Dynamics of Contentment

This work formulates a mathematical model aimed at prediction of temporal evolution of joint probability density of wealth and contentment in a society. A continuous variable changing between 0 and 1 is introduced to characterise contentment, or satisfaction with life, of an individual and an equation governing its evolution is postulated from analysis of several factors likely to affect the contentment. As contentment is strongly affected by material well-being, a similar equation is formulated for wealth of an individual. Subsequently, an evolution equation for the joint probability density of individuals' wealth and contentment within a society is derived from these two equations and an integral representation of marriage effects. As an illustration of this model capabilities, effects of the wealth tax rate over a long period of time are simulated for a society with an initially low variation of wealth and contentment: the model predicts that a higher taxation in the longer run may lead to a wealthier and more content society. It is also shown that lower rates of the wealth tax lead to pronounced stratification of the society in terms of both wealth and contentment and that there is no direct relationship between the average values of the latter two variables thus providing an explanation to the Easterlin paradox.