A Short Course on Functional Equations

Chapter 1 Introduction

Chapter 2 An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions.Two extension theorems

Chapter 3 Scale-invariant equal sacrifice in taxation. The linear-affine functional equation. Multiplicative and logarithmic functions

Chapter 4 General forms of ‘laws of science’ without dimensional constants. The case of the same ratio scale for all variables. Generalized homogeneous functions. Inequality measures

Chapter 5 General forms of ‘laws of sciences’ with (partially) independent ratio and interval scales. Multiplace multiplicative and logarithmic functions. Price levels.Endomorphisms of a real field. The exponential equation. Characters

Chapter 6 Pexider’s equation and its extension. Quasi-extension of Cauchy’s equation. Determination of all generalized Hicks-neutral production functions

Chapter 7 Determination of all Hicks-neutral production functions depending upon capital, labor and time (state of technology). The translation equation

Chapter 8 The associativity equation. Synthesis of ratio judgements. The quasiarithmetic means. The Jensen equations. A conditional linear-affine equation. A characterization of root-mean-powers and of the geometric mean

Chapter 9 Synthesis of measure judgements. Equations in a single variable. The Abel and Schröder equations. Iteration