I have been working on income distributions for a while, and I've been asked to do a theoretical justification for the idea that income distribution follows an exponential function for low incomes. There's a lot of literature about Pareto distributions in the upper tail of the distribution, but I haven't been able to find literature for the lower tail and the exponential.
There's empirical work on this topic, mainly done by physicists: https://arxiv.org/pdf/cond-mat/0008305.pdf
One of those physicists asked me to find economic theories that support the exponential hypothesis, but, as I've said, I haven't found any.
Could you point some pieces of economic literature to get me on the right way? Thank you.