I'm confused about the dollar, and maybe you are too.

No, I'm not talking about our currency's 13 percent appreciation against the euro since last summer. With Greece in danger of default, it's no mystery why bankers and currency traders would rather hold dollars.

What's confusing are the greenbacks in my pocket. Some folks say they are wasteful, because they wear out after just a few years. Should we feel guilty because we're not all using $1 coins?

On the other hand, Vice President Joe Biden recently said that we'll save $50 million a year by making fewer pieces of metal with dead presidents on them. How can something simultaneously be both good and bad for the federal budget?

As it turns out, both sides of this debate are stretching the truth. Biden's cost savings are real if you only consider production costs, but his budget math neglects the magic of seigniorage, the process by which a government turns cheap pieces of paper or metal into money.

In fiscal 2011, each $1 coin cost just 18 cents to make. The U.S. Mint's seigniorage on the coins amounted to $382.8 million. With the production cut, much of that profit will disappear, adding to the deficit.

However, Americans don't use the metal dollars, so 1.4 billion of them are sitting in Federal Reserve vaults. The only way to get those coins into circulation would be to stop printing $1 bills.

A couple of bills have been introduced in the current Congress to do just that, and a group called the Dollar Coin Alliance argues that the switch from paper to metal would save taxpayers money. Here again, though, the logic isn't so clear.

The Government Accountability Office, in a new study, estimates that switching from bills to coins would provide a net benefit to the government of $4.4 billion over 30 years. That's $148 million a year, on average, which is smaller than a $184 million annual estimate that the GAO made last year.

The benefit, though, does not come from lower production costs. Yes, bills wear out faster than coins, but they're much cheaper to make.

New cash-handling equipment at the Federal Reserve has reduced the wear and tear on greenbacks, and the average $1 bill now lasts 56 months, according to the GAO. A decade ago, its lifespan was 24 months.

The difference has made paper dollars more cost-effective than metal ones. Based on production costs alone, the GAO says, eliminating $1 bills would cost the government $1.8 billion over 10 years.

The $1 coin would still reduce the deficit through seigniorage. Based on the experience of Canada and Britain, which did away with their smallest bills decades ago, the GAO assumes that we would replace each dollar bill with 1.5 dollar coins.

That's because many people empty their pockets at the end of the day, throwing coins into a jar at home.

Think of the $1 coins in that jar as a sort of a voluntary tax. It would be your small contribution toward deficit reduction. And it's what the dollar-coin advocates rely on to make their case, because they don't have a strong argument based on efficiency.

In Congress, though, efficiency arguments matter less than interest-group politics. The Dollar Coin Alliance includes metal manufacturers and the Machinists union; greenback backers include Sen. Scott Brown, a Massachusetts Republican whose state is home to the company that makes paper for U.S. currency.

To those folks, dollars equal jobs, and that's math that everyone can understand.