How to theoretically explain an exponential income distribution? 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.
...find economic theories that support the exponential hypothesis, but, as I've said, I haven't found any.


I don't think you will. For purposes of economic argument, the characteristic of the Exponential distribution that stands out and must be defended, is that it has its maximum at zero.

Then, arguing that an Income distribution follows the Exponential, means that we accept that the most probable situation to be observed is zero income. Is it? I don't think so.

As regards the study you link to, the main piece of evidence for the fit of the Exponential to the data is Fig 1 page 2. The authors write that they consider it a very good fit. I most certainly don't: the histogram in Fig 1. has clearly a mode at strictly positive values and not at zero. Βut this is the most critical piece of evidence as to whether the data follows an Exponential or not. 

At page 4, the authors try to deal with this critical deviation of the data from the Exponential graph, by mentioning that there may be under-reporting at low values, but that's a very vague argument, unsupported and unsubstantiated.

a) From a theoretical perspective, it is not realistic to argue that the most probable income observed is zero
b) The data support this by providing a strictly positive mode for the frequency.

Therefore I don't see a case for the Exponential.