Economics of Human and AI Collaboration: When is Partial Automation More Attractive than Full Automation?

Wensu Li; Atin Aboutorabi; Harry Lyu; Kaizhi Qian; Martin Fleming; Brian C. Goehring; Neil Thompson

econ.GNMar 31, 2026

Economics of Human and AI Collaboration: When is Partial Automation More Attractive than Full Automation?

Authors: Wensu Li, Atin Aboutorabi, Harry Lyu, Kaizhi Qian, Martin Fleming, Brian C. Goehring, Neil Thompson

Organizations: Massachusetts Institute of Technology · École Polytechnique Fédérale de Lausanne · IBM Research · IBM’s Institute for Business Value

Abstract

This paper develops a unified framework for evaluating the optimal degree of task automation. Moving beyond binary automate-or-not assessments, we model automation intensity as a continuous choice in which firms minimize costs by selecting an AI accuracy level, from no automation through partial human-AI collaboration to full automation. On the supply side, we estimate an AI production function via scaling-law experiments linking performance to data, compute, and model size. Because AI systems exhibit predictable but diminishing returns to these inputs, the cost of higher accuracy is convex: good performance may be inexpensive, but near-perfect accuracy is disproportionately costly. Full automation is therefore often not cost-minimizing; partial automation, where firms retain human workers for residual tasks, frequently emerges as the equilibrium. On the demand side, we introduce an entropy-based measure of task complexity that maps model accuracy into a labor substitution ratio, quantifying human labor displacement at each accuracy level. We calibrate the framework with O*NET task data, a survey of 3,778 domain experts, and GPT-4o-derived task decompositions, implementing it in computer vision. Task complexity shapes substitution: low-complexity tasks see high substitution, while high-complexity tasks favor limited partial automation. Scale of deployment is a key determinant: AI-as-a-Service and AI agents spread fixed costs across users, sharply expanding economically viable tasks. At the firm level, cost-effective automation captures approximately 11% of computer-vision-exposed labor compensation; under economy-wide deployment, this share rises sharply. Since other AI systems exhibit similar scaling-law economics, our mechanisms extend beyond computer vision, reinforcing that partial automation is often the economically rational long-run outcome, not merely a transitional phase.

Figures & tables

Figure 1: Breakdown of occupation compensation by task-level automation type: different cases of partial equilibrium, ranked from most to least benefit from AI automation.

Figure 2: Quantifying Human-AI Work Allocation via Entropy and Cross-Entropy Loss

Figure 3: Highlighted empirical evidence linking task entropy to processing time across different time scales.

Parameter	Estimate	Std. Error
$A_{0}$	-1.448	0.046
$A_{1}$	0.752	0.050
$a_{0}$	-0.034	0.005
$a_{1}$	0.077	0.003
$B_{0}$	1.474	0.080
$B_{1}$	1.049	0.000

Table 1: Estimated Parameters for the Scaling Law

Number of Classes	$\alpha$	a	$\beta$	b	$\sigma$	c	G	k
2	0.40	0.02	9.03	0.40	71.35	0.59	-0.30	-0.10
5	0.79	0.09	23.62	0.42	94.61	0.55	-0.30	-0.24
10	1.33	0.14	48.87	0.43	117.13	0.52	-0.30	-0.35
50	4.46	0.27	264.34	0.46	192.26	0.46	-0.30	-0.59
100	7.52	0.32	546.91	0.48	238.01	0.43	-0.30	-0.69
500	25.24	0.44	2958.46	0.51	390.69	0.36	-0.30	-0.93

Table 2: Scaling Law Parameters under Varying Number of Classes (n)

Scenario	Performance	Data	Training Steps	Model Size	Total
	( $r$ )	( $\epsilon_{D}$ )	( $\epsilon_{T}$ )	( $\epsilon_{M}$ )	Elasticity
2-Class Classification Task
Small Scale (I)	0.804	0.010	0.046	0.046	0.102
Medium Scale (II)	0.911	0.009	0.021	0.007	0.037
500-Class Classification Task
Small Scale (I)	0.351	0.023	0.544	0.283	0.849

Table 3: Performance Elasticity

Number of classes	Elasticity of substitution
Number of classes	$\sigma_{DT}$	$\sigma_{DM}$	$\sigma_{TM}$
2	0.982	0.982	0.716
5	0.918	0.918	0.706
10	0.875	0.875	0.698
50	0.790	0.790	0.685
100	0.758	0.758	0.694

Table 4: Pairwise elasticities of substitution by task complexity

Figure 4: Pairwise Isoquant Contours Illustrating Substitutability among Data, Training Steps, and Model Size across Task Complexity (2-Class vs. 500-Class Classification Tasks)

Figure 5: Composition of Full and Partial Automation of Vision-Task Labor Compensation Across Deployment Scales

Figure 6: Fraction of Computer Vision Task Compensation Economically Attractive to Automate.

Figure 7: Fraction of the U.S. businesses (by business counts) over different deployment scales.

Figure 8: Counts of deployed computer vision models at industry group (4d) deployment scale by partial automation rates.

Figure 9: Top 20 Automation Rates across Occupations at Industry Group (4d) Deployment Scale. See Appendix Figure J.1 for all occupations.

Occupation / Task / DWA	Task Automation	Full	Partial	Time Proportion	#Task	#Class
Transportation Security Screeners Task: Inspect carry-on items using x-ray equipment to determine whether items contain objects that warrant further investigation. DWA: Inspect cargo to identify potential hazards.	2.80%	2.72%	0.08%	2.81%	2	10
Transportation Security Screeners Task: Inspect checked baggage for signs of tampering. DWA: Inspect cargo to identify potential hazards.	3.24%	3.24%	0.00%	3.24%	2	7
Transportation Security Screeners Task: Locate suspicious bags pictured in printouts sent from remote monitoring areas, and set these bags aside for inspection. DWA: Locate suspicious objects or vehicles.	4.09%	4.09%	0.00%	4.09%	2	3
Transportation Security Screeners Task: Monitor passenger flow through screening checkpoints to ensure order and efficiency. DWA: Monitor access or flow of people to prevent problems.	3.05%	3.05%	0.00%	3.05%	2	3
Transportation Security Screeners Task: Record information about any baggage that sets off alarms in monitoring equipment. DWA: Record information about suspicious objects.	2.79%	2.71%	0.08%	2.79%	13	3
Transportation Security Screeners Task: Send checked baggage through automated screening machines, and set bags aside for searching or rescreening as indicated by equipment. DWA: Inspect cargo to identify potential hazards.	3.08%	2.99%	0.09%	3.09%	3	7

Table 5: Task-Level Automation Profiles

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Value	Description	Source
$\kappa_{\text{init}}$	1000	Number of initial fine-tuning rounds for algorithmic development	Kadra et al. (2023) , Wistuba et al. (2022) , Zimmer et al. (2021)
$\kappa_{\text{recur}}$	6	Retraining frequency per year	Thompson et al. (2024)
$d_{\text{GPU}}$	0.22	GPU-specific annual price discount rate	Hobbhahn and Besiroglu (2022)
$d$	0.05	Discount rate applied across the economy	Sullivan (2023)
$L$	5	System operational lifespan in years	Assets (2003)
$p_{\text{data}}$	dynamic	Cost of collecting and labeling one datum	Thompson et al. (2024) , Singh et al. (2024) , Russakovsky et al. (2015) , Lin et al. (2015)

Appendix

Table B.1: Cost Function Parameters

Coeff.	Expression	Value (USD)
$c_{F}$	$\displaystyle C_{\text{impl}}+\frac{1-\left(1/(1+d)\right)^{L}}{1-1/(1+d)}\,C_{\text{maint}}$	$3{,}486{,}090$
$c_{D}$	$\displaystyle m\left[1+\kappa_{\text{recur}}\frac{1-\left(1/(1+d)\right)^{L}}{1-1/(1+d)}\right]p_{\text{data}}$	$6.19$
$c_{T}$	$\displaystyle 6\,m\left[\kappa_{\text{init}}+\kappa_{\text{recur}}\frac{1-\left(\frac{1}{(1+d)(1+d_{\text{GPU}})}\right)^{L}}{1-\frac{1}{(1+d)(1+d_{\text{GPU}})}}\right]\frac{p_{\text{GPU}}\,Z_{\text{input}}}{r_{\text{FLOP}}\,U_{\text{GPU}}}$	$3.83\times 10^{-6}$
$c_{I}$	$\displaystyle m\left[\frac{1-\left(\frac{1}{(1+d)(1+d_{\text{GPU}})}\right)^{L}}{1-\frac{1}{(1+d)(1+d_{\text{GPU}})}}\right]\frac{p_{\text{GPU}}}{U_{\text{GPU}}}\frac{40\times 50\,\delta_{i}N_{i}}{\tau/\tau_{\mathrm{GPU}}}$	$1.29\times 10^{-8}$

Appendix

Table B.2: Input prices under default parameter values (2024 USD).

	$\beta_{0}$	$\beta_{1}$	$\beta_{2}$	$\beta_{3}$	$\gamma_{1}$	$\gamma_{2}$	$\delta_{1}$	$\delta_{2}$	$\delta_{3}$	$R^{2}_{\mathrm{fitted}}$
Coefficient	2.86	14.22	-27.10	10.48	11.99	-1.82	-0.70	0.61	-0.62	0.98
Std. Error	0.06	0.82	1.74	0.96	0.52	0.29	0.01	0.01	0.05

Appendix

Table E.1: Fitted Coefficients for Mapping Accuracy to Cross-Entropy Loss.

Scenario	Performance	Data	Training Steps	Model Size	Total
	( $r$ )	( $\epsilon_{D}$ )	( $\epsilon_{S}$ )	( $\epsilon_{M}$ )	Elasticity
2-Class Classification Task
Small Scale (I)	0.804	0.010	0.046	0.046	0.102
Medium Scale (II)	0.911	0.009	0.021	0.007	0.037
5-Class Classification Task
Small Scale (I)	0.866	0.016	0.035	0.032	0.083

Appendix

Table I.1: Performance Elasticity Analysis Results

Figure J.1: Automation rates across occupations at industry group (4d) deployment scale.

Explore similar work

The Human-AI Substitution Principle: When will you be replaced by AI in your organization?
Jul 22, 2026Bonny Banerjee, Shreya SinghHuman-AI Collaboration AI and Labor
Independent Scholar and Consultant, USA · Chennai Mathematical Institute, Chennai, Tamil Nadu 603103, India
Global Automation Atlas
May 16, 2026Prashant Garg, Tommaso Crosta, Jasmin BaierAI and Labor
Department of Economics and Public Policy, Imperial College London, London, United Kingdom · Department of Economics, Bocconi University, Milan, Italy · Blavatnik School of Government, University of Oxford, Oxford, United Kingdom
Teaming Up with AI: Coordination and Cooperation
Jul 3, 2026Nicole Immorlica, Inbal Talgam-CohenHuman-AI Collaboration AI and Labor
Yale University · Microsoft Research · Tel Aviv University

Jul 22, 2026J/K move · Enter open · S save

The Human-AI Substitution Principle: When will you be replaced by AI in your organization?

Bonny Banerjee, Shreya Singh

Independent Scholar and Consultant, USA · Chennai Mathematical Institute, Chennai, Tamil Nadu 603103, India

Human-AI Collaboration AI and Labor

Open paper AskPDF arXiv

Artificial Intelligence (AI) is rapidly transforming organizations, raising a fundamental organizational and economic question: when will a human employee be replaced by AI? We present an analytical model for studying Human--AI Task Allocation (HAT) in hierarchical organizations. A central feature of the HAT model is that it formally encodes the economic asymmetry between human skill acquisition and AI capability scaling. The HAT model allows us to derive how risk-adjusted costs, skills, organizational depth, deployment scale, strategic adaptation, and risk jointly determine when, where, why, and under what structural conditions human--AI replacement occurs. A key result is the Human--AI Substitution Principle, which provides a precise condition --- grounded in the formal asymmetry assumption --- under which AI replaces human labor. Building on this result, we show that AI adoption can produce abrupt workforce transitions, hybrid human--AI organizations, including cases where risk heterogeneity sustains human and AI roles without requiring a minimum-human-fraction constraint, and flatter managerial hierarchies with wider spans of control. The HAT model identifies structural conditions under which middle-management roles exhibit elevated vulnerability to automation, and shows that the vulnerability of highly skilled workers depends on a skill threshold shaped by organizational depth, baseline costs, and risk differentials. More broadly, the paper connects automation economics, organizational design, AI governance, and workforce planning into a unified theory of AI-driven organizational transformation.

Abstract

Explore similar work

The Human-AI Substitution Principle: When will you be replaced by AI in your organization?

Global Automation Atlas

Teaming Up with AI: Coordination and Cooperation