In the crisis management of essential goods supply chains, equitable access is as important as resilience. The 2020 panic buying in Japan, triggered by a false “toilet paper shortage” rumor, exposed distribution inequities. To assess the impact of panic buying and the role of quota policies, this study develops a multi-tier agent-based model of the toilet paper supply chain with manufacturers, wholesalers, retailers, and consumers, and evaluates three scenarios: baseline, demand surge, and quota policy. The results show that the model can replicate typical phenomena observed during panic buying. Under the demand surge scenario, both retailers and wholesalers experience short-term stockouts, manufacturers face severe production delays, and the equity index declines sharply and recovers slowly. Under quota policy, excessive purchasing is effectively suppressed, inventory distribution becomes more balanced, and equity recovers to a normal level in a shorter period. Using an equity index that combines the Gini coefficient and service level, the study confirms that quota policy can accelerate equity recovery and improve allocation efficiency during crises.