We formulate a duopoly model involving a firm producing a fair-trade product in competition against a conventional firm producing a standard product. We make use of the concept of ''economic identity'' introduced by Akerlof and Kranton. We show how, in the short run, the parameters of the identity function can impact the equilibrium prices, and in the medium run, how they impact the conventional firm's choice of its position in the product space. In the long run, however, the fair-trade firm may be able to influence the parameters of the identity function, for its own advantage.