There is a federal income tax that all U.S. citizens must pay, regardless of where they live. Most citizens also owe a local income tax to the state or country they live in such as Ohio or China.

The title indicates that this problem is about vertical tax externalities, which result when someone owes taxes to two governments (e.g. China and Ohio) for the same income.

a. We can summarize the taxable income produced by a person (or a bunch of identical people) by the function TI (taxable income) = 200 - 100t. Why does it make sense for taxable incomedecreasesas the tax rate increases?

In general the tax revenue you collect is (taxable income)x(tax rate) so here it is R=(200-100t)t .

b. The federal government has decided to set a tax rate of t=0.15 meaning 15%. How much tax revenue does it collect?

c. China also taxes U.S. citizens who live in China. They must pay a tax rate of c=0.1 or 10%. This requires you to modify the equation for taxable income to factor in both taxes. Set up an equation for China's tax revenue and calculate how much tax revenue it collects from Americans, given that the U.S. tax is t=0.15.

d. With this new Chinese tax, how much revenue is the U.S. government collecting? Briefly explain why this makes sense.

e. Repeat the calculations on revenue from above except where TI(t) = 200 - 200t. Briefly explain what is going on using the word elasticity.