Assume instead there is uniform taxation, so all individuals face the same tax price. Recall that along each individual's demand curve, the price equals the marginal rate of substitution. Thus,

the marginal rate of substitution is proportional to income. Assume that income is symmetrically distributed, so that mean income equals the median. Explain why the majority voting equilibrium will be Pareto efficient. Now, assume that income is not symmetrically distributed, but rather is skewed toward higher incomes. Will the majority voting equilibrium still be efficient? Will there be an under- or oversupply of public goods?

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