Followup to "Thank You, Old Man Jevons, for My Job"
CW: Robots, deadly to drastically oversimplified models presented in previous posts

So, I think it’s about time I crush your misplaced optimism and onto the reasons for doom and gloom and why everyone’s going to lose their jobs.

There’s really one big reason why the model of labor markets in my last post can break down: market segmentation.

I kinda lied when I said a 20% increase in productivity means a 20% increase in per-worker profit. The naive mistake that people make when thinking about automation as decreasing employment within an industry implicitly holds the quantity of goods being produced constant, such that a 20% increase in productivity will result in a 20% decrease in employment within a sector. Of course, that’s not true, or even close to true in most cases — when productivity increases, the quantity of goods produced increases as well, since it becomes more profitable to produce this good. But the analysis I put forward made a different assumption: That prices are constant. This is roughly correct for small changes in productivity: a 1% increase in workers’ efficiency is unlikely to have major effects on the market. But it breaks down completely when you talk about something like a 20% increase in productivity, which can significantly affect prices.

At the same time, though, it’s important to realize that the total price of all goods in the economy are mostly controlled by macroeconomic policy. If the Federal Reserve wants to keep prices constant, it can damn well keep prices constant. To quote Ben Bernanke, “We have the keys to the printing presses, and we are not afraid to use them.”

But what if the labor market isn’t actually a labor market? There’s obviously a big difference between someone with a doctorate and a high school dropout — they’re not going to be competing for the same jobs, even slightly. So we still have to consider the effects on prices to see how output for a particular market (The one receiving the productivity shock) will be affected. The Federal Reserve can keep the average price level constant, but it can’t keep the price of every single good constant — if productivity improvements are concentrated in a single part of the market (e.g. goods and not the service sector), then prices in that market are going to take a beating

So let’s make all of this a bit more rigorous. Let’s start a labor market that hires workers to produce widgets. We’ll also assume perfect competition in all markets, because as we all know there are always infinitely many firms buying and selling any good. (This message brought to you by the Heritage Foundation^TM.) Now let’s define a couple variables:

1. MRP: Marginal Revenue Product, the additional revenue from hiring an extra worker. As noted previously, this is also the demand for labor curve — an employer will hire a worker if and only if the marginal worker’s wages are less than or equal to the MRP, as this is when they make a profit.
2. MP: A leech on our taxes who sits around in Westminster botching Brexit all day.
3. MP (Also): Marginal Productivity, the derivative of output with respect to the number of workers. Yes, workers are infinitely divisible. Please don’t tell OSHA.¹
4. P: Is stored in the balls. Means price, as usual. Don’t ask me how you can store a number somewhere.

In that case MRP = P*MP, i.e. the amount of money from hiring an additional worker is equal to the number of widgets he’ll produce, times the price of those widgets. So we get:

So whether a productivity shock increases or decreases unemployment depends mostly on that elasticity-looking thing in the middle. If it’s less than -1 (i.e. Prices change greatly in response to productivity shocks), then the MRP (and thus the demand for Laborers) will increase, while if it’s greater than -1 (i.e. Prices change greatly in response to changes in productivity) the MRP will decrease.

The second big problem, then, is that we’re modeling this all as a change to the productivity of workers. Historically, this has been true: New technologies in automation can be considered as increase the productivity of a worker because there are few goods that require little or no human involvement to manufacture from start to finish. Even if there were a robot capable of performing a portion of the manufacturing process without any human intervention, this can be modeled by considering this a productivity increase to the people involved in all the other steps of selling the good (e.g. in quality assurance) so long as these jobs require similar levels of skill. Using the example of ATMs from the last post, even though ATMs were a near-perfect substitute for human , this just ended up moving people from one job (Making withdrawals/deposits) to another (Selling financial services). But what if you get something that can do anything better than a person, like a sufficiently good AI? Well, in that case, the model breaks down. Instead of modeling automation as a process that increases the marginal productivity of workers, we have to model it as one where labor and automation are two separate goods, serving as substitutes for each other, and improvements in automation technology drive up the marginal productivity of those instead. Robots and workers are in competition, and demand for workers will fall as the efficiency of these robots increases.

That’s when you get dystopian visions of haves and have-nots coming true. Or alternatively, robots and rob-nots.

I may have written this post to make that pun.

Notes:

1. If the fact that workers aren’t infinitely divisible actually bothers you, just replace workers with “Man-hours” and the analysis is identical. Anyone who mentions the words “Planck time” in the comments will be shot.

Please let me know if you’re interested in more microeconomics in the comments. I think we need more people who can think well in terms of quantitative models. The two best subjects for teaching this style of thinking for me were microeconomics and physics, and I’m extremely interested in hearing y'all's thoughts.