Resource Renewability as a Regime: A RAYOBETH Classification of Natural Capital

Natural resource economics divides natural capital into renewable and nonrenewable resources. This article argues that renewability is not a property of a resource but a regime of its law of motion, set jointly by biology, institutions and the discount rate. Writing every stock and flow of natural capital as a special case of the RAYOBETH law, it proves a harvest gap theorem, an economic exhaustibility boundary, a recycling multiplier, a sink trichotomy and a service masking theorem, and assembles them into twelve regimes in five families that partition natural capital and map onto the SEEA. Open data on oil, copper, whales, fisheries, tropical land, solar and wind capital, atmospheric carbon dioxide and wildlife abundance place each class in its regime. The atmospheric uptake rate of carbon dioxide fell from 0.036 to 0.022 per year between the 1960s and the 2020s, a sink drifting from assimilative toward cumulative.