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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.18137 |
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Table of Contents:
- 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 $σ$. 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.