We formulate a model of personal income distributions within society. Our aim is to understand the origin of the ‘natural law’ first proposed by Pareto who suggested that the high end part of the income distribution follows a power law where f ₁(w) ∼ w ^−1−α . We generalise a model proposed the so-called CC-CCM model introducing the possibility of exchanges of money at random times. Unlike the CC-CCM model this generalisation predicts tail exponents greater than unity in line with Pareto’s prediction and empirical observation.