Exponential Income Distribution and Evolution of Unemployment Compensation in the United Kingdom

Abstract

We show that an exponential income distribution will emerge spontaneously in a peer-to-peer economic network that shares the publicly available technology. Based on this finding, we identify the exponential income distribution as the benchmark structure of the well-functioning market economy. However, a real market economy may deviate from the well-functioning market economy. We show that the deviation is partly reflected as the invalidity of exponential distribution in describing the super-low income class that involves unemployment. In this regard, we find, theoretically, that the lower-bound u of exponential income distribution has a linear relationship with (per capita) unemployment compensation. In this paper, we test this relationship for the United Kingdom from 2001 to 2015. Our empirical investigation confirms that the income structure of low and middle classes (about 90% of populations) in the United Kingdom exactly obeys exponential distribution, in which the lower-bound u is exactly in line with the evolution of unemployment compensation.

Decentralized Decisions and Technological Progress: A Formal Proof

“…Based on this theoretical result, Blanchet et al (2017Blanchet et al ( , 2018 used the generalized Pareto distribution to describe the income structure of the total population. In particular, the exponential distribution is a special case of the generalized Pareto distribution when the income structure turns to equal opportunity (Tao, 2021). This implies that the exponential distribution is expected to dominate the income structure of an equal-opportunity market economy, which indicates a well-functioning market economy.…”

“…In the economic literature, a peer-to-peer economy without an intermediary third-party is recognized as an equal-opportunity market economy (Einav et al, 2016;Davidson et al, 2018;Filippi et al, 2020;Hojckova et al, 2020). In this vein, Tao (2016Tao ( , 2021) used a long-run Arrow-Debreu economy (ADE), in which there are many households, each of whom independently operates a firm, to simulate a peer-to-peer economy that shares the publicly available technology. Furthermore, Tao (2016Tao ( , 2021 showed that an exponential income distribution will emerge spontaneously in such a peer-to-peer economy.…”

“…In this vein, Tao (2016Tao ( , 2021) used a long-run Arrow-Debreu economy (ADE), in which there are many households, each of whom independently operates a firm, to simulate a peer-to-peer economy that shares the publicly available technology. Furthermore, Tao (2016Tao ( , 2021 showed that an exponential income distribution will emerge spontaneously in such a peer-to-peer economy. Based on this finding, Tao (2016Tao ( , 2021 proposed to identify the exponential income distribution as the benchmark structure of the well-functioning market economy.…”

“…Furthermore, Tao (2016Tao ( , 2021 showed that an exponential income distribution will emerge spontaneously in such a peer-to-peer economy. Based on this finding, Tao (2016Tao ( , 2021 proposed to identify the exponential income distribution as the benchmark structure of the well-functioning market economy.…”

“…Hayek's theory of knowledge in the context of this peer-to-peer economy. Tao (2016Tao ( , 2021 has shown that the exponential income distribution emerges spontaneously in such a peer-to-peer economy. As a spontaneous economic order, the exponential income distribution consists of a set of general equilibrium allocations among households (Tao, 2016(Tao, , 2021, in each of which all households reach consensuses on resource allocation.…”