Differentiated bertrand duopoly with variable demand

Two one-product firms compete in prices on a market with differentiated products. Goods are differentiated because customers switch from one good to the other at different relative prices. With the specification that mean demand in the market is unit-elastic 1 pro vide conditions on the shape of the customer density which guarantee the existence of a unique Bertrand equilibrium.Duopoly equilibrium, price competition, product differentiation