# Black Median Voter Theorem Predictions for Democratic Society

Question

Consider a society that is trying to decide its tax policy on income as well as on bonuses that individuals receive at work. There is a continuum of individuals in society, indexed by i E [0, 1], where each individual i has a salaried income, y, and a personal bonus bi where bi is drawn from a bonus distribution function F(.) on [0, Do] with an expectation (average) / 1 and a median, in The society must decide on an income tax rate ty E [0, 1] and on a bonus tax rate 4 E [0, 1]. All tax proceeds are redistributed equally to individuals in the form of a transfer 71(ty tb) = tyy tbpd. An individual's total after tax income, h, is given by,

Ii = (1 ty)y (1 t )bi tb)

• Assume that tb is fixed at some level tb. Assume that the society is only deciding on ty. Do individuals have single peaked preferences? Would Black's median voter theorem have any predictions for the choice of ty in a democratic society?
• Assume that ty is fixed at some level ty*. Assume that the society is only deciding on tb. Do individuals have single peaked preferences? Would Black's median voter theorem have any predictions for the choice of tb in a democratic society?
• Assume that the society is deciding on both ty and tb. Do individuals have single peaked preferences over policies (ty, tb)? Would Black's median voter theorem have any predictions for the choice of (ty, tb) in a democratic society?

Summary: This question belongs to political economy and discusses about society that is trying to decide its tax policy on income as well as on bonuses and to find predictions of society.

Total word count: 735

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