The Average-Marginal Relationship and Tractable Equilibrium Forms. (arXiv:1611.02270v1 [q-fin.EC])

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. We discuss close connections to the theory of Laplace transform and completely monotone functions.