We consider a novel pricing and advertising framework in which a seller not only sets the product price but also designs flexible advertising schemes to influence customers' valuations of the product. We impose no structural restriction on the seller's feasible advertising strategies and allow her to advertise the product by disclosing or concealing any information. Following the information design literature, we model this fully flexible advertising as the seller choosing an arbitrary information policy that signals the product quality to customers. Customers observe the advertising signal and form a Bayesian posterior belief over the product quality. We investigate two questions in this work: (1) What is the value of advertising? To what extent can advertising enhance a seller's revenue? (2) Without any a priori knowledge of the customers' demand function, how can a seller adaptively learn and optimize both pricing and advertising strategies using past purchase responses? To study the first question, we quantify the value of advertising by comparing the optimal revenue from jointly designing advertising and a single posted price with the optimal revenue from pricing alone. We show that advertising can increase revenue by at most a factor of two, and this bound is tight. For the second question, we study the seller's dynamic pricing and advertising problem under demand uncertainty. Our main result for this question is a computationally efficient online algorithm that achieves the optimal $O(T^{2/3} (m\log T)^{1/3})$ regret rate when the valuation function is linear in the product quality. Here, $m$ is the cardinality of the discrete product quality domain and $T$ is the time horizon.

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