Authors: Renato Vieira dos Santos
A stochastic multiplicative wealth model with taxation and redistribution is extended to include two channels through which fiscal policy can reduce the economy's average growth rate: productive disincentive (a taxu2011dependent mean return) and administrative inefficiency (loss of part of the collected revenue). For uniform redistribution, the stationary density of normalized wealth remains an inverseu2011gamma law, but its shape parameter acquires a richer dependence on the tax rate. The central finding is the emergence of an emph{inequality Laffer curve}: when the disincentive is sufficiently strong, the Gini coefficient first decreases, reaches a minimum at a finite tax rate, and then increases again as taxation intensifies. In the extreme limit the stationary state collapses back to the condensed phase, restoring the oligarchic transition. Both channels also create a direct tradeu2011off between inequality and longu2011run average wealth, giving rise to a welfareu2011maximizing tax rate. The two channels are combined into a single analytically tractable model, and all predictions are validated by agentu2011based simulations. The results show that the qualitative existence of an optimal tax rate is robust whenever the aggregate growth rate responds to fiscal policy, while the inequality Laffer curve is a specific prediction of the productiveu2011disincentive channel.
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