Uplift is insensitive to σ, assuming ~8× code output

Homogeneous code model · CES production function

Diagram of how coding versus non-coding time and the coding speedup combine to produce the code-output multiplier.
Chart of researcher uplift U versus the elasticity of substitution sigma.
U = 2.83×
← Complements Substitutes →

When σ changes, two effects push U in opposite directions and largely cancel. If σ < 1 (complements), researchers shift time away from coding, so the per-hour speedup gn must exceed 8× to produce the observed output—but CES curvature dampens the value gain. If σ > 1 (substitutes), part of the 8× comes from more hours coding rather than faster coding—but CES curvature amplifies each unit of speedup. Because 8 ≈ e², these effects almost exactly cancel: U stays within ±3% of 2.83 for σ ∈ [0.5, 2].