Can a collective label survive the decline of its resource? Critical mass, species switching and the survival of labelling schemes

Collective labels are common in sectors that rely on natural resources. They are often assumed to last once the market recognises them. We question this assumption for schemes built on a common-pool resource that members do not control. In our model a member stays under two conditions. The label must pay for itself. And the occupation must remain better than an outside option. The label is a club good with a critical mass. Members may switch to a second species. Three results stand out. First, occupation exits can start the collapse of a scheme while its label still pays for itself. Second, during a decline the scheme survives only if the share of members able to switch exceeds a critical share. We derive this share in closed form. Third, switching protects the scheme only while its net income stays above a threshold. If the second resource falls below it switching merely delays collapse. Secondary results concern label coverage, the timing of shocks and entry. The viability of a collective thus depends on the economic options of its members and not only on its label. Stylised facts and orders of magnitude come from French line-caught sea bass labels. Simulations on ICES stock data illustrate the mechanisms. Survival levels depend on parameters that are only partly observed. We draw implications for label design, entry support and access to switching species.