The Substitution Spectrum

The Substitution Spectrum Three isoquant curves showing how trust and enforcement capital combine under different assumptions about substitutability: perfect substitutes (linear trade-off), Cobb-Douglas (diminishing returns), and perfect complements (Leontief, no substitution). An arrow indicates the unmeasured compliance-entropy hypothesis that at scale, trust and control become complements. 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 σ = 1/(1−ρ). Enforcement Capital (R) Trust Capital (T) Perfect Substitutes σ = ∞, ρ = 1 Cobb-Douglas σ = 1, ρ → 0 Perfect Complements (Leontief) σ = 0, ρ → −∞ all three intersect as scale increases Each curve: same coordination output Q₀ WHAT EACH ASSUMES More police perfectly compensate for less trust (naive assumption) Diminishing returns but smooth trade-off (standard economics) You need both — no amount of one compensates for the other's absence THE CLAIM At small scale, trust and enforcement trade off smoothly (Cobb-Douglas). At large scale, they become complements, not substitutes. The missing input is the binding constraint. Trust is always missing. The compliance-entropy hypothesis predicts σ → 0 at scale; this transition is unmeasured.
core conceptemergent / positiveconstraint / breakdown