We propose a new mathematical model to describe equilibria in competitive markets. Our approach transforms the well-known complementary formulation into a numerically more efficient optimization framework. In complementarity models, the actions of all elastic consumers in the market are implicitly represented by their aggregate demand. Instead, we introduce demand-induced utilities, which can be explicitly constructed individually for each consumer. We then consider the joint optimization of all agents’ costs, including the new demand-induced functions for elastic consumers, subject to market-clearing constraints. We prove that the primal-dual solution to this optimization problem yields an equilibrium equivalent to that found by a complementarity model. The computational efficiency of the new methodology is compared to that of the complementarity formulation on a large-scale instance, representing the Brazilian natural gas market. Our model exhibits excellent performance and captures distortions typical of multi-hub network-constrained markets, showing the impact of spatial arbitrage on regional price setting.