Does less inequality in wealth distribution imply better property rights protection? In this paper we show that this impact is non monotonous and is conditional on a) equilibrium type: conflict (rent-seeking) or peace, b) the reasons of changes in wealth distribution, and c) the size of the ruling class, "elite". In the conflict stage, institutional quality positively depends on the wealth of the elite, but negativelyon the size of the elite class. However, the transition from conflict to peace

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... stage (with no rent-seeking and fast growth) requires the reduction of inequality. This generates an institutional trap. Moreover, the intensity of rent-seeking behavior increases both with progressive redistribution of wealth and with widening of the ruling class. Our results allow characterizing wealth distributions, wherein it is better to redistribute wealth or to expand the ruling class in order to improve institutions and limit rent-seeking incentives.