The coronavirus pandemic has created a lot of economic challenges, but the latest one is not one anybody could have predicted. Because if it could have been predicted, it wouldn't have ever become a challenge in the first place.
We're talking about the national coin shortage, where pennies, nickels, dimes, and quarters have fallen into short supply across the United States. It turns out the coronavirus is responsible for that problem, because to fight off the coronavirus, many Americans are apparently tossing lots of coin to their witchers.
Oh, if only that were true! The Federal Reserve confirmed what the real story is in an official statement back on 11 June 2020.
The COVID-19 pandemic has significantly disrupted the supply chain and normal circulation patterns for U.S. coin. In the past few months, coin deposits from depository institutions to the Federal Reserve have declined significantly and the U.S. Mint’s production of coin also decreased due to measures put in place to protect its employees.
Nearly a month later, the problem has become severe enough that many retailers are being forced to cope with the resulting shortage of coins in circulation. One solution for many retailers has been to limit cash transactions by only processing transactions using credit or debit cards or checks for payment.
But at least one retailer is considering a different strategy, for which they solicited advice on Reddit's math subreddit:
I work at a shop where we have a multitude of items with wildly different prices. Due to the national coin shortage, my boss wants me to change the thousands of prices of our items so that we won't have to use change, or get the change to come out on the lower end so we can round down without too much loss. My question is if this is even possible. Is there a magic amount of change to charge on each very differently priced item so that it will come out even? Is this undertaking a waste of time?
r/math was the wrong forum for the question, but it's an interesting question none-the-less. In effect, the boss in this question wants to transform the shop into what we'll call "The Whole Dollar Store". No change needed! Ever!
So how would you do that? Well, in mathematical terms, what you need is for the transaction price at the register to ring up as a whole dollar amount. To set prices to make that work, what you need then is to divide a series of integers (1, 2, 3, ...) by the quantity (1 plus the Sales Tax Rate) to get back to each item's ideal shelf price.
So if the store is located in a place that has a sales tax rate of 8.5%, you would divide each integer sale price by (1 + 0.085), or 1.085. Or you could multiply by 0.9217, its reciprocal rounded to 4 decimal places.
Then, to get a final transaction of $1.00 even, you would set the shelf price for the item to $0.92. For a $5.00 transaction, you would set the shelf price to $4.61. And so on, for the range of item prices for everything the store sells.
But that will leave a roughly 92 cent gap between shelf price levels, which the store can make work for them in one of two ways:
- Set each item shelf prices whose regular price is within 46 cents (half the gap between shelf price increments) of these levels to these amounts.
- Package multiple units of items together to get their combined regular shelf price close to these levels, then set the price to these levels. So if you have an item that regularly sells for $0.33, package 3 together and then set the bundle's shelf price at $0.92 (or 3 for $0.92).
The store would really only need to do that with the lowest regular price items, where customers might be put off if the unit price is too far off from the regular shelf price. For items with much larger unit prices, the potential difference won't be as significant.
In any case, whether that's a waste of time depends on how much time will have to be invested in changing all the prices to make "The Whole Dollar Store"-concept a reality!