Author Topic: Swedish rounding  (Read 1736 times)

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Swedish rounding
« on: May 04, 2009, 07:45:15 PM »
Denominations of 3, 15, 30 etc. make some sense from a mathematical pont of view. If your purpose is to use the optimal number of coins in transactions (taking cost into account), a 1-2-5 series is optimal (multiply by 10, 100, 1000 etc. to obtain other denominations). Examples of perfect 1-2-5 series are France before the introduction of the euro and the euro (no coincidence, I think).

If you want to minimize the number of coins for each individual transactions without regard to cost, you will need a 1-1.5-2-3-5 series. However, you will soon find that the 1.5-3 denominations are not much used, because they are the least needed to complete a whole gamut of transactions.

Given your mathematical bent, what do you think of the New Zealandish habit of pricing goods down to the cent but then rounding the price to the nearest ten cents at the till? My own feeling is that it's not worth the effort, and you should not price lower than your lowest denomination of coin. All goods could be repriced according to the rounding principle. After all, who is worried about being a mere 9 cents down?

Offline Figleaf

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Re: Swedish rounding
« Reply #1 on: May 04, 2009, 08:36:57 PM »
The rounding principle is a wonderful device used by politicians when one side in the debate says the lowest decimal is a nuisance and the other says that withdrawing small coins will increase inflation. Macro-economically and mathematically, rounding and rounded re-pricing is equivalent, provided that each player makes enough cash transactions to make it so. Since rounding is a (tiny) bother, it should be slightly better not to round off.

There is an exception to the rule. It pays to round when prices are net of sales tax, as in the US. This is because this system will produce odd prices. Suppose a loaf of bread costs 100 and the tax rate is 14%, so that price including sales tax is 114. Now make the smallest coin a 10 by withdrawing the 5. If loaves are usually not bought in combination with other articles, the shop loses 4 on most loaves sold. However, by increasing the price to 101, the shop gains about 5. In the first situation, the cash price including tax is 110, in the second, it is 120. The shop will be tempted to raise the price, just because of rounding.

While it sounds insignificant, multiply the +5 and the -4 by the number of customers times the number of times they buy bread and you're talking about large sums. If people spend about 5% of their annual income on bread in a solitary purchase and, as in the above example, the price increases would amount to almost 22 basis points of extra inflation. With current inflation rates between 0 and 200 basis points, that is a lot. However, when inflation is near zero, you should be grateful for every bit of inflation you can get.

An unidentified coin is a piece of metal. An identified coin is a piece of history.

Offline chrisild

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Re: Swedish rounding
« Reply #2 on: May 04, 2009, 11:10:11 PM »
I've always hated the so-called Swedish rounding system over here in New Zealand,as to me,it implies that traders are allowed to get away with ripping off & scamming people.

Interesting; while I am pretty familiar with the rounding of cash totals, I had not heard the term "Swedish rounding" before. Just did a quick web search, and it seems that the term is popular particularly in AU and NZ. In my opinion, this rounding works fine, and its positive effects outweigh the disadvantages. Sure, if I bought one single item at a supermarket, priced 0.99, I would pay 1.00 when using cash. Well, I hardly ever buy just one item at such places. And in places such as bakeries, such threshold prices are much less common anyway. Indeed, the small pieces are primarily a nuisance.