Pareto, Zipf, firm sizes — why does the same math keep appearing everywhere in economics?
Power laws appear wherever a few extreme observations dominate and the relationship between variables is scale-free rather than bell-curve-shaped. Established examples: Pareto's Law (top 20% hold ~80% of wealth, tail decays as x⁻ᵅ with α≈1.5–3); Zipf's Law for city sizes (the nth-largest city is proportional to 1/n); firm size distribution (a handful of giants coexist with millions of small firms). The spending–growth relationship being scale-free makes theoretical sense: the braking effect of each additional unit of government spending does not reset to zero at any threshold — it compounds with the existing level, producing the characteristic steep-then-flat curve.