### Tax holiday, not math holiday

For the first time since I was a kid, I wrote a letter (or email) to the newspaper today. Today's Boston Globe had an editorial entitled "Let retailers host tax holiday." Although I agree with the general sentiment that the state should allow retailers to pay the tax on the part of consumers if they want to, the editorial got the math wrong. As a long-time math geek, I couldn't let this one pass. My email to the Globe:

In today’s editorial, “Let retailers host tax holiday”, the Globe got the policy right but the math wrong. I am in favor of allowing retailers to pay the sales tax on the part of the consumer. But, for this to be revenue neutral to the state and the consumer, the math doesn’t work.

If an item is sold for $100, there would normally be a $6.25 tax charged by the retailer and sent to the state. The consumer is out $106.25, the retailer makes $100, and the state gets $6.25. If the retailer wants to ‘pay the tax’ on the part of the consumer, they would charge the consumer $100, but what do they send to the state?

If they send the state $6.25, that implies that the item cost, without the tax, was $93.75 (a 6.25% discount). That would normally mean that $5.86 in tax would be charged, for a total consumer cost of $99.61. So, the retailer would be overcharging the consumer 39 cents and passing this on, in full to the state. That keeps the state revenue neutral, but overcharges the consumer. And, the consumer would pay a total of $100 vs. $106.25, a 5.88% discount (not 6.25% as was incorrectly calculated in the editorial).

An alternative would be to charge the consumer $100 and send the state $5.88. This reflects an underlying item cost of $94.12. The $5.88 is 6.25% of this. This is neutral to the consumer and would reflect a 5.88% discount. However, the state loses $0.37 or 5.92% of the original tax revenue. This is probably what you meant when you said ‘have the retailer pay the tax’, but will cost the state some money (but nowhere near as much as a state tax holiday). In these tough times, the state probably can’t even afford this.

To keep the state and consumer neutral and have the whole thing funded by the retailers, the best idea would be to keep the item price at $100, charge the consumer $106.25 total, including the $6.25 sales tax, and do an after-the-fact rebate of $6.25 to the consumer. The state gets their full $6.25, the consumer only pays $100 net, and the retailer ends up with $93.75. No law needs to be changed or passed for this to happen. It’s not clear that a 6.25% rebate would be attractive to consumers, but that’s the one that makes the math work.

The bottom line to all of this is that to undo a 6.25% mark-up (our sales tax), you only need to take a 5.88% discount. Perhaps it’s this confusion that caused our elected representatives to take a voting holiday on this issue. Let’s hope they spent the time studying arithmetic.

Sincerely,

Mike Feinstein

It's a fine point, but somehow or another, retailers have to report their sales and tax payments to the state. So, the math has to be right. And, basic math seems to elude even well-educated editorial writers at times.