Does purchase without search explain counter-cyclic pricing?

Previous studies have found that price promotions lead to a decrease in the average prices of seasonal goods in high demand season, countering the predictions of basic supply and demand. I explain this trend by proposing that price-sensitive consumers are less likely to search in low demand periods, changing consumer composition and decreasing aggregate price elasticity. Simultaneously, consumer search allows the firm to use price promotions to attract price-sensitive consumers while maintaining high average prices. I show this using a theoretical model where a multi-product monopolist prices to heterogeneous, rational, searching consumers. Under certain conditions, price promotions are an outcome of search costs and heterogeneity. Furthermore, seasonal trends can result in the firm engaging in counter-cyclic pricing through price promotions. I test the predictions of this model using a seasonal dynamic structural inventory model where consumers make decisions on whether to search, which reveals price promotions and allows consumers to purchase. Matching the theoretical model, price-sensitive consumers make up 29% of searching consumers in low demand season versus 39% in high demand season, resulting in increased price elasticity. The results suggest that the firm changes consumer composition due to the different search incentives of different segments