Valuing Scarcity: A General Framework for Bitcoin, Gold, and Traditional Assets

This paper challenges the conventional divide between productive and non-productive assets by proposing that scarcity, rather than internal cash flow generation, is the fundamental source of value across all asset classes. Interim payments such as dividends, rents, or coupons, represent one modality of monetizing scarcity, but terminal resale and other mechanisms serve equivalent roles. We develop a valuation framework in which scarcity is modeled as a latent, time-varying state variable shaped by economic pressures on demand and supply. A class of monetization functions, characterized by monotonicity and curvature, maps scarcity states into observable or forecast cash flows. This formulation allows discounted cash flow (DCF) logic to be reinterpreted as a general pricing mechanism for intertemporal scarcity. The framework accommodates both terminal-value assets, such as Bitcoin or gold, and income-generating assets, such as equities or bonds. We formally demonstrate the equivalence between terminal and periodic payoff structures and introduce a classification of assets according to their scarcity mechanism, whether physical, contractual, algorithmic, or reputational. By embedding scarcity at the core of valuation, this approach dissolves artificial distinctions in asset classification and establishes a unified foundation for pricing financial claims across diverse contexts.