The Profitability of Purchase Limits During Shortages

Abstract

Pandemics, natural disasters (e.g., hurricanes, droughts, fires), strikes, piracy, and other events can unexpectedly disrupt supply or spike demand, creating shortages. Unlike ordinary stockouts caused by store-specific inventory policies, shortages involve the entire supply chain. One tool for managing shortages is imposing purchase limits. Purchase limits restrict the quantity each shopper can purchase of the scarce product (e.g., gasoline, toilet paper, sanitizers, meat, batteries), possibly increasing availability to other shoppers. Although altruistic stores might use purchase limits for egalitarian goals (e.g., reducing hoarding, waste, panic buying, arbitrage, unfair distribution), the authors find that profit-maximizing stores can use purchase limits to increase profits during shortages. These findings suggest that stores’ price-and-limit strategies depend on shortage severity, store size, competition, and seasonality. For moderate shortages, large multiproduct stores, where average shopping basket sizes are large, should maintain low prices and impose limits, whereas small stores should increase prices and not impose limits. For severe shortages, by contrast, large stores should keep low prices but not impose limits, whereas small stores should increase prices and impose limits. Generally, large stores benefit from increased future store traffic when they impose limits. Interestingly, purchase limits can improve both store profits and, with lower prices, consumer surplus.