Rollover Credit versus Vertical Integration in Aquaculture Supply Chains

This paper models the relationship between an aquaculture feed manufacturer (A) and a fish-farm operator (B) as a choice between two governance regimes: rollover trade credit, under which A repeatedly advances feed against an outstanding, potentially un-recoverable debt, and a locked-in forward-delivery agreement, under which B forgoes cash repayment and commits future harvest to A at a fixed price, letting A capture downstream processing margin. Outstanding debt under rollover credit is modeled as a linear ordinary differential equation net of A's own financing cost, yielding a closed-form debt path, steady state, and hazard-discounted value function. Feed credit and harvest output are linked through a fixed feed-conversion ratio of 1.6 kilograms of feed per kilogram of fish weight gain, so both regimes describe the same underlying production process. We state and prove a Mutual Switching Lemma giving a closed-form condition under which integration is a Pareto improvement implementable through bargaining, together with a Corollary establishing a minimum efficient harvest scale. Comparative statics show integration becomes more attractive as default hazard and financing burden rise and as feed-conversion efficiency improves; B's own market risk shapes how the resulting surplus is shared, not whether switching itself is efficient.