Dear Canadian retailers: Now that we're phasing out the penny...

Dear Canadian retailers:


Now that we're phasing out the penny, you probably want to set your prices so that you're always rounding up to the nearest nickel to your advantage (rather than down, which would benefit the customer). So I worked out the prices that maximize this return for you, based on 13% HST. Just make sure your base price before tax ends with one of these numbers and you'll make an extra $0.02 on each purchase:

0.03, 0.07, 0.16, 0.20, 0.25, 0.29, 0.34, 0.38, 0.47, 0.51, 0.56, 0.60, 0.65, 0.69, 0.78, 0.82, 0.87, 0.91, 0.96, 1.00, 1.04, 1.09, 1.13, 1.18, 1.22, 1.31, 1.35, 1.40, 1.44, 1.49, 1.53, 1.62, 1.66, 1.71, 1.75, 1.80, 1.84, 1.93, 1.97, 2.02, 2.06, 2.11, 2.15, 2.24, 2.28, 2.33, 2.37, 2.42, 2.46, 2.55, 2.59, 2.64, 2.68, 2.73, 2.77, 2.81, 2.86, 2.90, 2.95, 2.99, 3.08, 3.12, 3.17, 3.21, 3.26, 3.30, 3.39, 3.43, 3.48, 3.52, 3.57, 3.61, 3.70, 3.74, 3.79, 3.83, 3.88, 3.92, 4.01, 4.05, 4.10, 4.14, 4.19, 4.23, 4.27, 4.32, 4.36, 4.41, 4.45, 4.50, 4.54, 4.58, 4.63, 4.67, 4.72, 4.76, 4.85, 4.89, 4.94, 4.98, 5.03, 5.07, 5.16, 5.20, 5.25, 5.29, 5.34, 5.38, 5.47, 5.51, 5.56, 5.60, 5.65, 5.69, 5.78, 5.82, 5.87, 5.91, 5.96, 6.00, 6.04, 6.09, 6.13, 6.18, 6.22, 6.31, 6.35, 6.40, 6.44, 6.49, 6.53, 6.62, 6.66, 6.71, 6.75, 6.80, 6.84, 6.93, 6.97, 7.02, 7.06, 7.11, 7.15, 7.24, 7.28, 7.33, 7.37, 7.42, 7.46, 7.55, 7.59, 7.64, 7.68, 7.73, 7.77, 7.81, 7.86, 7.90, 7.95, 7.99, 8.08, 8.12, 8.17, 8.21, 8.26, 8.30, 8.39, 8.43, 8.48, 8.52, 8.57, 8.61, 8.70, 8.74, 8.79, 8.83, 8.88, 8.92, 9.01, 9.05, 9.10, 9.14, 9.19, 9.23, 9.27, 9.32, 9.36, 9.41, 9.45, 9.50, 9.54, 9.58, 9.63, 9.67, 9.72, 9.76, 9.85, 9.89, 9.94, 9.98.

That's my 2 cents. You're welcome. Enjoy.



UPDATE (2012-03-30):


I've been asked what happens when customers buy more than one item at the same time. Does the advantage stay with the retailer? So I decided to figure it out, and the result is fascinating. When you add any two of these numbers together, you never get a number that is also on the list. You will end up with a $0.02 advantage to the customer 74.86% of the time, a $0.01 advantage to the customer 12.89% of the time, and already rounded to nearest nickel 12.25% of the time. Remember these are all numbers which, when taken *individually*, if you add 13% HST and round to the nearest penny, produce a number that ends in a digit 3 or 8, so that rounding to the nearest nickel always means rounding up by 2 cents (a $0.02 advantage to the retailer). But any two together, NEVER produce an advantage to the retailer, but an average $0.0163 advantage to the customer.



But wait, it gets better! If you take the list of numbers that, taken individually, produce only a $0.01 advantage to the retailer, and add any two together, you get a number that produces a $0.02 advantage to the retailer 75.2% of the time, a $0.01 advantage to the retailer 12.6% of the time, and a $0.02 advantage to the customer 12.2% of the time. That's an average $0.0139 advantage to the retailer.


So retailers, if you think your customers are usually going to buy two items at a time, price them so that individually there is only a $0.01 advantage to you after you add the 13% HST instead of aiming for $0.02, as it will turn out better in the long run. You will be delighted to learn that 9.95 and 9.99 both qualify, because I KNOW how much you LOVE prices like $9.95 and $9.99. Here is the complete list:


0.08, 0.12, 0.17, 0.21, 0.26, 0.30, 0.39, 0.43, 0.48, 0.52, 0.57, 0.61, 0.70, 0.74, 0.79, 0.83, 0.88, 0.92, 1.01, 1.05, 1.10, 1.14, 1.19, 1.23, 1.27, 1.32, 1.36, 1.41, 1.45, 1.54, 1.58, 1.63, 1.67, 1.72, 1.76, 1.85, 1.89, 1.94, 1.98, 2.03, 2.07, 2.16, 2.20, 2.25, 2.29, 2.34, 2.38, 2.47, 2.51, 2.56, 2.60, 2.65, 2.69, 2.78, 2.82, 2.87, 2.91, 2.96, 3.00, 3.04, 3.09, 3.13, 3.18, 3.22, 3.31, 3.35, 3.40, 3.44, 3.49, 3.53, 3.62, 3.66, 3.71, 3.75, 3.80, 3.84, 3.93, 3.97, 4.02, 4.06, 4.11, 4.15, 4.24, 4.28, 4.33, 4.37, 4.42, 4.46, 4.55, 4.59, 4.64, 4.68, 4.73, 4.77, 4.81, 4.86, 4.90, 4.95, 4.99, 5.08, 5.12, 5.17, 5.21, 5.26, 5.30, 5.39, 5.43, 5.48, 5.52, 5.57, 5.61, 5.70, 5.74, 5.79, 5.83, 5.88, 5.92, 6.01, 6.05, 6.10, 6.14, 6.19, 6.23, 6.27, 6.32, 6.36, 6.41, 6.45, 6.50, 6.54, 6.58, 6.63, 6.67, 6.72, 6.76, 6.85, 6.89, 6.94, 6.98, 7.03, 7.07, 7.16, 7.20, 7.25, 7.29, 7.34, 7.38, 7.47, 7.51, 7.56, 7.60, 7.65, 7.69, 7.78, 7.82, 7.87, 7.91, 7.96, 8.00, 8.04, 8.09, 8.13, 8.18, 8.22, 8.31, 8.35, 8.40, 8.44, 8.49, 8.53, 8.62, 8.66, 8.71, 8.75, 8.80, 8.84, 8.93, 8.97, 9.02, 9.06, 9.11, 9.15, 9.24, 9.28, 9.33, 9.37, 9.42, 9.46, 9.55, 9.59, 9.64, 9.68, 9.73, 9.77, 9.81, 9.86, 9.90, 9.95, 9.99.


I suppose I could continue and calculate this for buying three, four, five, etc. items at a time but that's enough. :)

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