A long standing controversial issue in the literature surrounding the bilateral monopoly is the determinacy of equilibrium price and quantity when the seller and buyer maximize their joint profits. This controversy led to incorrect presentation of bilateral monopoly solutions in the literature. In this study, we employ a dynamic optimization model to simultaneously determine the equilibrium price and quantity transacted between the buyer and seller. We also show that for the bilateral monopoly to achieve equilibrium they must transact the intermediate product at the hint profit maximizing level. Any deviation from this level will result in one party exercising greater control than the other, and thus, will lead to a situation of either pure monopsony or monopoly, or nonexistence of both parties. [D43, C78, C61].