Random parameters demand system estimates can generate upward sloping demands and imply margins outside of the theoretical bounds for profit maximization. If such violations are numerous enough, they can confound merger simulation exercises. Using Lerner indices for multiproduct firms playing static Bertrand games, we find that up to 35 per cent of implied margins for beer are outside the bounds. We characterize downward sloping demand and the theoretical bounds for profit maximization as prior information and extend the GMM objective function, incorporating inequality moments for product‐level own‐elasticities and brand level or product level Lerner indices. Very few violations remain when an inequality constrained estimator is used.