The class began with what I’d planned – the fair value and average values of a lottery ticket, computed as weighted averages. The difference is the house advantage, which you may be willing to pay for a variety of reasons (raise money for the PTA, the thrill of the possible win).
Then we did the problem from the book on the state lottery figures (from 2006). 69% of what is collected is returned as prize money, so the fair value of a $5 ticket is 0.69*$5. That was easy. Then we looked at the fact that $761 million was returned to cities and towns. Reading further told us that was 23% of what was taken in. I asked the class to compute the gross lottery revenue – and got blank stares, followed by guesses about what to multiply or divide by what. Very disappointing since we’d spent the first two weeks of the semester on just that kind of calculation. I asked them to figure out the answer working in groups of three (as they were seated). The tutor and I spoke to each group, to make sure that everyone really understood the principle that led to the calculation 761/0.23. The fact that this was necessary so late in the term leads me to question the value of all the lectures… maybe lectures really don’t work at all, even mine, which I like to imagine (hope) are really interactive. Perhaps I should try (next semester) to have the class spend a much larger percentage of time doing group work. It’s been valuable each time I do it, but find it difficult to bring myself to do it more.
I used the fact that the lottery raised money for “cities and towns” but that I never played led to a discussion of a regressive tax. This one is paid by people who are poorer and who do not know much about quantitative reasoning. It soon became clear from the class responses that most of the students had no idea how taxes were collected! So we spent the last half hour on the tax code: state sales tax (6.25% on most retail purchases), state income tax (5.3%), federal income tax ( found the brackets and percentages on line), social security tax (6.x% on the first $106K).
Many believed (unthinkingly) that when you moved to a higher (federal) bracket you paid a higher percentage of all your income (s0 could be worse off by making more). That classic error was part of some political ad in the last presidential campaign.
We computed the effective tax rate on an income of $10,000 – turns out to be about 25%. Didn’t get to work out the taxes on an income of $1,000,000 – with plausible deductions, the cap on social after the first $106K and the fact that rich people spend a much smaller fraction of their income on taxable goods the effective tax rate might be smaller. This would make a really good spreadsheet!
All in all, I think the class was very informative – for me and for them. And I will never skip the class on taxes again.
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