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.

这项工作制定了一个数学模型，旨在预测社会中财富和满足的联合概率密度的时间演变。引入了一个在 0 和 1 之间变化的连续变量来表征个人的满足感或对生活的满意程度，并且通过对可能影响满足感的几个因素的分析假设了一个控制其进化的方程。由于满足感受到物质幸福感的强烈影响，因此为个人财富制定了一个类似的等式。随后，根据这两个方程和婚姻效应的积分表示，推导出一个社会内个人财富和满足的联合概率密度的演化方程。作为此模型功能的说明，模拟财富税率在很长一段时间内的影响，适用于最初财富和满足感变化较小的社会：该模型预测，从长远来看，较高的税收可能会导致社会更加富裕和满足感。研究还表明，较低的财富税税率会导致社会在财富和满足感方面出现明显的分层，并且后两个变量的平均值之间没有直接关系，从而为伊斯特林悖论提供了解释。