The Economics of Collectibles: Balancing Scarcity, Pricing and Scalping in Limited-supply Markets

Scalping in limited-supply markets, particularly in collectible goods such as toys and action figures, poses a significant challenge for producers and consumers alike. When supply is intentionally constrained, speculative reselling in secondary markets can distort pricing, undermine perceived fairness and damage brand reputation. This study develops a mathematical model to formally analyse the strategic decisions producers face in pricing and enforcement under such conditions. The framework integrates heterogeneous consumer demand through a logistic distribution, models scalper participation as a function of expected arbitrage profits, and incorporates enforcement costs and reputational penalties into the producer’s optimisation problem. The model yields closed-form solutions that characterise optimal pricing and enforcement strategies. It reveals how enforcement levels influence scalper entry and how pricing affects residual demand in the secondary market. The findings indicate that producers face a trade-off between short-term profitability and long-term reputational risks, and that moderate enforcement combined with strategically set prices can mitigate scalping more effectively than either approach alone. By explicitly modelling the interdependence between market tiers and accounting for consumer heterogeneity, the study extends prior theoretical approaches that treat scalping exogenously. Although developed for collectibles, the analytical framework is applicable to any limited-supply market where scarcity and resale distortions coexist, including ticket resale, digital goods and essential commodities in constrained supply contexts.