We determine the most general demand functions S(p, v) of a single-product depending on the price p and on the exogenous variable advertising expenditure v. We assume that additive or multiplicative changes in the unit price or the advertising expenditure yield an additive or multiplicative change in sales, where the increments or factors depend on the price or the advertising expenditure increments and either the initial prices or advertising expenditures. This leads to 32 different models. For some of them, the equilibrium strategy for the monopoly and duopoly, Cournot and Stackelberg cases, are obtained. Finally, some methods of estimation are given.
