Abstract
This paper proposes a stochastic dynamics model in which people who are endowed with different discount factors chose to buy the capital stock periodically with different periodicities and are exposed to randomness at arithmetic progression times. We prove that the realization of a stochastic equilibrium may render to the people quite unequal benefits. Its proof is based on Erdös Discrepancy Problem that an arithmetic progression sum of any sign sequence goes to infinity, which is recently solved by Terence Tao [1]. The result in this paper implies that in some cases, the sources of inequality come from pure luck.
Highlights
The existence of inequality of wages, assets, and other incomes in a society has been gaining wide attention recently especially since Pikkety [2] (Atkinson et al [3], Gabaix et al [4], Grossman and Helpman [5], Jones [6], Jones and Kim [7], Kasa and Lei [8], Mankiw [9] to name only a few)
This paper proposes a stochastic dynamics model in which people who are endowed with different discount factors chose to buy the capital stock periodically with different periodicities and are exposed to randomness at arithmetic progression times
Its proof is based on Erdös Discrepancy Problem that an arithmetic progression sum of any sign sequence goes to infinity, which is recently solved by Terence Tao [1]
Summary
The existence of inequality of wages, assets, and other incomes in a society has been gaining wide attention recently especially since Pikkety [2] (Atkinson et al [3], Gabaix et al [4], Grossman and Helpman [5], Jones [6], Jones and Kim [7], Kasa and Lei [8], Mankiw [9] to name only a few) Many researchers tackled this problem by providing models that explain the empirical data, say, the large gap between capital income and labor one, or inequality among labor incomes, and its extent of that inequality. We provide a simple stochastic model in which the ex-post realization of the equilibrium stochastic process is quite biased among people To complete this purpose, we have to investigate the existence of some regularity within randomness.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
