Choice of representation system for economic analysis

Abstract

Many well-known economic assumptions and desired restrictions can be readily established with the proper choice of a coordinate representation system. For example, the homotheticity assumption can be readily established with the polar coordinate system, the concavity restriction with the Muntz-Sartz series, the convexity restriction with the polynomial series, the orthogonality of regression functions with the orthonormal bases expansion, and the covariance stationary process with the Fourier series expansion. To describe a backward-bending curve, the radial regression can be defined and utilized. Thus, many economic assumptions and desired properties have their own corresponding coordinate representation systems.