I had occasion to read the letter “Reasons for Pittsburgh population loss” (April 7, TribLIVE). I wanted to draw your readership’s attention to this argument:
“People who live in the city pay a 3% wage tax. So, if you and your spouse work, you now lose 6% of your total income.”
Let me assure the readership of the Trib that as someone who personally just paid his and his wife’s income taxes, the rate is not 6% for married couples. We can show this is false through the distributive property of multiplication, which I will now demonstrate.
The distributive property of multiplication holds that X times the sum of Y and Z is equal to X times Y plus X times Z. If we take X to be the city’s 3% wage tax, Y to be a husband’s salary, and Z to be a wife’s salary, we can see that the tax rate does not change simply by adding Y and Z together.
Here’s a practical example you can do with a calculator. You can prove the distributive property for yourself. Take a couple earning $100,000 each. The city assesses a 3% tax against each of them. What is the tax assessed on each spouse? Now add the tax bills together. What is the total tax liability? Next, add the spouses’ incomes together. What is their total income?
Now, divide their total tax liability by their total income. What is the percentage?
Andrew Bryk
Friendship