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 Trust Attractor 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