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We motivate the formulation of market equilibrium as a mixed complementarity problem which explicitly represents weak inequalities and complementarity between decision variables and equilibrium conditions. The complementarity format permits an energy-economy model to combine technological detail of a bottom-up energy system with a second-best characterization of the overall economy. Our primary objective is pedagogic. We first lay out the complementarity features of economic equilibrium and demonstrate how we can integrate bottom-up activity analysis into a top-down representation of the broader economy. We then provide a stylized numerical example of an integrated model -within both static and dynamic settings. Finally, we present illustrative applications to three themes figuring prominently on the energy policy agenda of many industrialized countries: nuclear phase-out, green quotas, and environmental tax reforms.JEL classification: C61, C68, D58, Q43