Investigation of fundamental cycles of economic activity and rebate time in winner-take-all systems
Abstract
We investigate the emergence of fundamental economic cycles of activity and rebate time with the introduction of taxes in winner-take-all systems. For systems with time-dependent rebates, which are distributed after a fixed period, economic activity and rebate time are found to be independent of initial income distribution and the fraction Ptax to be taxed per transaction. However, when the rebates are threshold-dependent, such that they are distributed when the accumulated tax reaches a particular fraction Prebate of the remaining wealth within a population, a tradeoff was determined between the fraction to be taxed and the threshold fraction of the remaining wealth. For the Ptax = 15% corresponding to real economic systems, the practice of distributing rebates according to a threshold contributes to significantly greater economic activity than when rebates are regularly distributed after a year or 260 (working days). Economic activity is optimal for higher values of Ptax and lower values of Prebate, while rebate time is independent of initial income distribution and population or wealth growth.