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We investigate the dynamics of wealth inequality in an economy where households have positional preferences, with the strength of the positional concern determined endogenously by inequality of wealth distribution in the society. We demonstrate that in the long run such an economy converges to a unique egalitarian steady-state equilibrium, with all households holding equal positive wealth, when the initial inequality is sufficiently low. Otherwise, the steady state is characterised by polarisation of households into rich, who own all the wealth, and poor, whose wealth is zero. A fiscal policy with government consumption funded by taxes on labour income and wealth can move the economy from any initial state towards an egalitarian equilibrium with a higher aggregate wealth.