The Substitution Spectrum

How trust and enforcement combine to produce coordination

Q = [α · Tρ + (1−α) · Rρ] 1/ρ

ρ controls substitutability: how easily one input compensates for the other's absence. Elasticity of substitution σ = 1/(1−ρ).

The Substitution Spectrum Three isoquant curves, each the same coordination output, showing how trust capital (horizontal) and enforcement capital (vertical) combine under different assumptions about substitutability: perfect substitutes (a dashed straight line), Cobb-Douglas (a smooth curve with diminishing returns), and perfect complements (Leontief, a right-angled corner, no substitution). All three meet at one point. A green arrow labeled "as scale increases" runs from the Cobb-Douglas curve toward the Leontief corner, marking the unmeasured compliance-entropy hypothesis that at scale, trust and enforcement become complements. Enforcement capital (R) Trust capital (T) Each curve: same coordination output Q₀each curve: same output Q₀ Perfect substitutes σ = ∞, ρ = 1 Cobb-Douglas σ = 1, ρ → 0 Perfect complements (Leontief) σ = 0, ρ → −∞ as scale increases all three intersect

What each assumes

Select a row to spotlight its curve in the plot; select it again, or press Escape, to show all three.

The hypothesis

At small scale, trust and enforcement trade off smoothly (Cobb-Douglas).

At large scale, they may become complements, not substitutes.

The scarce input becomes the binding constraint, and enforcement can no longer replace missing trust.

The compliance-entropy hypothesis predicts σ → 0 at scale; this transition is unmeasured.