The impact of advertising in a duopoly model

We investigate the impact of advertising in a simple static differentiated duopoly model. First, we consider the Nash equilibrium of the situation in which the duopolistic firms compete simultaneously with two instruments, i.e. the prices and the advertising expenditures. Second, we examine the Nash equilibrium of the situa-tion in which the firms only compete in prices and do not advertise at all. Next, we compare the two different Nash equilibria in order to assess the impact of advertising. In particular, we characterize in terms of the model parameters the circumstances in which the profits, outputs and/or prices of each firm are greater (smaller) in the Nash equilibrium with advertising than in the Nash equilibrium without advertising. We show that the results depend on (a) the size of the (positive) effect of advertising of a firm on its own demand, (b) the size and nature (stimulating or adverse) of the cross-effect of the advertising of each firm on the demand of the other firm, and (c) the size of the autonomous demand of the firms.