We analyze an assignment problem of indivisible goods to a continuum of consumers in the presence of binding budget constraints and widespread externalities. We consider a benchmark model in which an indivisible good generates pollution. We introduce costly sharing to the model. In the presence or absence of sharing, we find the market permit equilibrium price and allocation for any pollution target and distribution of income. Except for a relatively small sharing cost parameter, the market allocation necessarily differs across one or more groups. We find that all individuals are indifferent among the allocations of the indivisible good, the lower the sharing cost, the less skewed the distribution of income is toward the poor, or the larger the middle class. over another. In the absence of any re-distribution of income the outsiders may be worse off in the market outcome relative to the laissez-faire outcome. Since a market-based policy favours the upper income group while compensating outsiders through a redistribution of income (based on ownership), we compare a market-based outcome (that targets a given pollution level) to the laissez-faire outcome. We provide necessary and sufficient conditions for the Pareto domination of the laissez-faire outcome by the targeted market equilibrium outcome. Pareto domination occurs the lower the sharing cost, the less skewed the distribution of income is toward the poor, or the larger the middle class.