A Short Course on Functional Equations: Based Upon Recent Applications to the Social and Behavioral Sciences

Section 1. An aggregation theorem for allocation problems. Cauchy equation for single- and multiplace functions. Two extension theorems..- Section 2. Scale-invariant equal sacrifice in taxation. The linear-affine functional equation. Multiplicative and logarithmic functions..- Section 3. General forms of 'laws of sciences' without dimensional constants. The case of the same ratio scale for all variables. Generalized homogeneous functions. Inequality measures..- Section 4. General forms of 'laws of science' with (partially) independent ratio and interval scales. Multiplace multiplicative and logarithmic functions. Price levels. Endomorphisms of a real field. The exponential equation. Characters..- Section 5. Pexider's equation and its extension. Quasi-extension of Cauchy's equation. Determination of all generalized Hicks-neutral production functions..- Section 6. Determination of all Hicks-neutral production functions depending upon capital, labor and time (state of technology). The translation equation..- Section 7. 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..- Section 8. Synthesis of measure judgements. Equations in a single variable. The Abel and Schroder equations. Iteration..- References.- Index of names.