United States citizens living in Switzerland must pay taxes on their income to both the United States and to Switzerland. Suppose that the United States tax is 28% of their taxable income after deducting the tax paid to Switzerland. Suppose that the tax paid to Switzerland is 42% of their taxable income after deducting the tax paid to the United States. If a United States citizen living in Switzerland has a taxable income of $75,000, how much tax must that citizen pay to each of the two countries?

To calculate the tax paid to each country, we'll start by finding the taxable income after deducting the tax paid to each country.

Step 1: Calculate the tax paid to Switzerland.
The tax paid to Switzerland is 42% of the taxable income after deducting the tax paid to the United States.

Taxable income after deducting US tax = $75,000 * (1 - 28%) = $75,000 * 0.72 = $54,000
Tax paid to Switzerland = $54,000 * 42% = $22,680

Step 2: Calculate the tax paid to the United States.
The tax paid to the United States is 28% of the taxable income after deducting the tax paid to Switzerland.

Taxable income after deducting Swiss tax = $75,000 * (1 - 42%) = $75,000 * 0.58 = $43,500
Tax paid to the United States = $43,500 * 28% = $12,180

Therefore, the citizen must pay $22,680 to Switzerland and $12,180 to the United States.