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An analytical model of Disequilibrium and decentralized productive Exploration

Nazaria Solferino

Abstract

This paper studies the economic role of persistent dispersion in allocations across agents. We develop a tractable model in which firms allocate resources under imperfect information and behavioral updating, generating sustained heterogeneity in beliefs and actions. While dispersion induces static misallocation, it also fosters decentralized experimentation, allowing the economy to explore a broader set of productive opportunities. We show that the economy converges to a stationary equilibrium with strictly positive dispersion and that, under plausible conditions, such disequilibrium can dominate the perfectly coordinated benchmark. The model provides a novel interpretation of observed dispersion in productivity and returns as reflecting both inefficiency and productive exploration. It also yields testable predictions linking dispersion to growth and innovation dynamics.

An analytical model of Disequilibrium and decentralized productive Exploration

Abstract

This paper studies the economic role of persistent dispersion in allocations across agents. We develop a tractable model in which firms allocate resources under imperfect information and behavioral updating, generating sustained heterogeneity in beliefs and actions. While dispersion induces static misallocation, it also fosters decentralized experimentation, allowing the economy to explore a broader set of productive opportunities. We show that the economy converges to a stationary equilibrium with strictly positive dispersion and that, under plausible conditions, such disequilibrium can dominate the perfectly coordinated benchmark. The model provides a novel interpretation of observed dispersion in productivity and returns as reflecting both inefficiency and productive exploration. It also yields testable predictions linking dispersion to growth and innovation dynamics.

Paper Structure

This paper contains 5 sections, 3 theorems, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Baseline Model: Disequilibrium, Misallocation, and Productive Dispersion
  3. Disequilibrium and Welfare Comparison
  4. Discussion and Policy Implications
  5. Conclusion

Key Result

Proposition 1

Suppose $|\rho|<1$ and $\alpha \in (0,2)$. Then the stochastic process $(\theta_t, m_t, v_t)$ admits a unique invariant distribution. Moreover, $v_t$ converges deterministically to a unique fixed point $v^*$. $\blacktriangleleft$$\blacktriangleleft$

Figures (2)

  • Figure 1: Output and welfare dynamics under equilibrium and disequilibrium. Disequilibrium initially entails lower output and welfare but surpasses equilibrium in the long run due to decentralized experimentation.
  • Figure 2: Trade-off between exploration and misallocation. Aggregate output is maximized at an interior level of dispersion, illustrating that disequilibria can be beneficial.

Theorems & Definitions (6)

  • Proposition 1: Ergodicity
  • proof
  • Proposition 2: Productive Disequilibrium
  • proof
  • Proposition 3: Optimal Disequilibrium
  • proof