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Full-Text Articles in Social and Behavioral Sciences
Simple Economies With Multiple Equilibria, Ted C. Bergstrom, Ken-Ichi Shimomura, Takehiko Yamato
Simple Economies With Multiple Equilibria, Ted C. Bergstrom, Ken-Ichi Shimomura, Takehiko Yamato
Ted C Bergstrom
This paper studies a general class of pure exchange economies that have multiple equilibria, which extend an example presented by Lloyd Shapley and Martin Shubik. For such economies, we find easily verified conditions that determine whether there are multiple equilibria. We also provide simple methods for constructing economies in which arbitrary pre-specified sets of prices are equilibria. These economies have simple comparative statics, since prices at interior competitive equilibrium depend on the parameters of utility but not on the endowment quantities.
Log-Concave Probability And Its Applications, Ted Bergstrom, Mark Bagnoli
Log-Concave Probability And Its Applications, Ted Bergstrom, Mark Bagnoli
Ted C Bergstrom
In many applications,assumptions about the log-concavity of a probability distribution allow just enough special structure to yield a workable theory.This paper catalogs a series of theorems relating log-concavity and/or log-convexity of probability density functions,distribution functions,reliability functions,and their integrals. We list a large number of commonly-used probability distributions and report the log-concavity or log-convexity of their density functions and their integrals. We also discuss a variety of applications of log-concavity that have appeared in the literature. (The current draft corrects a typo in Table 3.)