For the determination of monetary profit of the economy as a whole one has to start with the most elementary case of a pure consumption economy without investment, government, and foreign trade.* 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 scattered 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, innovation, 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.
Economists who observe a single firm and generalize what they see do not understand that what is true for a molehill (= micro) is NOT true for the universe (= macro). Micro profit theory is simply a Fallacy of Composition.
The profit theory has been false from Adam Smith/Karl Marx until now.
* (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. Note that ALL variables are measurable.
For more details see 'How the intelligent non-economist can refute every economist hands down' and 'The future of economics: why you will probably not be admitted to it, and why this is a good thing' and 'Economists cannot do the simple math of profit — better keep them out of politics' and 'A tale of three accountants' and cross-references Profit.
The balances of the business sector, the household sector, the government sector and the rest of the world are interrelated as follows Qm≡-Sm+Yd+I+(G-T)+(X-M). This is the Proft Law for an open economy (X-M) with a government sector (G-T) and with business investment I and distributed profit Yd.
You say: “My first conclusion is that Qm is a measure of production and Sm is a measure of consumption. In a ‘perfect’ economy, everything that is produced is consumed.”
Not quite, monetary profit Qm and monetary saving Sm are nominal variables, the real variables are output O and quantity bought/sold X. All variables are related to a period of defined length, usually the calendar year. Because ALL variables are measurable all conclusions are testable. There is no ambiguity of any sort.
For a detailed verbal and graphics supported description of the elementary consumption economy see ‘How the intelligent non-economist can refute every economist hands down’.
(i) You say: “I do not understand that type of diagram.”
Think of a Cartesian coordinate system#1. Take the first quadrant = north east and throw the other three quadrants away. The first quadrant has only positive values on the axes. Make this four times. Now, put the four first quadrants together, then you get a new coordinate system with ALL axes positive. Thus you can easily walk from one quadrant to the next because the axes have the same dimension, e.g. L = hours per year, or C = dollar per year, or O, X quantity per year. Negative axes are not needed in economics because output O or working hours L are always greater or at least equal zero.
(ii) Productivity is a real magnitude with the dimension quantity per hour.
(iii) The Marxian definition of profit is ultimately based on the labour theory of value which does not relate to the economy as a whole. But Marx applied also macro reasoning, for example: “How can they continually draw 600 p. st. out of circulation, when they continually throw only 500 p. st. into it? From nothing comes nothing. The capitalist class as a whole cannot draw out of circulation what was not previously in it.” This question is answered by the Profit Law Qm=-Sm (see above).#2
#1 Wikipedia Cartesian coordinate system
#2 For more details see ‘Marx, the moron’ and ‘Proﬁt for Marxists’
You say: “But surplus is not synonymous with profit.”
No, surplus is a real magnitude and profit is a nominal magnitude. For the relationship between the two see Section 4 ‘Profit, surplus, real shares’ in ‘Proﬁt for Marxists’.
Everybody who has ever used knife and fork or a wheelbarrow or a cooking spoon somehow understands the concept of lever and can apply it successfully in everyday situations. Science, though, goes beyond the endless multitude of concrete instantiations of the lever and tries to figure out the common denominator of ALL variants of levers past, present, and future. Science abstracts from the superficial reality of the Here and Now and tries to figure out the underlying fundamental reality, which has been found to be Fb/Fa=a/b: “This is the law of the lever, which was proven by Archimedes using geometric reasoning.” (Wikipedia)
The failure of economics is mainly due to the Fallacy of Insufficient Abstraction.#1 In other words, economists cannot rise above the level of storytelling. One story line is that of supply-demand-equilibrium and the wonderful feats of the Invisible Hand, the other story line is that of the struggle between the good guys=workers and the bad guys=capitalists. Storytelling is scientific rubbish but people like it.
Economics, understood as science, must go beyond common sense, plain description, and storytelling: “The highest ambition an economist can entertain who believes in the scientific character of economics would be fulfilled as soon as he succeeded in constructing a simple model displaying all the essential features of the economic process by means of a reasonably small number of equations connecting a reasonably small number of variables. Work on this line is laying the foundations of the economics of the future …” (Schumpeter)
So the first thing to do is to formulate ‘a simple model’ of the abstract entity economy, more precisely, the simplest possible model. 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.
The most elementary economy is given with three equations Yw=WL, O=RL, C=PX, two conditions X=O, C=Yw and the definition of total monetary profit Qm≡C-Yw.#2 This yields P=W/R (1), i.e. the market clearing price P is equal to unit wage costs W/R. This is equivalent to W/P=R (2), i.e. the real wage W/P is equal to the productivity R. This holds, no matter how the wage rate W is set. A wage reduction leads to a proportional fall of the market clearing price P. Profit Qm does NOT change because the budget is balanced, i.e. C=Yw, and from this follows Qm=0, i.e. profit is zero.
In the elementary monetary economy, workers always get the whole output O, the real wage W/P is equal to the productivity R. If productivity increases over time the real wage rises, if productivity falls over time then at some point the real wage hits the subsistence level. This, though, has NOTHING to do with exploitation or surplus or profit. So, as a matter of principle, the elementary consumption economy can reproduce itself at any level of employment L for an indefinite time as long as there are no external limits. It is impossible for the business sector as a whole to make a profit.
So, where does profit come from? Not from a longer labor time L, not from higher productivity R, not from a lower wage rate W, not from more greed, not from monopoly power, not from risk taking, not from wishful thinking or any other subjective factor.
It was Marx who asked the right question: “How can they continually draw 600 p. st. out of circulation, when they continually throw only 500 p. st. into it? From nothing comes nothing. The capitalist class as a whole cannot draw out of circulation what was not previously in it.”
Trivially true. As long as the budget is balanced, i.e. C=Yw, total monetary profit/loss Qm is zero. Because we know already that the Profit Law states Qm=-Sm it is quite obvious that the business sector as a whole can only draw more out of the circulation, i.e. C greater Yw, if the household sector throws more into the circulation, in other words if the household sector dissaves, i.e. if Sm≡Yw-C is negative, i.e. if C is greater than Yw.
From nothing comes nothing, even economists understand this.#3
#1 For details see ‘Economics and the Fallacy of Insufficient Abstraction’
#2 For the detailed verbal description see ‘How the intelligent non-economist can refute every economist hands down’
#3 For more details see ‘The Emergence of Profit and Interest in the Monetary Circuit’