Epistemic status: moderate confidence about internal validity, low about external validity. I have a background in Economics and think the key argument that automation does not necessarily grow the economy holds. However, more realistic models would need to consider numerous additional factors.

TL;DR

The profit motive can drive firm owners to automate even if it leads to a decline in total output. Conceptually simple solutions, such as transfers proportional to the new output, can address this problem.

Introduction

A common assumption suggests that automation, despite causing layoffs, increases aggregate output. This idea often stems from counterarguments to the Lump of Labor fallacy, which posit that displaced workers may find new, better jobs. However, this argument breaks down under full automation.

The Profit Motive in Automation

Consider a simplified closed economy where income and output are divided between firm owners and employees. Let $w$ represent the labour share of income, which ranges between 50% and 70% in most economies. Firm owners will be motivated to automate if the following inequality holds:

$$q^{\prime }>q\times (1-w)$$

Here, $q^{\prime }$ and $q$  are the new and old levels of output, respectively. Given the above numbers, there's a profit-driven motivation to automate even with a 50% to 70% drop in aggregate output. Essentially, firm owners aim to secure a slightly larger share of a significantly smaller economic pie.

Edit: An Example – Automated Taxis

Imagine a single taxi firm where drivers, also employees, earn and spend on the service. When automation becomes viable, firm owners will decide to go ahead if it increases the number and/or the quality of rides they  use, i.e. if the condition $q^{\prime }>q\times (1-w)$ is met. Upon automating, drivers lose their income and, consequently, access to the service. 

Policy Solutions: Proportional Transfers

One remedy would involve post-automation transfers to the former employees. Let $t$ represent the proportion of these transfers relative to the whole economy. Then, firm owners will automate if and only if:

$$q^{\prime }\times (1-t)>q\times (1-w)$$ 

Specifically, setting $t=w$ ensures that automation occurs only when it results in a Pareto improvement, making someone better off without making anyone else worse off.

Conclusion

The key takeaways are:

• The profit motive can drive firm owners to automate even if it leads to a decline in total output.
• Conceptually simple solutions, such as transfers proportional to the new output, can address this problem.

Acknowledgements: Thanks to my friend Krišjānis whose feedback helped me clarify the argument. Also, I used GPT-4 to improve the clarity of the writing and some formatting aspects, and Bing Image Creator/DALLE-3 for the preview image.