Treasury Department set to phase out the penny

[Bernardo de La Paz]

158. Thx. The Joys of Being Wrong, the diligence of DUer "SunSeeker", and the Elimination of the Penny

Long story short: I made an assumption that was wrong, but then I found that I was kind of right in one way but the situation is a bit mixed.

Long story short on Elimination of Penny: Using Lombra distribution of prices, there is a cost to the poor of about 3 tenths of a cent per cash transaction if there is not a sales tax, but no cost if there is sales tax.

The joy is learning that I was wrong. Now I know better. I was however right in how it works in Canada based on grocery bills because they almost always have at least one taxable item (food not generally taxable).

There was a big discussion in GD about Eliminating the Penny. There was a lot of back and forth about greed and history and ways of doing it and fairness. I made an assumption to think mathematically about it and made arguments for fairness based (implicitly) on math. My assumption was wrong.

This came to my attention from a paper quoted by SunSeeker, who had done more due diligence in the thread than all of the rest of us put together. Hat tip to SunSeeker

In the paper by Shapiro 2017 it references a paper by Lombra from 2001, which I had to really dig for to find. Reading Lombra's paper I suddenly realized my folly. I had assumed random prices. I should have seen the obvious: a lot of prices end in 99 cents. There was veiled reference to a counter study with regard to sales taxes. Lombra rebutted it in 2007. His rebuttal seemed weak. Then I found the counter by Warples in 2007 considering the effect of sales taxes that Lombra was rebutting. Shapiro seemed to be ignoring Warples.

I wondered if the studies were done on slow old machines because 5,000 transactions seemed pitifully small for a simulation. I thought, "I can whip up a Python program lickety-split". Thus I embarked on hours long nerdiness tuning a program I wrote.

I ended up doing 16 simulations with over three hundred million transactions simulated. They were in four groups of four, each being about 20 million transactions. I simulated prices randomly in the range of 20 cents to 9.99, but I made the tail digit distributions fall into four classes. Lombra had 3,585 prices, I had 4,000. In each group I ran with no tax, medium tax, high tax and random tax in the range to the high tax. (Random taxes simulates a nationwide range.)

A summary of the summary: Rounding prices is the fairest, but not the most realistic policy. Random price tails is as expected even (fair) but does not exist. Realistic price distributions, either Lambro or another reasonable one are unfair by about 3 cents per transaction in the absence of taxes, but taxes make the rounding fair (not to forget that sales taxes are regressive). The level of taxation (when not zero) did not affect any scenario differently.

The fuller report and the Python program are in the Science Forum.