In a horizontal differentiated duopoly we compare Nash and Stackelberg

equilibria in which the firms endogeneously choose to behave as a price or

quantity setter. Using the utility function introduced by Dixit (1979) we

generalize the model of Boyer and Moreaux (1987) and show that it is always

more profitable to strategically set the price (quantity) if the goods

are complements (substitutes). For every degree of product differentiation,

consumer surplus and total welfare are maximal in the standard Bertrand

equilibrium, followed by the price Stackelberg, the quantity Stackelberg and

the Cournot equilibrium. In contrast to Boyer and Moreaux we show that

there is no unique ranking of prices, quantities and profits of the leader and

follower depending on the degree of product differentiation and the type of

competition. Furthermore, we show that the price (quantity) Stackelberg

equilibrium is bounded by the Bertrand and the mixed Nash equilibrium in

which firm 1 sets the price (quantity) and firm 2 the quantity (price).