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<p>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 nonlinear price manifold into a linearized <i>transcendent space</i>. Within this framework, we identify the emergence of network <i>singularities</i>, 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 <i>synergism</i> –is uniquely determined by the substitution elasticity <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>. Our findings transform industrial policy into an <i>inverse problem</i> 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.</p>

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Nonlinear Domar aggregation over transforming production networks

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月27日

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  • Satoshi Nakano,
  • Kazuhiko Nishimura

摘要

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 nonlinear price manifold into a linearized transcendent space. Within this framework, we identify the emergence of network 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 synergism –is uniquely determined by the substitution elasticity \(\sigma \) σ . Our findings transform industrial policy into an 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.