Emergent CES and the Quadruple Role of Curvature

Abstract. The CES (Constant Elasticity of Substitution) production function is not merely a convenient functional form -- it is the unique aggregation function compatible with constant returns to scale and consistency across levels of aggregation. This article introduces the CES framework at an undergraduate level, presents three independent proofs of its emergence, and shows that a single curvature parameter K simultaneously controls four economic phenomena: superadditivity, correlation robustness, strategic independence, and network scaling.