AI as Coordination-Compressing Capital: Task Reallocation, Organizational Redesign, and the Regime Fork

TL;DR

Task-based AI models typically fix organizational structure, but this paper introduces coordination compression via agent capital $K_A$ to endogenize organizational design. The framework yields five propositions: coordination compression increases output, expands spans, reduces manager demand, and raises manager–worker wage dispersion under elite complementarity while also expanding the task frontier endogenously when $\delta>0$. A regime fork emerges based on $\beta$ (elite complementarity) and $\delta$ (task creation elasticity): broad-access infrastructure realises broad productivity gains with wage compression, whereas elite-access coordination yields superstar concentration and sharper inequality growth. Numerical simulations in a newsroom setting show that coordination compression expands employment and lowers unemployment across regimes, but the pace of inequality reduction hinges on who controls coordination gains ($\beta$), with economy-wide inequality falling in all cases albeit at regime-dependent speeds.

Abstract

Task-based models of AI and labor hold organizational structure fixed, analyzing how technology shifts task assignments within a given firm architecture. Yet emerging evidence shows firms flattening hierarchies in response to AI adoption -- a phenomenon these models cannot generate. We extend the task-based framework by introducing agent capital (K_A): AI systems that reduce coordination costs within organizations, expanding managerial spans of control and enabling endogenous task creation. We derive five propositions characterizing how coordination compression affects output, hierarchy, manager demand, wage dispersion, and the task frontier. The model generates a regime fork: depending on whether agent capital complements all workers broadly (general infrastructure) or high-skill managers disproportionately (elite complementarity), the same technology produces either broad-based productivity gains or superstar concentration, with sharply divergent distributional consequences. Numerical simulations with heterogeneous managers and workers across a 2x2 parameter space (elite complementarity x endogenous task creation) confirm sharp regime divergence: in settings where coordination compression substantially expands employment, economy-wide inequality falls in all regimes, but the rate of reduction is regime-dependent and the manager-worker wage gap widens universally. The distributional impact of AI hinges not on the technology itself but on the elasticity of organizational structure -- and on who controls that elasticity.

Figures (5)

• Figure 1: Coordination cost and span of control as functions of $K_A$ for varying $\gamma$. The left panel shows $c(K_A)$ falling hyperbolically; the right panel shows span expanding linearly. Higher $\gamma$ produces faster compression and wider spans.
• Figure 2: Regime heatmap at $K_A = 5$ showing manager Gini (left) and output (right) across the $(\beta, \delta)$ plane. The inequality surface rises primarily along the $\beta$ axis; the output surface rises along both axes.
• Figure 3: Full-economy Gini (solid) vs. manager-only Gini (dashed) across the four regimes. The gap between the lines reveals the between-layer inequality that manager-only metrics miss. The regime fork persists at the economy level: low-$\beta$ regimes show faster inequality reduction as $K_A$ rises.
• Figure 4: Wage densities for employed workers (blue) and managers (red) at four levels of $K_A$ (0, 3, 7, 10), comparing Rising Tide (top row) and Winner Takes All (bottom row). The progressive separation of manager and worker distributions visualizes the regime fork in distributional shape.
• Figure 5: Six-panel dashboard showing output index, economy Gini, manager Gini, manager--worker wage gap, top-10% earnings share, and unemployment rate across all four regimes under PAM. Lines are distinguished by color, linetype (solid vs. dashed), and point markers at integer $K_A$ values. Each metric tells a consistent story; taken together, they confirm that the regime fork is the paper's central structural finding.

Theorems & Definitions (10)

• Proposition 1: Output Effect
• proof
• Proposition 2: Span Expansion
• proof
• Proposition 3: Manager Demand
• proof
• Proposition 4: Wage Dispersion
• proof
• Proposition 5: Task Frontier Expansion
• proof