Supermarket consumers typically purchase more than one item at a time. Retail prices, in turn, are likely to depend on demand relationships between multiple categories of goods in consumers' shopping baskets. In this paper, we develop a model of retail price competition that explicitly models the effect of complementary demand relationships between products that appear in consumer shopping baskets. We derive inferences for retail market power when shopping baskets contain products from complementary categories and compare outcomes with the predictions derived from conventional models that assume consumers make discrete choices among independent product categories. Our findings reveal that cross-category product complementarity in consumer shopping baskets facilitates substantially greater retail market power relative to the benchmark case of discrete choice over independent goods.