In this paper, a new optimization model of competitive facility location and pricing is introduced. This model is an extension of the well-known (r|p)-centroid problem. In the model, two companies compete for the client’s demand. Each client has a finite budget and a finite demand. First, a company-leader determines a location of p facilities. Taking into account the location of leader’s facilities, the company-follower determines a location of its own r facilities. After that, each company assigns a price for each client. When buying a product, the client pays the price of the product and its transportation. A client buys everything from a company with lower total costs if their total costs do not exceed the budget of the client. If the cost of buying a product from both companies is the same, the demand of clients is distributed equally among them. The goal is to determine a location of leader’s facilities and set the prices in which the total income of the leader is maximal. Results about the computational complexity of the model are presented. Several special cases are considered. These cases can be divided into three categories: (1) polynomially solvable problems; (2) NP-hard problems; (3) problems related to the second level of the polynomial hierarchy. Finally, the complexity of the maxmin-2-Sat problem is discussed.