Martin W. Adler Edson X. Albuquerque Edmund G. Anderson Lewis Aronow Leslie E. Bailey Paul Bass John A. Bevan C. Paul Bianchi Leslie C. Blaber David A. Blake Floyd E. Bloom Carl K. Buckner Theodore J. Cicero E. E. Daniel William C. de Groat J. W. Downie Linda Dykstra Hugh L. Evans James A. Ferrendelli Lawrence J. Fischer William W. Fleming Ray W. Fuller Gerard L. Gebber James W. Gibb Shri N. Gi...

This paper provides a simple model of endogenous horizontal product differentiation that has two important implications. First, the model can explain the “empirical Bertrand paradox” – the failure to observe homogeneous product Bertrand oligopoly. If product differentiation is possible at reasonable cost, then Bertrand firms would always invest in product differentiation. Using a quadratic util...

This paper compares Bertrand and Cournot equilibria in a di®erentiated duopoly with R&D (research and development) competition. Cournot competition is shown to induce more R&D e®ort than Bertrand competition. However, the price is lower and output is higher in Bertrand than in Cournot competition. Furthermore, the Bertrand equilibrium is more e±cient than the Cournot equilibrium if either R&D p...

Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822-1900). Specifically, it is a model of price competition between duopoly firms which results in each charging the price that would be charged under perfect competition, known as marginal cost pricing. The model has the following assumptions: There are at least two firms producing ho...

Alfred North Whitehead wrote a letter to Charles Hartshorne in 1936 in which he referred to William James as the American Plato. Especially given Whitehead’s admiration of Plato, this was a high compliment to James. What was the basis for this compliment and analogy? In responding to that question beyond the partial and scattered references provided by Whitehead, this article briefly explores t...

This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with R6D (research and development) competition. It shows that Cournot competition induces more R6D effort than Bertrand competition. However, the price is lower and output is larger in Bertrand than in Cournot competition. Furthermore, the Bertrand equilibrium is more efficient than the Cournot equilibrium if eithe...

This paper reports the study of properties of the curve pairs of the Bertrand types using our automated reasoning program based on Wu’s method of mechanical theorem proving for differential geometry. A complete list of results about Bertrand curves in metric and affine spaces is derived mechanically. The list includes most of the known results of various Bertrand curves. We also derive some new...