"widely-used exposure indices, which aggregate task-level automation risk using linear formulas, will overstate displacement when tasks are complements" [linear formulas]
"automation decisions are discrete and can require bundled adoption even when automation quality improves smoothly" [bundled adoption]
"labour income can rise under partial automation because automation scales the value of remaining bottleneck tasks" [remaining bottleneck tasks]
The article argues that prospective AI impact studies (Frey & Osborne 2017, Webb 2020, Felten et al. 2021, Eloundou et al. 2024) all use linear summation formulas to aggregate task-level exposure scores, but this approach treats jobs as additive bundles rather than systems where output is multiplicative in task qualities. When a bottleneck task remains, automating other tasks concentrates worker effort on the bottleneck, raising its quality and value. This structural insight generalizes beyond the specific occupations studied: any job with quality-complementary tasks will see its true automation risk understated by linear indices.
Proposition 5 demonstrates that there exist parameter ranges where automating a single task reduces surplus (S(1) < S(0)) yet automating two tasks increases it (S(2) > S(0)). This occurs because automating one task raises output Y(k), which dilutes the proportional cost burden of the next automation (the 'cost wedge'), while simultaneously raising the quality threshold for the next task (the 'focus barrier'). The implication is that automation platforms or integrated systems that automate multiple steps simultaneously may be privately optimal even when piecemeal adoption is not, a pattern likely to recur across industries as AI systems mature.
Proposition 8 formalizes this: the bargained wage bill W(ω) is weakly increasing in automation quality ω when the worker remains necessary. The intuition is that automating some tasks concentrates the worker's fixed time endowment on fewer tasks, raising their quality from a(h/n) to a(h/m) where m < n. Since output is multiplicative, this raises the total surplus Y(k) - rk, and the worker captures a share ε of that increment. The ATM/bank teller case exemplifies this: ATMs automated routine cash handling, but tellers shifted to relationship banking, raising their value. This pattern likely generalizes to professional services (law, radiology, consulting) where automation of routine components frees time for higher-value advisory work.