||The "power retailing" phenomenon, which refers to very large retailers that compete primarily on price, has received much attention in the popular and trade press, and more recently, from academics. The academic concern so far has been with relative power in the channel. In contrast, we take a modelling approach to examine the effect on horizontal competition and customer shopping behaviour in the grocery retailing industry. Assuming rational cost-minimizing consumers, who purchase both perishable and nonperishable goods from two stores differentiated by price and location, we derive the consumers' optimal shopping policies. We show how it may be optimal for consumers to have a planned multi-store shopping policy, even when the stores sell identical goods and there is no price uncertainty. As well, the market share exhibits increasing returns to scale to price reductions, but only when price differentials become large enough. This is offered as a possible reason for the unexpected (to the incumbents) success of power retailers in the grocery industry.