Generally, two facts occur with strategic complementarities and fixed prices: (i) the equilibria are multiple and (ii) if the complementarities are strong, the law of demand is violated and the equilibrium is unstable. In this paper, we analyse the effect of price flexibility on these features as well as on market welfare properties. Assuming an exchange economy with H agents consuming two goods with one strategic complement, we show that flexibility of prices may remove both the multiplicity of the equilibria and the instability of behavior when the externalities are strong. Moreover, we find conditions to correct instability when it is caused by perverse wealth effects. When preferences are quasilinear and identical, if the externality is beneficial, any equilibrium is Pareto optimal despite the externality. But if the externality is detrimental, corrections are required.