Nonlinear Domar aggregation over transforming production networks

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.