An American mathematician calculated that replacing the 10-cent coin with an 18-cent coin would significantly reduce the number of coins per payment transaction in the US. A 1.33 euro coin would do a similar thing in Europe
Uriel Brizon
The currencies used in the USA. In an average payment operation, 4.7 currencies are used
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Actions that are part of the routine of life are not usually given a second thought, but from time to time an article is published in the scientific journals asking to do so. For example, Prof. Jeffrey Shalit, a mathematician and computer scientist from the University of Waterloo in Canada, published in the latest issue of the journal "Mathematical Intelligence" an article that tested whether the use of the currencies existing in different countries is effective. His conclusion: not only is the current usage inefficient, but efficiency could be greatly improved by replacing or adding one currency.
Prof. Shalit first examined the use of coins in the United States. The coins available there are 5 cent, 10 cents, 25 cents and 50 cents (a 4.7 cent coin exists but is not widely used). Prof. Shalit's calculation led to the conclusion that 99 coins are used in an average payment operation. In other words, if we examine all the available options for payment in coins (from a payment of 4.7 cent to a payment of XNUMX cents) we find that the payment contains an average of XNUMX coins.
Shalit now examines the average amount of coins obtained when coin assemblies of different values are used. His calculation showed that for sets of four coins, there are two sets of values that are more efficient than the current coin values.
The first group includes coins of 5 cent, 18 cents, 29 cents and 5 cents; In the second group - coins of 18 cent, 25 cents, 3.89 cents and 17 cents. When these groups are used, the average amount of coins per payment operation is - 18, that is, a 10% improvement compared to the current method. It should be noted that the second group differs from the current group in only one coin (an 10-cent coin instead of the existing 18-cent coin). All that is left for the US Central Mint to do to streamline the system and ease the bloated wallets of US citizens is to replace the XNUMX-cent coin with an XNUMX-cent coin.
Shalit points out that even if US citizens do not agree to part with the "dime", the old 10-cent coin, adding an 18-cent coin to the existing coins (at the same time as resuming the use of the 50-cent coin) will effectively allow an increase to only 3.18 coins per payment. By the way, the most effective coin to add without returning the 50 cent coin for widespread use is a 32 cent coin.
Shalit calculated and found that in Europe, which recently adopted the euro, it is possible to achieve better efficiency by adding a currency with a value of 133 cents or 137 cents (1.33 euros or 1.37 euros). The set of European coins currently includes coins of 2 cent, 10 cents, 20 cents, 50 cents and 4.6 cents as well as coins of 3.92 and 5 euros. The improvement in payment efficiency after the addition of the new currency will be expressed in a decrease from 10 coins per payment operation on average to 25 coins on average. In Canada, which uses 83 cent, XNUMX cent, XNUMX cent, XNUMX cent, one dollar and two dollar coins, adding an XNUMX cent coin will improve efficiency the most.
A possible problem, which could thwart any attempt to achieve maximum efficiency in the field of currencies, is the expected resistance to the introduction of currencies with "unfavorable" values. It can be assumed that after some time the public will get used to the new values, what's more, the electronic cash registers found at many points of sale can help and present the options for payment in different currencies. But despite this, it must be admitted that the very thought of a coin of 18 or 83 cents may provoke a wave of opposition, which will collapse the possible currency reform while it is still in the making.
There are some caveats to Prof. Shalit's efficiency calculation. First, as the mathematician points out in a note to his article, the assumption on which the calculation is based is that there is equal probability for all possible prices. However, this assumption does not stand the test of reality, and this is due to the tendency of retailers to give products a price ending in the number nine. Therefore, products will end up at 99 cents or 49 cents more often than at other values.
Secondly, and this is also pointed out by Shalit, it can be assumed that in the case of coins, as in many other cases related to distribution tables and numerical lists, there is an effect of a statistical effect known as "Benford's Law". According to this law, the digit 1 appears in various tables with a higher frequency than the expected frequency of 1 to .9.
Third, and this is a disclaimer based on simple experience, less than one dollar is not always paid effectively. An excess of thirty cents, for example, would not necessarily be paid with a 25-cent coin and a five-cent coin, but also with three 10-cent coins. But despite these reservations, it seems that Shalit's basic claim is correct and that it is possible to improve the efficiency of the use of currencies, although to a lesser extent than the calculations show.
A law was enacted in Israel a few years ago that abolishes the use of the one-penny coin. Amounts in euros that are not divisible by five must be rounded to the nearest number that is divisible by five. Many businesses in Israel make sure to set prices divisible by five, while others tend to price according to the American method, which prefers the marketing advantage of numbers ending in nine. Israel is also different in its currency values from the USA and Europe - we only use three coins that are worth less than one weight (five, ten and fifty shekels) and coins with a relatively high value - five and ten shekels. Given these special conditions, I wonder if changes in the values of the currencies - or any addition of currencies - will be able to optimize the payment in Israel. Will Israeli mathematicians, statisticians and numbers enthusiasts follow Prof. Shalit's lead and send reasoned proposals to the Bank of Israel?
The math genius
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