1. A proportional tax requires everyone to pay fixed share a > 0 of total income y in

taxes, so that their tax bill is t(y) = ay.

Verify using properties of the Lorenz curve that inequality is unchanged by a proportional tax.

2. A progressive flat tax has the form t(y) = ay - s, where a > 0 is the marginal tax rate and s > 0 is a grant. Does a progressive flat tax lead to more equal distribution of after tax income?

Explain.