But for some founders of the new logic, the dissociation that Quine mentions simply forced new problems to surface. Bertrand Russell, for example, in his early account of the subject, explicitly rejects the existence of variable objects yet courts the following quandary: “x is, in some sense, the object denoted by any term; yet this can hardly be strictly maintained, for different variables may...

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...

We experimentally test the effect of sunk costs on decision making. In the experiment, subjects play the role of price–setting duopolists. Both firms have identical costs, including an exogenous sunk cost that varies across sessions over six different values. We observe that the sunk cost has a U–shaped effect: from low to medium levels, average prices decrease, but from medium to high levels, ...

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...

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...

“reasoning involving proof—the one compelling argument for teaching mathematics” in the new national draft curriculum (ACARA, 2010). The rationale for the subject Queensland Senior Mathematics B (Queensland Studies Authority, 2008) includes the aim that students should appreciate the “nature of proof” and “the contribution of mathematics to human culture and progress”. Although the study of pro...

The Bertrand Oligopoly situation with Shubik’s demand functions is modelled as a cooperative TU game. For that purpose two optimization problems are solved to arrive at the description of the worth of any coalition in the so-called Bertrand Oligopoly Game. Under certain circumstances, this Bertrand oligopoly game has clear affinities with the well-known notion in statistics called variance with...

We present a way out of Russell's paradox for sets in the form of a direct weakening of the usual inconsistent full comprehension axiom scheme, which, with no additional axioms, interprets ZFC. In fact, the resulting axiomatic theory 1) is a subsystem of ZFC + " there exists arbitrarily large subtle cardinals " , and 2) is mutually interpretable with ZFC + the scheme of subtlety. 1. NEWCOMP. Be...

We study oligopoly price competition between multiproduct firms, firms whose products interact in the profit function. Specifically, we focus on the impact of intra-firm product interactions on the level of equilibrium profits. This impact is divided into two effects: a direct effect and a strategic effect (i.e., through the competitors’ actions). We derive conditions such that the strategic ef...