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α: calibrated so average coauthorship-adjusted count equals average raw count
The formulation of market equilibrium problems as mixed complementarity problems (MCP) permits integration of bottom-up programming models of the energy system into top-down general equilibrium models of the overall economy. Despite the general appeal of the integrated MCP approach, dimensionality imposes limitations on practical application. A complementarity representation involves both primal and dual relationships, often doubling the number of equations and thereby the scope for error in specification. When an underlying optimization model of the energy system includes upper and lower bounds on many decision variables, the explicit treatment of income effects may become intractable. We present a decomposition of the integrated MCP formulation that permits a convenient combination of top-down general equilibrium models and bottom-up energy system models for energy policy analysis. We advocate the use of complementarity methods to solve the top-down economic equilibrium model and quadratic programming to solve the underlying bottom-up energy supply model. A simple iterative procedure reconciles the equilibrium prices and quantities between both models.