The Average-Marginal Relationship and Tractable Equilibrium Forms

Economic variables with familiar tractable functional forms (constant-elasticity or linear) are only reweighted in the change from their average to marginal versions. They are also simple, featuring only one or two terms. These properties allow for closed-form solutions. We explicitly characterize all equilibrium systems obeying a generalization of these properties, showing they form a hierarchy of tractability. The resulting forms are more realistic (e.g. bell-shaped demand and U-shaped cost) but highly tractable. These forms have importantly different implications for policy analysis, as we illustrate with applications from innovation, industrial, international, auction and public economics.