Nonlinear Domar aggregation over transforming production networks

TL;DR

This paper analyzes how nonlinear production networks respond to productivity shocks, revealing the role of substitution elasticity in network stability, singularities, and optimal policy strategies.

Contribution

It introduces a novel framework mapping nonlinear price manifolds into a linear transcendent space, identifying network singularities and linking elasticity to optimal industrial policy.

Findings

Identification of network singularities and thresholds

Elasticity determines the nature of productivity shock interactions

Policy implications for sector concentration versus diversification

Abstract

An economy-wide production network, manifested through monetary input-output coefficients, inherently destabilizes during the general equilibrium propagation of sectoral productivity shocks when substitution elasticities are non-neutral. This study explores the global properties of such networks by mapping the non-linear price manifold into a linearized \textit{transcendent space}. Within this framework, we identify the emergence of network \textit{singularities}, identifying the metabolic thresholds where productivity declines lead to supply-chain paralysis or efficiency gains render primary factors redundant. Furthermore, we demonstrate that the interaction between productivity shocks -- the sign of \textit{synergism} -- is uniquely determined by the substitution elasticity $\sigma$. Our findings transform industrial policy into an \textit{inverse problem} of network topology: we provide a rigorous justification for why an inelastic network necessitates selective concentration on bottleneck sectors, whereas an elastic network favors a diversified investment strategy.