Every economist can know from the Palgrave Dictionary that the profit theory is false (Desai, 2008). Or, as Mirowski put it, “... one of the most convoluted and muddled areas in economic theory: the theory of profit.” In other words, economists have NO idea what the pivot of their subject matter is.#1
Because profit is ill-defined, income/distribution is ill-defined, and this is due to the Humpty Dumpty Fallacy ― one of the worst idiocies of economics.
In the elementary investment economy, macroeconomic profit Q is defined as the sum of profit in the consumer goods industry, i.e. Qc≡C−Ywc, and the investment goods industry, i.e. Qi≡I−Ywi, that is, Q≡(C−Ywc)+(I−Ywi) or Q≡C+I−Yw (i). Profit Q is greater than zero if the value of output C+I is greater than total wage income Yw.
Now, Humpty Dumpty introduces a redundant definition by saying that profit may be called “income of the business sector” and that this “income” can be added up with the wage income of the household sector to “total income” Ψ thus
(a) Ψ≡Q+Yw and now (i) is rewritten
(b) Q+Yw ≡C+I and then, hey presto,
(c) Ψ≡C+I that is, “total income” is “by definition” identical to “value of output” or in the usual sloppy parlance “income = value of output” which obviously contradicts (i) and ― strangely enough ― makes profit invisible.
This definitional idiocy can be traced back to Keynes “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (GT p. 63)
Without the true profit theory, there is no true distribution theory. The axiomatically correct macroeconomic Profit Law is given as Q≡Yd+(I−S)+(G−T)+(X−M) , Legend: Q macroeconomic profit, Yd distributed profit, I investment expenditure, S household sector saving, G government expenditures, T taxes, X exports, M imports. For the world economy as a whole holds X, M=0.
The nominal labor "share" λ is defined as the quotient of wage income Yw and the sum of wage income and profit, that is, λ≡Yw/(Q+Yw) with Q given by  above. To recall, Ψ≡Q+Yw is redundant/inadmissible, hence profit is NOT a "share" of "total income Ψ".
The fact is that neither market power nor capital intensity nor information technology nor union weakness can ultimately account for a falling nominal labor "share" λ. The main drivers of increasing macroeconomic profit Q have been in the past decades the increased deficit spending of the household- and the government sector. The other factors can only account for the distribution of profit Q between firms but NOT for the total amount.#2, #3
Traditional distribution theory is scientifically worthless because the foundational economic concepts of profit and income and saving are ill-defined.* Worse, because profit is ill-defined/ poorly understood the whole of economics is proto-scientific garbage.
#1 The Profit Theory is False Since Adam Smith. What About the True Distribution Theory?
#2 Keynes, Lerner, MMT, Trump and exploding profit
#3 For details of the big picture see cross-references Profit and cross-references Refutation of I=S.
* Wikimedia AXEC129d