  In the so-called ``fair'' models of peer-to-peer wealth exchanges, economic
inequality tends to reach its maximum value asymptotically. This global trend
is evident as the richest continuously accumulate a larger share of wealth at
the expense of others. To address the mounting issue of inequality, different
strategies of taxes and redistribution are commonly employed. Our study delves
into the interplay between wealth and trade (consumption) tax bases, probing
their impact on wealth distribution within wealth-conservative economies. The
ultimate aim is to unearth an optimal framework that adeptly curbs
inequality.Through a meticulous analysis of varying tax rates and the
allocation of the collected tax to the most economically vulnerable strata, we
unveil a compelling pattern resembling two distinct phases. These phases
delineate the most effective systems for inequality mitigation. Our findings
underscore the synergistic potential of amalgamating these tax systems,
surpassing the individual efficacy of each. This synthesis beckons policymakers
to weave together tax rates and precision-targeted redistribution, crafting tax
systems that wield the potential for tangible and substantial reductions in
economic disparity.
