The government typically collects redistributes income through distortionary taxation.

Consider now the problem when the government taxes two productive people, not in order to redistribute but to collect taxes that are used for government spending.

There are two people in the economy, each productive.

Person 1 producesY1() = 1a1

Person 2 producesY2() = 1a2.

Parametersa1anda2are both in the interval [0.5,1].

If the government sets a tax[0,1], what is the tax revenue

that it collects from agent 1? From agent 2? What is the total tax revenue?

What is the tax ratethat maximizes the total tax revenue that the government can collect? If the government currently sets a tax rate > , what would your policy recommendation be?