Ending the penny won't lead to more nickels

Donald Trump has ordered the U.S. Mint to stop producing the penny because it is unprofitable, costing 3.69 cents to produce each one.

In response, the lobbyists that earn big profits from the ongoing existence of the penny have come out in full force with dubious arguments for why the penny is still vital. Their newest bit of disinformation is that removing the penny will increase reliance on the nickel, which costs 13.74 cents to produce, thus putting the U.S. public in a worse position than before. This shift-to-nickels claim is wrong, but all sorts of media sources [CNN | Bloomberg | ABC News | TIME ] are repeating it without challenging it.

While it's true that the nickel is unprofitable to produce, usage of the nickel will *not* increase when the penny is removed. I'm going to show why shortly, but first a quick comment on the general idea of ending the penny.

For long-time penny critics like myself, Trump's idea is tragically undeveloped, even clumsy. All serious minds agree that the U.S. penny is pure monetary pollution and needs to be abolished. It's too small to be meaningful, yet society is forced to continue counting in pennies because the political mechanism for improving America's coinage system is broken, having been captured by the coin lobbyists and conspiracy theorists. (I wrote about the coin lobby in Pennies as state failure.)

However, to liberate society from the hassles of the penny the U.S. government can't just stop minting it, as Trump seems to think, because this doesn't prevent the existing stock of pennies that has accumulated over the last century or two from continuing to pollute Americans' economic lives. To solve this, the government must establish a rounding rule for individuals and retail establishments. When paying for goods at the checkout counter, all amounts owed must be rounded to the nearest five cents in order to prevent already-existing pennies from infiltrating day-to-day shopping experiences. 

What would this rounding rule look like? Say that your grocery bill comes out to $10.87. You pay the cashier $11 in cash. Instead of getting 13 cents change (a dime and three pennies) your bill would now be rounded down to $10.85, and you'd get a 15 cents in change instead—a nickel and a dime.

If your bill came to $10.88, it would be rounded up to $10.90, and you'd get 10 cents change instead of 12 cents.

Voila, the penny-infiltration problem is solved. No annoying one-cent pieces required in day-to-day economic life.

Now that we've got rounding out of the way, we can tackle the big penny-to-nickel lie that the coin lobbyists are circulating. Mark Weller, director for the lobby group Americans for Common Cents, was quoted in CNN last week:

"Without the penny, the volume of nickels in circulation would have to rise to fill the gap in small-value transactions. Far from saving money, eliminating the penny shifts and amplifies the financial burden."

Weller goes on to caution that the U.S. Mint may be forced to make in the range of 2–2.5 billion nickels a year if it stops producing pennies permanently, far higher than its normal run-rate of 1.0–1.6 billion over the past decade. The implicit threat here is that it's better for America to be wounded by the penny than have their throats slit by the nickel. Keep in mind that Weller and his lobbying group are sponsored by Artazn LLC, the firm that sells coin blanks to the U.S. Mint for eventual stamping into pennies.

The idea that more nickels will be required in day-to-day transactions if the penny disappears is superficially seductive, but it's wrong. That's because the removal of pennies does *not* require that nickels do any more transactional work than before. 

First, let's rebut it with a real-life example. In 2012, Canada abolished its one-cent piece and implemented five cent rounding. No nation is more similar to the U.S. than Canada, so it serves as a great foil. Did Canada experience a doubling or tripling in nickel production in order to fill the gap left by the penny? Below is the Royal Canadian Mint's nickel production from 2005 to present:

No, the amount of nickels didn't jump in 2013 or 2014, the year after the penny's abolition. In fact, since the penny ban in 2012, Canadian nickel production has remained well-below its pre-2012 level of 200 million to 250 million.

Having rebutted Weller's fill-the-gap claim by working through an example, now we'll rebut it mathematically.

Let's take a look at all retail transactions that end in 1 cent to 99 cents, and how these transactions differ in a penny and post-penny world. A store will want to have enough change on hand to facilitate each of these one hundred transaction types. In the table below, I’ve listed all one hundred transactions and, assuming the customer pays with the next whole-dollar amount (e.g., if $40.71 is due, they pay with $41), how much coin change is required.

First, let's look at the yellow half of the table, which shows how much change must be returned to the customer when the penny is still in circulation. In total, 200 pennies will be required for all one hundred transactions, with the one-cent piece showing up in 80% of all transactions. As for the nickel, a total of 40 nickels will be required, with the customer getting a nickel back in 40% of all transactions.

Now let's remove the penny and introduce rounding to the nearest five cents. Will more nickels be required to "fill the gap" left by the penny, as alleged by the coin lobby? 

Take a look at the orange area, which shows the shopping experience in a post-penny world. In the first column, I provide the rounded amount that the customer must pay. The demand for pennies has obviously fallen to zero in this world, as the policy intended. But the total amount of nickels required in our one hundred transactions remains at 40, as before. Nothing has changed. Note that the total number of dimes and quarters required also stays constant in both worlds, at 80 and 150 respectively, with 60% and 70% of all transactions needing these larger coins as change.

What is happening? If you look more closely, you'll see that certain transaction amounts that didn't require a nickel in change before, like $0.96, now require a nickel (since the amount due is rounded down to $0.95.) But other amounts that once required a nickel, like $0.92, no longer do (since the amount is rounded down to $0.90, for which dimes are the most efficient change.) In short, for every amount owed by the customer that now requires a nickel in change, another amount owed no longer requires a nickel. 

So when lobbyists like Mark Weller say that "the volume of nickels in circulation would have to rise to fill the gap," their math is flat out wrong: the removal of the penny does not require more nickels as change. 

In real life, these one hundred transactions may not be entirely random or uniformly distributed; shopkeepers may have certain preferred prices points, thus skewing the amount of coins required as change. But I doubt the effect is very large, as suggested by the Canadian example.

So both mathematically and empirically, Americans shouldn't be afraid of dropping the penny because they'll be saddled with even more awful nickels. That's just lobbyist propaganda. In a post-penny America, you get all the benefits of zero pennies with no extra nickels required.