sm. This generalization, though, does not alter the fact that your treatment of profit is false.*
* For details see cross-references Profit