Question

Dear Mitch,

My whole family has a question for you, and we even have answers, but the problem is that our answers are all DIFFERENT, and we are really hoping you'll settle the matter, or at least try to, *please*.

Okay, the other day my father read us an article that said that because copper was getting more expensive than it used to be, and there's some real copper in every penny, now pennies are worth almost five cents each! So my older brother said, "Then that means **nickels** are worth **25 cents**!" He headed upstairs to his piggy bank to see how much more money he had than he thought. (He's always counting it because he wants to buy some toy that's really big and loud.) So anyway, on his way up he shouts, "And that means that every **quarter** is worth **one-dollar-and-twenty-five cents**!" My mom and I didn't know if we should break the bad news to him that nickels and quarters don't have any copper in them, so the rise in copper prices wouldn't change a thing about them, just the pennies. My father, however, actually agreed with my brother and said a coin doesn't have to have any copper in it, as long as the pennies still are worth five cents each. My mom and I say NO, it's only the coins with copper. So who's right?

Sincerely,

Small Change

Answer

Dear Big-Change-On-Its-Way,

Good news: Everyone is right, and I'm not kidding! (I know usually in math they tell you that there is a right answer to every question and all others are wrong, but it turns out that many problems can be solved in different ways and you can come up with different answers that are equally correct. (You could also come up with many different answers, all of which are wrong, but luckily we don't have that here!)

First, as it happens, I came across the same article or another that expressed the same thing, and I must say I found myself curious to see what the outcome will be. Here's what I think: The copper certainly is a very important factor in the whole question, so if the article is correct in expressing that pennies are worth (or soon might be worth) close to five cents each because of this, it is easy to envision the first result: a certain percentage of people will try to hang on to their pennies more than previously, and perhaps even make a little effort to collect them more by waiting for small change when making transactions, etc. Of course the trend will only remain for as long as the price of copper stays high; if it goes down, then the value of the penny will come down as well. However, history has shown that most things gradually or quickly become more expensive over time. Your question about the other coins needs to be considered in more specific terms than simply their "worth". We have to ask "to whom" are these coins worth this much?

Why does the "to whom" part matter? It matters because in order to get each of the other coins to jump up in value a person would have to do a little work (But not much). She (or he) would have to cash these other coins in at a bank or store and get its **usual standard value **back, and get it **ALL** in pennies. Of course, the person would have to carry out this exchange with someone who was thinking of pennies only in terms of their old standard value (I believe that would include most people, and certainly all banks).

So each nickel you collect you would have to exchange for five pennies, and for each dime collected you'd have to get ten pennies. Quarters would be twenty-five pennies each, and fifty-cent pieces would be fifty pennies each. Then, as long as each penny can be sold for five cents (but probably not five pennies because very few people would fall for that... trading five of their pennies for each one of yours!!), you would indeed find yourself presented with an interesting potential transaction. You'd have to gather pennies into groups of twenty to get $1.00 for each group from someone who values them at five cents each, such as a business that uses copper.

In theory, and I mean *mathematical* theory, once a penny is really worth five cents, then all the other coins should shift values upward accordingly, which would be five times their old value. But in short time I believe there would be a 'ripple-up' effect, and dollar bills that could be bought for 20 pennies would also be revaluated to make sense.

And so dollars would get cheaper (worth less than their value before the shift), so the prices of items in stores would have to climb until they were five times their old price. And that would make all the effort of obtaining and exchanging pennies worthless (or just breakeven). But since most people are probably not interested or able to spend their time collecting pennies and trading them in or 'reselling' them, I think for a short time until a lot more people catch on, one could do some of these interesting things and make a profit.

However, such an opportunity typically does not last long; what happens is that when the government learns that coins are removed from circulation because their ingredients are more valuable than the coin, it stops production on the undervalued coin and officially takes it out of circulation. The coin is "retired". In this country there was once a half-cent coin and a two-cent coin, for example, but now both of these are virtually impossible to see outside a museum. So that leads to what is often the last twist in the history of a coin like the penny, and it's this: once the government retires a coin, it becomes a little more valuable to people who collect coins as a hobby. People seem to want things that are "no longer available". And when that happens, a penny probably will be worth more than five cents – but not if it's been melted! Either way, the next time you see a penny on the sidewalk, you just might think a little harder before ignoring it, or at least pause a little longer. Serious mathematicians, though, will probably pause for five times as long as they once did.

Hope that helps,

Mitch

P.S. If I had a million dollars for every time someone asked me a question like this, I'd now be a millionaire!