Pareto Improving Taxation in Incomplete Markets
When asset markets are incomplete there are almost always many Pareto improving policy interventions. Remarkably, these interventions do not involve adding any new markets. Focusing on tax policy, I create a framework for proving the existence of Pareto improving taxes, for computing them, and for estimating the size of the Pareto improvement. The protagonist is the price adjustment following an intervention. Its role is to improve on asset insurance by redistributing endowment wealth across states. If taxes targeting current incomes are Pareto improving, then they must cause an equilibrium price adjustment. Conversely, if the price adjustment is sufficiently sensitive to risk aversions, then for almost all risk aversions and endowments, Pareto improving taxes exist. I show how to verify this sensitivity test with standard demand theory, which Turner (2003a) extends from complete to incomplete markets. I show that different policies generically admit Pareto improving taxes, by showing they all pass this same sensitivity test. These include (a) taxes on asset purchases, (b) lump-sum taxes on present income plus one flat tax on asset purchases, (c) asset measurable taxes on capital gains, (d) excise taxes on current commodities. To numerically identify the Pareto improving taxes, I give a formula for the welfare impact of taxes. The formula requires information about individual marginal utilities and net trades, and about the derivative of aggregate, not individual, demand with respect to prices and taxes. To bound the rate of Pareto improvement, I define an equilibrium's insurance deficit. Pareto optimality obtains exactly when the insurance deficit is zero. If the tax policy targets only current incomes, then the implied price adjustment determines the best rate, by integration against the covariance of the insurance deficit and net trades across agents
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