According to a recent article, if memory serves (I'm too lazy to actually look up minor details like whether I'm correct), it now costs more money for the U.S. Treasury to produce a penny than the penny is actually worth.
Let's consider this: Is it actually worth the time to mess around with pennies? Let's say it takes 5 seconds to pick up a penny and put it somewhere like your wallet. If that were your job, you'd make (calculatory skillz...) $7.20 per hour. This is less than minimum wage. Therefore, it actually saves money to just leave the penny on the counter.
However, this solution loses you a bit of cash. Let's try to figure out how to keep your cents (if discarding sense, ha ha ha; that needed saying) without using pennies. How can you pay someone 1/5 of the smallest denomination possible, if we junkify pennies and just use nickels? Here's where you get to use your probability skillz (or lack thereof): What if you give someone a 1/5 chance that they win a nickel? The expected value of that is 1 cent. Idea!
Now, the question is, how can one make a really fast coinflip that both the customer and the cashier consider fair? If you put a randomization function into the cash register, the customer might get suspicious. Therefore, try this functional randomizer (repetition!).
Whenever someone doesn't feel like getting small change, he adds that amount to a display that counts unused change. If that amount exceeds 5 cents, then he gets a nickel and the count is reduced by 5. Otherwise, the counter remains in place for the next customer. This does indeed give you the right probability for getting a nickel, if you assume all numbers 0-4 are equally likely. In fact, this lets you customize your level of accuracy; if you don't give a cheese about anything less than a quarter, you can just not collect that. If enough people do this, then it speeds up cash transactions AND it gives you the right expected payoff. It seems to work for everyone. Skillziness!
Comment if you think this is brilliant or numbskulled, or if you have a suggestion. I can edit this thing to include your ideas...
Or mine. It just occurred to me: Couldn't someone exchange $10,000,000 for a billion pennies from the Treasury, then melt it all together and sell them the metal for $10,100,000 (or whatever the exact number is)? It'd be funny, at any rate...
To John's comment: By strategically waiting in line, you're getting yourself 4 cents, max. Not even that, in fact. Let's assume everyone else's purchases have randomly distributed costs (meaning, 0-4 extra cents is random). Letting someone go ahead of you when the counter is at 0 (the best case) is then going to get you, on average, 2 cents. If we use my "minimum wage" cost-effectiveness model, we find that line-waiting pays minimum wage when it takes less than 10 seconds for the person in front of you to do business. I don't recall it ever taking less than 30 seconds. So, no rational person would do that. Insane people could be doing far worse things than cheating you out of 4 cents. The possibility is therefore negligible.
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3 comments:
You should determine the cost of implementing such a system. If you levy taxes on the sale of pennies to collectors, and you save like .2 cents per penny not minted (by the way, we save .73 cents for each nickel not printed, so actually you should have the counter go up to 10), how long will it take to earn the money back?
Also, you should consider the fact that people will do stuff like "strategic line waiting" to get the money...
You certainly don't want people fighting for the fourth place in line, or something. However, it'll probably work. Nickels are irritatingly small, too, by the way. I don't like quarters, even!
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