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Linearity, Geometry, and Substitution in Aggregate Production

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  • Christopher P. Chambers
  • Alexis Akira Toda

Abstract

We study aggregate production under efficient input allocation across heterogeneous production units. With constant returns to scale, every profit-maximizing allocation generates a cone on which the aggregate production function is linear, whose dimension is the rank of active units' input vectors. Under concavity, the maximal cone at a supporting price is generated by component-technology contact sets. Higher-dimensional cones exist exactly when the pointwise maximum of strictly concave component technologies is nonconcave on the unit simplex. As an application, coexistence of land-using and land-free activities implies infinite aggregate elasticity of substitution at sufficiently high nonland-to-land ratios.

Suggested Citation

  • Christopher P. Chambers & Alexis Akira Toda, 2023. "Linearity, Geometry, and Substitution in Aggregate Production," Papers 2309.15760, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:2309.15760
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    File URL: https://arxiv.org/pdf/2309.15760
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