This paper analyzes price competition in the case of two firms operating under constant returns to scale with more than one production factor. Factors are chosen sequentially in a two‐stage game generating a soft capacity constraint and implying a convex short‐term cost function in the second stage of the game. We show that tacit collusion is the only predictable result of the whole game, that is, the unique payoff‐dominant pure strategy Nash equilibrium. Technically, this paper bridges the capacity constraint literature on price competition and that of the convex cost function.