Restricting advertising is one way governments seek to reduce consumption of potentially harmful goods. There have been increasing calls to apply a similar policy to the junk food market. The effect will depend on how brand advertising influences consumer demand, and on the strategic pricing response of oligopolistic firms. We develop a model of consumer demand and dynamic oligopoly supply in which multi-product firms compete in prices and advertising budgets. We model the impact of advertising on demand in a flexible way, that allows for the possibility that advertising is predatory or cooperative, and we consider how market equilibria would be impacted by an advertising ban. In our application we apply the model to the potato chip market using transaction level data. The implications of an advertising ban for consumer welfare depend on the view one takes about advertising. In the potato chip market advertising has little informational content. The advertising may be a characteristic valued by consumers, or it may act to distort decision-making. We quantify the welfare impacts of an advertising ban under alternative views of advertising, and show that welfare conclusions depend on which view of advertising the policymaker adopts.