“If you haven’t got a penny, a ha’penny will do,

“If you haven’t got a ha’penny, then God bless you. …”

You haven’t got a ha’penny, of course, and even if you did, any self-respecting Christmas caroler would be insulted to be offered so little. A half-penny today would rightly be seen as worthless, and a burden to carry around in pocket or purse.

Indeed, that’s why the U.S. Mint stopped producing half-cent coins, way back in 1857.

But whoever made that decision must surely be spinning in the grave. Because our government continues to churn out billions of pennies per year, even though the one-cent coin today is worth a tiny fraction of the 1857 ha’penny.

According to economist Robert Whipple of Wake Forest University, the purchasing power of a half-cent in 1857 was greater than that of today’s dime – 11.3 cents, to be exact.

That’s adjusting for consumer price inflation. Adjusting for changes in wages, it’s even more dramatic; a half-penny then was worth as much to the average worker as a quarter is today.

So why are we still hauling around coins worth a tenth (or a twenty-fifth) as much as those considered too small to be useful 150 years ago?

Good question.

It gets even stranger when you consider that the U.S. Mint now loses nearly three-quarters of a cent on every penny it mints.

The culprit is the rising cost of zinc, which makes up 97.5 percent of each penny. (Copper was basically abandoned after 1982 because of the same problem.)

If you melted down a penny and sold the zinc on the world commodity market, you’d make approximately a tenth of a cent in profit.

That may not be enough to make you consider installing a smelter in the back yard. But it ought to be sufficient reason to make the U.S. Treasury finally pitch the penny into the piggy-bank of history.

Governments, after all, don’t like to lose money when they make money. Seignorage – the difference between a coin’s monetary value and the cost of producing it – has been a mainstay of public-sector finance since approximately the time of Charlemagne.

It’s how many medieval princes built their palaces and supported their armies. And even in modern times, it pays some bills.

Not long ago, I noticed some handsomely refurbished meeting rooms at the Philadelphia Federal Reserve Bank’s building on Independence Mall. Our tax dollars at work? I asked. Nope – seignorage.

That’s one big reason for the Mint’s recent burst of numismatic creativity, which you can see in such projects as those quarters with state-inspired designs on the back – or the recently announced campaign to once again try to get people to use a dollar coin.

As you may have read, the Mint next year will issue $1 coins carrying the images of presidents on the front and the Statue of Liberty on the back.

The Treasury apparently thinks Washington, Jefferson and James Buchanan can succeed where Susan B. Anthony and Sacagawea did not.

Or maybe they don’t care. Unlike pennies, all those dollar coins sitting in drawers or jars or collection albums represent actual profits to the Treasury, which spends substantially less than $1 to produce each one.

According to the Website coinflation.com, for example, each Sacagawea dollar coin contains less than six cents worth of metal at current world prices.

Critics of the $1 coin maintain that the government can’t be serious because it’s continuing to print greenbacks alongside the new coins. So Americans have little incentive to change their spending habits.

So maybe it’s time for both the dollar bill and penny to disappear.

Certainly that’s what fiscal prudence would dictate. Consider that the U.S. Mint is expected to produce around 9 billion pennies this year. At a loss of 0.75 cents per coin, that’s $67.5 million less we taxpayers would have to pony up.

Not a ton of money by Washington standards. But hey, every penny counts.

Andrew Cassel is a columnist for The Philadelphia Inquirer.