On a dynamical model of happiness^*

¹ Departamento de Matemática Aplicada II, Universidade de Vigo, 36310 Vigo, Spain
² Instituto de Matemáticas, Universidad de Talca, Casilla 747, Talca, Chile

^** Corresponding author: eliz@uvigo.es

Received: 21 April 2022
Accepted: 16 February 2023

Abstract

It is now recognized that the personal well-being of an individual can be evaluated numerically. The related utility (“happiness”) profile would give at each instant t the degree u(t) of happiness. The moment-based approach to the evaluation of happiness introduced by the Nobel laureate Daniel Kahneman establishes that the experienced utility of an episode can be derived from real-time measures of the pleasure and pain that the subject experienced during that episode. Since these evaluations consist of two types of utility concepts: instant utility and remembered utility, a dynamic model of happiness based on this approach must be defined by a delay differential equation. Furthermore, the application of the peak-end rule leads to a class of delay-differential equations called differential equations with maxima. We propose a dynamical model for happiness based on differential equations with maxima and provide results which shed some new light on important experimental observations. In particular, our model supports the U-shaped profile of the age-happiness curve, which is a widely observed pattern: well-being is high in youth, falls to a minimum in midlife (midlife crisis), and rises again in old age.