Costs of production are prices
As Robinson (1953) pointed out in her critique of the neoclassical production function all the costs of production are prices of the inputs used to produce a good or service, and any price is made up of wages and profits; the former and the latter are the payment of each factor of production, namely, labor and capital, respectively.
From the aforementioned we can deduce that the total income distribution of a country can be split into wages, and profits. Hence, such a distribution can be formulated as the following:
Y= w + r
From the equation above we can see that, given a total income level Y, when wages w rise the profits r drop, and vice versa. It is true at least in the short term.
It is noteworthy to point out that in a society the total production equals the total income because each good and service in the economy required labor and capital to be produced and paid for each of those factors of production, therefore, the total product in terms of value equal the total income (wages and profits). This time Y represents total income, although it can perfectly represent the total production of a society.
If the number of workers and capital are taken into account, the above mathematical expression can be written as follows.
Y= w*L + r*K
Total income Y equals the wages w times the number of workers L plus the profits r times the amount of capital K required to produce.
The only way to have more wages and more profits at the same time is through increases in productivity.
Mathematically, the formula below shows that keeping the same amount of labor and capital, we can get more production per worker, and higher wages with higher profits at the same time (note that the formula has not changed, it just was divided by the number of workers L to get Y/L , which is production per worker).
Y/L = w*(L/L) + r*(K/L)
Y/L = w + r*(K/L)
The increase in labor productivity Y/L takes time because it is the outcome of several variables such as capital accumulation, changes in the way how the resources are managed, technical change (better technology embodied in capital or intermediate goods), learning-by-doing processes, among other variables.
In the short term, it is about who takes the biggest part
At least in the short term, the struggle between labor and capital to take a bigger chunk of the pie will be characterized by the contradiction of such a distribution where there are losers and winners, a good example of a zero-sum game.
As it has been stated by the orthodox theory in a mechanical way the rise in productivity makes room for both wages and profits to grow all together with everyone happy. Marx (1865) agreed that capital accumulation brings about the possibility for wages to grow, nevertheless, asserted that such a win-win condition does not come up mechanically or spontaneously, because the interest of each class (workers and capitalists) remains and so does the contradiction; possibility of getting better payment is not a certainty and the bargaining power has great relevance in the income distribution.
Marx, Carl (1865). Value, Price, and Profit.
Robinson, Joan (1953). The Production Function and the Theory of Capital. http://theme.univ-paris1.fr/M1/hpe/HPEM1-TD4.pdf