Linearity, Geometry, and Substitution in Aggregate Production

Christopher Chambers and Alexis Akira Toda

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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.

Date: 2023-09, Revised 2026-08
New Economics Papers: this item is included in nep-eff
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