Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Turing Valley: How AI Capabilities Shape Labor Income

Enrique Ide, Eduard Talamàs

TL;DR

This paper analyzes how AI capabilities across two knowledge dimensions influence labor income in a multidimensional knowledge economy, emphasizing the role of human–AI communication regimes. It extends the canonical knowledge-economy model to a two-dimensional setting and derives equilibrium wages under additive and superadditive communication, showing that progress in the strong AI dimension consistently raises labor income, while progress in the weak dimension has regime-dependent effects. The authors establish the Turing Valley as the wage map over AI knowledge and demonstrate that, depending on human knowledge levels, the optimal AI profile may be uniformly high (AGI-like) under additive communication or jagged (high in one dimension, low in the other) under superadditive communication. These results highlight the critical importance of empirical assessments of how humans and AI integrate partial solutions, with direct implications for labor markets and policy during the transition toward AGI.

Abstract

Current AI systems are better than humans in some knowledge dimensions but weaker in others. Guided by the long-standing vision of machine intelligence inspired by the Turing Test, AI developers increasingly seek to eliminate this "jagged" nature by pursuing Artificial General Intelligence (AGI) that surpasses human knowledge across domains. This pursuit has sparked an important debate, with leading economists arguing that AGI risks eroding the value of human capital. We contribute to this debate by showing how AI capabilities in different dimensions shape labor income in a multidimensional knowledge economy. AI improvements in dimensions where it is stronger than humans always increase labor income, but the effects of AI progress in dimensions where it is weaker than humans depend on the nature of human-AI communication. When communication allows the integration of partial solutions, improvements in AI's weak dimensions reduce the marginal product of labor, and labor income is maximized by a deliberately jagged form of AI. In contrast, when communication is limited to sharing full solutions, improvements in AI's weak dimensions can raise the marginal product of labor, and labor income can be maximized when AI achieves high performance across all dimensions. These results point to the importance of empirically assessing the additivity properties of human-AI communication for understanding the labor-market consequences of progress toward AGI.

The Turing Valley: How AI Capabilities Shape Labor Income

TL;DR

This paper analyzes how AI capabilities across two knowledge dimensions influence labor income in a multidimensional knowledge economy, emphasizing the role of human–AI communication regimes. It extends the canonical knowledge-economy model to a two-dimensional setting and derives equilibrium wages under additive and superadditive communication, showing that progress in the strong AI dimension consistently raises labor income, while progress in the weak dimension has regime-dependent effects. The authors establish the Turing Valley as the wage map over AI knowledge and demonstrate that, depending on human knowledge levels, the optimal AI profile may be uniformly high (AGI-like) under additive communication or jagged (high in one dimension, low in the other) under superadditive communication. These results highlight the critical importance of empirical assessments of how humans and AI integrate partial solutions, with direct implications for labor markets and policy during the transition toward AGI.

Abstract

Current AI systems are better than humans in some knowledge dimensions but weaker in others. Guided by the long-standing vision of machine intelligence inspired by the Turing Test, AI developers increasingly seek to eliminate this "jagged" nature by pursuing Artificial General Intelligence (AGI) that surpasses human knowledge across domains. This pursuit has sparked an important debate, with leading economists arguing that AGI risks eroding the value of human capital. We contribute to this debate by showing how AI capabilities in different dimensions shape labor income in a multidimensional knowledge economy. AI improvements in dimensions where it is stronger than humans always increase labor income, but the effects of AI progress in dimensions where it is weaker than humans depend on the nature of human-AI communication. When communication allows the integration of partial solutions, improvements in AI's weak dimensions reduce the marginal product of labor, and labor income is maximized by a deliberately jagged form of AI. In contrast, when communication is limited to sharing full solutions, improvements in AI's weak dimensions can raise the marginal product of labor, and labor income can be maximized when AI achieves high performance across all dimensions. These results point to the importance of empirically assessing the additivity properties of human-AI communication for understanding the labor-market consequences of progress toward AGI.
Paper Structure (18 sections, 3 theorems, 22 equations, 4 figures)

This paper contains 18 sections, 3 theorems, 22 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Model
  3. The Baseline Setting
  4. Discussion of the Model
  5. Equilibrium Characterization
  6. Single-layer (non-automated) firms.
  7. Bottom-automated firms ($b$).
  8. Top-automated firms ($t$).
  9. The Turing Valley
  10. Jagged AI
  11. How AI Capabilities Shape Labor Income
  12. The Labor-Income Maximizing AI
  13. Conclusion
  14. Proofs Omitted From Section \ref{['sec:eq']}
  15. Proof of Proposition \ref{['prop:1']}
  16. ...and 3 more sections

Key Result

Proposition III.1

Fix $\tau\in\{S,A\}$. The competitive equilibrium maximizes total output. The equilibrium rental rate is $r^*=F(\boldsymbol{m})$ and the equilibrium wage is Moreover, in equilibrium, all humans are allocated to the organizational form with the highest marginal product of labor.

Figures (4)

  • Figure 1: Two Polar Forms of Human–AI Communication Notes. Problems are distributed over the two-dimensional space shown in the figure. Region $B$ is the set of problems that both humans and machines can solve independently; $H$ is the set of problems that only humans can solve independently. $M$ is the set of problems that only machines can solve independently $I$ denotes problems that require the integration of human and machine knowledge. Under additive communication, human-AI hierarchies can solve the problems in $B\cup H\cup M$. Under superadditive communication, human-AI hierarchies can solve the problems in $B\cup H\cup M\cup I$.
  • Figure 2: The Effects of Machine Improvements in Different Dimensions
  • Figure 3: The Four Possible Firm Configurations
  • Figure 4: Equilibrium Regions: Additive vs. Superadditive Communication Notes. Parameter values: $h_1=1/2$, $h_2=3/5$, and $c=1/2$, assuming $F(\boldsymbol{x})=x_1 x_2$.

Theorems & Definitions (6)

  • Proposition III.1: Equilibrium characterization
  • proof
  • Proposition IV.1: Local comparative statics in the Turing Valley
  • proof
  • Proposition IV.2: Global Optimality: Jagged AI vs. AGI
  • proof