Functional Equations in Several Variables

How to Explain Ubiquity of Constant Elasticity of Substitution (CES) Production and Utility Functions Without Explicitly Postulating CES

“…i for some A i and α i ; see, e.g., [4]. For differentiable functions, this can be easily proven if we differentiate both sides of this equation by c and take…”

“…In mathematics, functions invertible in the sense of Definition 1 are called generalized quasigroups; see, e.g., [4].…”

Econometric Models of Probabilistic Choice: Beyond McFadden’s Formulas

“…When p = 1, the lottery L(1) coincide with the very good alternative a 1 and is, thus, better than a: a < L (1). When p = 0, the lottery L(0) coincides with the very bad alterative a 0 and is, thus, worse than a: L(0) < a.…”

Some Remarks on Subquadratic Functions

“…If the sign "<" is replaced by ">" then tp is called superquadratic and if we have " = " instead of " < " in (1) then we say that ip is quadratic function. There are plenty papers devoted to quadratic functions [1], [2], [3] (and references there). In this note some properties of the solutions of (1) will be proved, particularly we will investigate nonpositive solutions of (1).…”

“…There are plenty papers devoted to quadratic functions [1], [2], [3] (and references there). In this note some properties of the solutions of (1) will be proved, particularly we will investigate nonpositive solutions of (1). Also interesting question of finding sufficient conditions on subquadratic function to be quadratic one will be considered.…”