Differential Calculus Of Labor Utopia

The Pen Of Darkness
5 min readSep 17, 2020

How ironclad is the dogma of diminishing returns? Is it the same concept applied to both individual effort and group productivity, or b) an extrapolation of individuals to groups or c) an inference from groups to individuals

Effort has diminishing returns to personal utility. Moderate exercise is fun, extreme exercise is suffering. Moderate work is intellectually and physically stimulating, extreme work is suffering. Yet the returns on this investment aren’t a simple diminishing curve, but a set of discontinous paradigms such that within the first ‘tranche’, there are diminishing returns to effort, say musical practice of 1hr to 4hrs, but then once that threshold is crossed, you up-shift to the next paradigm and unlock a huge treasure of benefits. Within this paradigm again there are diminishing returns until you get to level 3 where there is a huge jump again. Incentives are therefore structured along the lines of the marginal benefit of effort such that incentives have diminishing returns until they take a big one-time quantum leap when they shift to the next paradigm. If these incentive structures did not reflect the marginal benefit of effort, then the only feedback we have is the internal experience of effort which only tends towards suffering. So I quit at 2hrs of music practice when I realize the additional hour I spend isn’t giving me proportionate increase in returns. I quit at 15mins of meditation and 30mins of exercise. I remain at the first paradigm in all my activities. If everybody does this, we get a pathological mediocritization of society, so we try and protect the incentive structures that drive individuals to ignore personal suffering and unlock new levels of achievement. We make it possible for obsessives to be rewarded for their suffering, even if we just get a handful of them per field. Musicians. Sportsmen. Billionaires. Artists. Is there room for the democritzation of rewards? Should a billionaire really be paid a million times more than a junior exec? Is LeBron James a million times better than the lowest paid NBA player? If they played 1–1, would the score be million:1? If they played a million 1–1 games, would LeBron win all of them? He is disproportionately rewarded, but he would not exist if someone like him were not disproportionately rewarded. Neither can the incentive structure be democratic, nor can it be linear such that he is still rewarded more but proportionately. A linear incentive means the marginal cost of effort will quickly overtake the marginal benefit since costs are non-linear.

The same paradigmatic view of diminishing returns must therefore apply to individuals and firms as well. The marginal product of labor is a diminishing curve. The textbook example of the bakery has additional units of labor creating a crowded inefficient atmosphere where Y=(K,L+5) — F(K,L+4) << F(K,L+1) — F(K,L). But should we stop here? If there are digital tranches with points of discontinuity leading to new paradigms, a better workspace layout design, efficient operations management, division of labor or gains from cooperation, then there is a theoretical state where dY/dL at L+5 >> at L. If we constrain ourselves to the possibility of unlocking these reversals of diminishing returns at certain thresholds, then we get the ascending flower petal of paradigmatic non-linearity. But if we start reducing the gaps between these thresholds, ie the distance between points of discontinuity, we tend towards a continuous linear curve, or even a quadratic curve depending on which point of the curve we intervene in the system to unlock greater marginal benefits. In reality this translates to reducing the intervention to a single unit of labor, a human being, such that the overall system is modified with every single additional worker in order to unlock the non-zero gains from cooperation with that employee, ie d2Y/dL2 = +ve for every single employee. Do this for society and we have entirely replaced competition with cooperation while still retaining the gains from competition (innovation, energy) by making these parts of the design of non-zero gains from cooperation

The bottleneck is K, the capital available both to the firm and the individual. Energy is neither created nor destroyed. It takes capital to change the system, society, or the bakery, in order to ensure DY/DL is +ve at every point of the curve and accommodate the additional baker. If this bottleneck is inevitable, then it is a different curve altogether, one where Y=F(K’,L+1) and not F(K,L+1), failing the ceteris paribus test. If it were easy everyone would do it. The successful firm therefore isn’t one that puts in the time and effort needed to change K to K’ such that DY/DL is always +ve, but instead the one that minimizes the change K to K’. At the radical end of this continuum is the firm that has figured out how to set this change to zero, ie the initial design of the system has K such that it is capable of absorbing additional units of L while modifying its orientation to maximize the production function F.

if d(Profit) = P*MPL — W, a firm reaches equilibrium where MPL = W/P. Every unit of labor after this point is unemployed. One way of unlocking some surplus is to offer a latter unit of labor, with lower MPL the opportunity of employment at lower W = MPL*P, a solution that unions will not suffer. The other way is to question the lowering of MPL at all. Do this at an individual level and you get life-long improvers, learners, and GOATs. Do this at a firm-level and you have market leaders. Do this at the level of the economy and you have just solved one of the fundamental problems of neoclassical market economics. Do this at the level of society and you’ve solved politics.

The history of human civilization is really the history of inventing systems to unlock non-zero sum outcomes of human cooperation. Necessity pulled us together in tribes, cities, and nation states. The moral arc of civilization bends not towards justice but towards marginal returns and the costs of solitude. The classical free market didn’t shy away from our natural state of self-regard but instead harnessed and unleashed it in order to further the gains from cooperation. Until the free market came along as the organizing principle under which groups of humans could interact profitably, the only thing keeping us together was our commonality of essence and objective. We were attracted therefore to people who were like us, and who wanted the same things. Individual differences are to be feared, mistrusted, and swept under the rug when present within a group that has agreed to work together. The free market instead accentuates individual differences as the fuel on which a healthy society can function and outperform competing societies that repress individuality. A neoclassical economy is successful precisely because the baker is good at X, the wheat-farmer at Y, and the toaster maker at Z. Unfortunately, this means we’ve reduced humans to instruments, analyzed solely through the lens of their talents, what they can bring to our civilizational table. In a tribe of 50 hunter gatherers, this is fine, in a nation of 1.5 billion people, it’s less fine. Somewhere between 50 and 1.5 billion, neoclassical economics breaks down due to the diminishing returns of labor, of life itself. A true Marxist utopian ideal therefore isn’t one that aims for egalitarianism, where the baker = farmer = toaster maker, where every single person’s production function F is exactly the same, and MPL = a constant C such that DY/DL = 0. Instead, a Marxist Utopia is designed to ensure D2Y/DL2 > 0 for all L.

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The Pen Of Darkness

A novel insightful exercise to determine the pragmatic difference in intellectual payoff between a novel insight and an obvious fact mistaken for novel insight.