<p>This study investigates multiproduct pricing in the mining industry, where primary products and by-products are jointly produced. It assumes a mining producer who supplies the primary product in a perfectly competitive market and the by-product in a Cournot oligopoly market, with a non-additively separable production cost between them, reflecting the mining process. Additionally, given that the maximum producible amount of the by-product depends on the production of the primary product, this study examines two situations: whether the profit-maximizing production level of the by-product exceeds its maximum feasible level. The theoretical analysis yields two key insights. First, regardless of whether the profit-maximizing production of the by-product is constrained by the production of the primary product, the prices of the primary and by-product sold under different competitive conditions are not decoupled but maintain a specific linear relationship. Second, however, the sign of this relationship varies depending on the effectiveness of the production constraint and the direction of demand shocks. Employing a cointegration test allowing for multiple structural breaks, this study empirically analyzes whether the equilibrium relationship between the prices has been maintained despite changes in its sign, focusing on cobalt and its primary product. These findings provide a deeper understanding of multiproduct pricing and offer insights into the cobalt and primary product markets.</p>