The Economics of AI as a Public Utility

Mathematical Models, Quantitative Analysis, and Supporting Data

A Technical Companion to “AI as a Public Utility: Why Americans Deserve Free AI Access”

Abstract

This technical paper provides the mathematical foundations, economic models, and quantitative analysis supporting the proposition that artificial intelligence should be treated as a public utility. Drawing on cooperative game theory, network economics, public goods theory, and productivity modeling, we present rigorous frameworks for understanding data valuation, the economics of AI infrastructure, and the societal benefits of universal access. Our analysis integrates empirical research from 2025, including studies of 64 large language models, productivity measurements across multiple economies, and infrastructure cost projections exceeding $5 trillion through 2030.

1. Mathematical Framework for Training Data Valuation

1.1 The Shapley Value Approach

The foundational mathematical framework for data valuation derives from cooperative game theory, specifically the Shapley Value introduced by Lloyd Shapley in 1953. The Shapley Value provides a unique solution satisfying fairness axioms for distributing collective gains among contributors. For AI training data, this framework has been adapted as Data Shapley by Ghorbani and Zou.

Definition (Shapley Value)
For a cooperative game with n players and utility function
v: 2ⁿ → ℝ,
the Shapley value φᵢ for player i is given by:

φᵢ(v) = Σ [ |S|! (n − |S| − 1)! / n! ] × [ v(S ∪ {i}) − v(S) ]

where the summation is over all subsets S of players not containing i.

Key Properties

Efficiency: All contributions sum to total utility
Symmetry: Equal contributors receive equal value
Null Player: Non-contributors receive zero
Additivity: Linear in utility functions

1.2 Data Shapley for Machine Learning

In machine learning contexts, the utility function v maps subsets of training data to model performance. Given a dataset
D = {z₁, z₂, …, zₙ}
and learning algorithm A, which produces model θₛ when trained on subset S ⊆ D, the utility is defined as:

v(S) = Performance(A(S), D_val)

The computational barrier is extreme: exact Shapley estimation requires 2ⁿ utility evaluations, rendering direct solutions intractable for modern-scale models.

1.3 The Kandpal–Raffel Labor Cost Model (2025)

Kandpal and Raffel introduced a labor-based method for estimating minimum dataset value by calculating the cost of recreating training data through human labor.

Model Specification

C_data = T × (words/token)⁻¹ × (words/hour)⁻¹ × hourly_wage

Conservative Assumptions

Minimum wage: $15/hour
Writing speed: 1,000 words/hour
Token-to-word ratio: 0.75
No expertise premiums
No quality constraints

Empirical Findings Across 64 LLMs (2016–2024)

Data costs exceed compute costs by 10× to 1,000×
8 of 10 major AI firms have data values exceeding 10% of total revenue
3 of 10 exhibit data valuations exceeding 100% of total revenue

Conclusion: Training data represents the dominant capital asset in modern AI systems.

2. Network Effects and Platform Economics

2.1 Metcalfe’s Law

Metcalfe’s Law states that network value scales with the square of participating users:

V(n) = k × n²

Empirical validation confirms this quadratic scaling for large network platforms.

2.2 Reed’s Law for Group-Forming Networks

For systems enabling group formation:

V(n) = 2ⁿ

This model captures the combinatorial explosion of collaborative AI communities and collective intelligence networks.

2.3 Conservative Bounding Models

Odlyzko and Briscoe proposed a more realistic lower bound:

V(n) = n × log(n)

For AI platforms:

n × log(n) ≤ V(n) ≤ n²

3. Public Goods Theory and Game-Theoretic Foundations

3.1 The Public Goods Game

Each of n players chooses contribution cᵢ ∈ [0, e] with payoff:

uᵢ = (e − cᵢ) + r × (Σⱼ cⱼ)/n

3.2 The Free-Rider Nash Equilibrium

If r < n, the unique Nash Equilibrium is:

cᵢ = 0 for all i

Since ∂uᵢ/∂cᵢ = −1 + r/n < 0, rational agents free-ride despite large collective gains.

3.3 Application to AI Infrastructure

Using U.S. investment and productivity estimates:

Annual AI economic value ≈ $3.5 trillion
Annual infrastructure investment ≈ $290 billion

Multiplier:

r ≈ $3.5T / $0.29T ≈ 12

This creates a textbook public goods failure: massive positive externalities with systematic private underinvestment.

4. Productivity Models and Economic Impact

4.1 Cobb–Douglas Production Function

Y = A · K^α · L^(1−α)
where α ≈ 0.36

4.2 Hulten’s Theorem

Δlog A = Σᵢ (pᵢYᵢ / GDP) · Δlog Aᵢ

Sector productivity gains propagate proportionally to GDP exposure.

4.3 Empirical Productivity Estimates (2024–2025)

Anthropic: TFP +1.1% annually, labor +1.8%, 10-year horizon
Penn Wharton: TFP +0.09–0.2% annually (2027–2035)
CEPR: TFP +0.25–0.6% annually
St. Louis Fed: Immediate +1.1% productivity, +33% per AI labor hour
McKinsey: Long-run labor +0.1–0.6% annually through 2040

TFP ≈ Labor Productivity × Labor Income Share (≈ 0.60–0.64)

5. Infrastructure Economics and Investment

5.1 Data Center Capital Expansion Scenarios

Accelerated Growth Scenario
Power capacity: 205 GW
Total capital outlay: $7.9 trillion
Annual spend: $1.58 trillion
Base Case Scenario
Power capacity: 125 GW
Total capital outlay: $5.2 trillion
Annual spend: $1.04 trillion
Constrained Growth
Power capacity: 78 GW
Total capital outlay: $3.7 trillion
Annual spend: $0.74 trillion

Global data center investment in 2024 was approximately $290 billion, implying a 4–6× capacity ramp.

5.2 Unit Economics of AI Data Centers

AI rack cost: $3.9 million
Traditional rack: $500,000
Power density: 40–250 kW vs. 10–15 kW
GPU cost: $10K–$40K per unit
Hyperscale AI facilities: $500M–$7B+

6. Public Utility Pricing Theory

6.1 Natural Monopoly Condition

AC(Q) < AC(Q₁) + AC(Q₂), where Q = Q₁ + Q₂

Frontier model training alone now exceeds $100M, creating structurally subadditive cost curves.

6.2 Two-Part Tariff Solution

Total Payment = F + pQ

Optimal public AI design:

p = 0 (zero marginal price)
Fixed costs covered via taxation
External returns recaptured via productivity tax growth

7. Quantifying the Digital and AI Divide

Gini Coefficient

G = ΣᵢΣⱼ|xᵢ − xⱼ| / (2n² μ)

2025 Global Access Inequality

2.6 billion people remain offline
Europe: 89% access — Africa: 40%
264 million fewer women online than men
Urban: 81% — Rural: 50%
High-income nations: 93% — Low-income: 27%
United States: 24 million lack broadband

Implication: Without public AI access, inequality compounds geometrically.

8. Cost–Benefit Framework for Public AI

Annual Benefits

U.S. share of global AI productivity gains: $0.78–$1.32 trillion

Annual Costs

Infrastructure: $300–$500B
Operations: $50–$100B
Total: $350–$600B

Benefit–Cost Ratio

BCR = $0.78–$1.32T ÷ $0.35–$0.6T
BCR = 1.3 to 3.8

This matches historic infrastructure successes such as the Interstate Highway System.

9. Conclusion

This analysis establishes the quantitative case for AI as a public utility:

Training data is 10–1,000× more valuable than compute
Network value scaling is at least n·log(n) and plausibly n²
Game theory predicts systematic private underinvestment
Expected TFP growth of 0.25–1.1% annually
Projected $5.2T base-case infrastructure investment
Strongly positive BCR of 1.3–3.8

Taken together, the mathematical and economic evidence strongly supports treating AI as public infrastructure essential to national productivity and civic participation.

About the Author

Brian Curry is a Kansas City–based AI Strategist, Marketing Economist, and Applied Researcher. He is the founder of Vector1 Research, an independent lab advancing marketing economics, causal inference, cognitive AI systems, and the economics of intelligent automation.

He has led data science and analytics initiatives across major enterprises including Koch Industries ($125B), Tractor Supply ($14B), Vail Resorts, Hallmark, Garmin, and AT&T. His work applies economic thinking and causal inference to connect marketing investment to outcomes, operational decisions to economic value, and AI adoption to competitive advantage.

Research contributions:

Papilon — Open-source platform for marketing analytics, causal inference, and simulation
Memory-Node Encapsulation (MNE) — Cognitive AI architecture for artificial episodic memory
The Autonomy Economy — Macroeconomic framework for AI-driven transformation
Daedalus — Platform for causal and economic analysis

Full profile: Brian Curry: Enterprise AI Strategist, Marketing Economist & Applied Researcher

Contact: brian at vector1.ai | Vector1 Research | LinkedIn

This article may be shared with attribution under Creative Commons Attribution 4.0 International (CC BY 4.0).

References

Anthropic (2025). Estimating AI Productivity Gains.
Ghorbani, A., & Zou, J. (2019). Data Shapley: Equitable Valuation of Data for ML. ICML.
Hulten, C. (1978). Growth Accounting with Intermediate Inputs. Review of Economic Studies.
Kandpal, N., & Raffel, C. (2025). The Most Expensive Part of an LLM Should Be Its Training Data. ICML.
McKinsey & Company (2023). The Economic Potential of Generative AI.
McKinsey & Company (2025). The Cost of Compute: A $7 Trillion Race to Scale Data Centers.
Metcalfe, R. (1980). Metcalfe’s Law.
Odlyzko, A., & Briscoe, B. (2006). Metcalfe’s Law Is Wrong. IEEE Spectrum.
Penn Wharton Budget Model (2025). Projected Impact of Generative AI on Productivity Growth.
Shapley, L. (1953). A Value for n-Person Games.
UNCTAD (2025). Technology and Innovation Report 2025.