Social welfare functions derived from revealed preference

The social welfare functions used in policy evaluation typically put more weight on poorer people, justifying redistribution from the rich to the poor. The reasoning is that the marginal benefit of a unit of money is greater for the poor than the rich. However, people with a greater marginal value of money are more motivated to earn and save, other things equal, so more likely to become rich. In this case, the rich have on average a higher marginal benefit of money than the poor, or a lower marginal cost of accumulating it. If the justification for redistribution is an interpersonal utility comparison, then revealed preference suggests a greater Pareto weight for richer people, thus redistribution in the opposite direction to the usual.

If the marginal utility of money decreases in wealth or income, then people earn until the marginal benefit equals the marginal cost, so the comparison between the rich and the poor depends on their marginal cost of earning, evaluated at their current wealth and income. The cost and benefit of earning may both be higher or lower for richer people. In a one-shot model, whoever has a greater benefit should receive redistributive transfers to maximise a utilitarian welfare criterion. Dynamic indirect effects sometimes reverse this conclusion, because incentives for future work are reduced by taxation.

Those with a high marginal utility of money are more motivated to convince the public that their marginal utility is high and that they should receive a subsidy. The marginal utility is the difference between a benefit and a cost, which determine whether the poor or the rich have a greater incentive to lobby for redistributive transfers. The marginal cost of an hour of persuasion equals the person’s hourly wage, so depends on whether her income is derived mostly from capital or from labour. For example, both rentiers and low-wage workers have a low opportunity cost of time, so optimally lobby more than high-wage workers. If lobbying influences policy (which is empirically plausible), then the tax system resulting from the persuasion competition burdens the high-wage workers the heaviest and leaves loopholes and low rates for capital income and low wages. This seems to be the case in most countries.

A tax system based on lobbying is inefficient, because it is not the people with the greatest benefit that receive the subsidies (which equal the value of government services minus the taxes), but those with the largest difference between the benefit and the lobbying cost. However, the resulting taxation is constrained efficient under the restriction that the social planner cannot condition policy on people’s marginal costs of lobbying.

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