4 Redistribution in democracy Assume that each individual, i, gets income yi, and the average income is . The tax rate is t, where 0 t 1. Each…

4 Redistribution in democracy
Assume that each individual, i, gets income yi, and the average income is ȳ. The tax rate is t, where 0 ≤ t ≤ 1. Each individual also get a universal transfer, f . This transfer comes from tax net of deadweight loss f = (t − 0.5bt2)ȳ.
4 What does higher b suggest?
What is each individual’s net income, Ï€i?
What is the optimal tax rate for each individual, ti, respectively?
Will the rich prefer a positive tax?
Assume that the tax rate is decided by majority voting. Denote the median income as ym. What will the voted tax rate be?
Assume that the median income is smaller than the average income. Given the average income, does lower median income suggest more or less severe inequality?
Will more severe inequality (given ȳ, lower ym) increase or decrease the voted tax rate? Why?
Will higher efficiency in tax collection, i.e., lower b, increase or decrease the voted tax rate? Why?
Why does this makes sense? Hint: For each individual, what are the implications of a higher tax rate? How will higher efficiency in tax collection affect those implications?