It’s the quotient rule for derivatives.

R = d(k_A/k_B)/dt = (dk_A/dt k_B - dk_B/dt k_A) / k_B**2 = (p X_A 1 - p X_B k) / 1**2 = p X_A - k p X_B.

Oh the coincidence! This one is going to be a great read, thank you.

The Xs are the total profits obtained by the two classes. R is the derivative of the ratio of capital with respect to time, k_A/k_B, where the derivative of each is assumed to be proportional to its corresponding X (the constant being p), and k_A = k while k_B = 1.

Noted, thanks a lot!

Interesting post, I can’t say I personally agree with it, but it poses interesting questions and hypotheses.

I think unions could actually be useful in this hypothetical scenario. They could increase the amount of funding for the working class, as well as make competitors less competitive against the cooperative conglomerate, which in turn would offer jobs to workers to give them a better bargaining position in unions. Hope this helps your line of thought.

Interesting, that’s a great conclusion to extract.

I would like to see next how much difference in expenses can be tolerated. Since the model predicts a higher R in the salary region than I expected, that seems to indicate at least some headroom for disadvantage, which might increase with improvements in productivity and decrease with attempts by the bourgoise class to make negotiation asymmetrical.

I wonder if analyzing the more general case could show the relationship between the development of productive forces and the various mechanisms of capitalism.

Anything else I should note? This is turning out to be an even more interesting learning path than I thought :)

Thank you, very good point! I will certainly use them now that I feel more confident with this kind of problems.

Not exactly. The region where A and B would switch roles is near the bottom right, that’s why R is negative (both gain capital, but B gains it faster).

Beyond the first solid line, A and B both live off their own capital, but A has more manpower to capital ratio, and therefore makes better use of its capital.

Beyond the white line, A works for B (the expected initial state). Instead of increasing B’s capital faster than A’s, this model suggests A would be able to bargain a salary that, while benefiting both, would let A grow even faster than expected from capital and labor alone.

I used SymPy to symbolically reduce the cases to an optimization problem over w, which I solved numerically via SciPy. Then, I made use of Matplotlib for the graph itself.

Indeed… Sadly, the assumptions in this problem absolutely do not hold irl. But I feel like game theory could offer insights that are actually useful to us, beyond dummy problems like this.

Oh, they are the output elasticities of capital (alpha) and labor (beta).

Last week I fell on the classic oxymethazoline dependence trap. Whole week breathing through my mouth.

Explain how the two parties are bad. Then explain why lobbying causes them to be bad, and the electoral system keeps them in power regardless. Finally, explain how, obviously, none of the two parties will remove either problem, and therefore the system must be destroyed. Bonus if they also agree that capitalism must end.

Just applied it. Super cool!

Rule 34/34

Exactly my thought. You’re supposed to adjust for irrelevant variables.

Members of my party (me included) displayed a huge banner during the kickoff event yesterday.

This is a positive thing. I hope more governments do this, especially in South America, it could reduce the severity of anti-government protests fueled by outside campaigns.

I work for the (edit: Basque/Spanish) public healthcare system (as a medical doctor), and many of my colleagues do in some way or another look down to private clinics in a moral sense. These clinics regularly do such things as:

• Unnecessary tests, meaning higher costs and usually more radiation.
• Expensive treatments that are either not necessary or straight up ineffective.
• Not performing tests to check whether a treatment is necessary, choosing to always apply it instead, and therefore carrying higher risks and undesirable effects.
• Not properly informing patients of the actual effectiveness/prognosis/treatment options.

Basque Country mentioned!