externalities scale superlinearly

I think this point is obvious enough that I’m certain it’s not original. No matter, since it’s important also: the % of value and disvalue that takes the form of externalities should grow over time as the economy develops, as the result of basic math.

Suppose a spherical cow economy with only one externality: spherical cows producing spherical methane, which leads to global warming. Over time, economic development leads to both human population and cows per human increasing, say each by 2% each year. Total cows (hence total methane) grows at 4% per year. (We’ll conveniently generously assume that animal welfare laws ensure these cows a neutral-to-them existence that is unaffected by global temperature.) Assume no critical points in global temperature and thus that the disvalue of ppm methane in atmosphere per person scales linearly. Then - since every person on earth “enjoys” the disvalue of the methane - methane disvalue grows at 6% a year.

If each cow provides an internalized value of 1 to its owner, and -1/100,000 value to everyone else via methane output, and we have a starting population of a thousand people with one cow each in year 1, then by year 100 total people and cows per person have the multiplied by about 7 each, total cows by about 50 each, and total methane externalities by over 300 - and in turn from a 1% to an about 7% drag on the economy. By the year 200, it represents a drag of about half world GDP, GDP per capita reaches its total (at around 25x original welfare), and for the next decade and a half we have a “repugnant conclusion”-style world where GDP per capita falls but is compensated by a growing population. Total GDP starts falling around year 214, and both total and per capita GDP become negative in the 230s - a life worse than death.

(We’ve also created a real, non-spherical hell this way - see below - but here my point is more abstract.)

We've Created Hell. It's Called Factory Farming.

Obviously, not all externalities are global in scope. If you’re blasting music from your boombox, that’s providing an externality (positive or negative, depending on how well your tastes align with those of your neighbors) to everyone within a certain radius, not all over the world. But anything with a radius should also scale with population overall, because populations get more dense as their absolute number grows.

In any particular case we should expect all sorts of particular, ad hoc effects to dominate. Random technical shocks will shift us this way and that. But ceteris paribus, you should expect the externalized effects to grow over time.

Concrete examples include:

• x-risks associated with cutting-edge technical developments

• endogenous growth theory and positive learning spillovers of new production

• the contribution of factory farming to pandemics

• the effect of reneging on deals on trust

• why big cities are both left-wing, poorly governed, and richer - externality effects are mostly highly salient there

This is a highly abstract point, while any particular policy response will depend plenty on the ad hoc concerns noted above. However, I think it should affect our broader intuitions in the following ways:

• If we are constructing a human-scale toy model (“imagine a single farm with a spherical cow…”) and then extrapolating out by multiplying its size, we may underestimate how the (otherwise small enough to ignore) externalities scale up with it as we imagine a full world

• Intuitions and models developed in a lower-density world - such as that which produced all our traditions of economics - likely underestimate the significance of externalities

• If we expect (or even just hope!) for population growth to continue, then we should expect the higher-population future to be one that is further externality-heavy than today