Bernard Beauzamy (the owner of SCM SA) had set up a 500 euros prize for whoever could find a way for the business model riddle featured on Tuesday. Bernard tells me that nobody won the prize, here is the answer:

....The answers we received fall into two categories:

Those who want to send 10 000 left-hand gloves, and then 10 000 right-hand gloves, and declare them of value zero.

This answer does not make sense ! Do you think that the customs will be stupid enough not to observe that they see only left-hand gloves, and only later right-hand gloves ? They would confiscate both, and the sender would go to jail, for attempt to cheat the customs. Many years of jail !

Those who want to create a branch of the company in the destination country, and claim that they would evade the customs this way.

This answer does not make sense either ! It only reduces the profits, since one has to pay all the people in the local structure. And it changes nothing to the fact that customs tax the final selling price. If you have 10 intermediaries, you will have to give a salary to the ten, and the customer pays the same price, so the producer gets less money. In all circumstances, customs or not, the fewer intermediaries you have, the better you feel.

The answer, as we expected, was not found by anyone, because all our readers, by education or taste, want to build mathematical models, and this is a situation where no model is possible. It defies imagination and logics, and contradicts all existing economical models.

First of all, the solution looks impossible. If we sell each pair at its maximum price, that is 200 Rubles, the customs takes 160, we keep 40, and this is exactly equal to the production cost, so we have no benefit at all. It is even worse if we sell at a lower price.

The solution is this : we have to impose fabrication defects to 5 000 pairs (both left and right gloves). After that, we export 5 000 pairs, of which the left one is normal and the right one is defective (for example a big scar across one finger). These gloves are declared as "fabrication rejects", for a very small price, for instance 20 Rubles a pair. Note that selling and exporting "fabrication rejects" is quite ordinary and legal, and is common practice.

Then, next month, we do the converse : we export 5 000 pairs, of which the left one is defective and the right one is normal. We put all gloves together, and we get 5 000 pairs of normal gloves, which we sell at the maximum price. The total cost is 400 000 Rubles (fabrication), plus 160 000 Rubles (customs). The sales bring 1 000 000 Rubles, so we have a benefit of 840 000 Rubles. We can of course sell the defective gloves, just to have some receipts for the customs.

The ideal solution, but this is a remarkable industrial achievement is to program the fabrication machine so that it put defects on one pair out of two.

We observe that the solution is perfectly legal. Fabrication defects exist and are sold worlwide, for a low price. Each pair is perfectly declared at is correct value.

We said earlier that mathematical modeling is impossible. In fact, this example shows that all Nobel prizes given to economists since 1969 (year of creation of the prize) should be withdrawn, because they have no value at all.

Precisely, we see here that the notion of price is not mathematically well-defined. We cannot talk about the price of a glove, even not of a pair of gloves. We see that the price is not a continuous function, nor an increasing function, nor an additive function. The price of two objects together is not the sum of their individual prices. Still, the economists will build nice models, defective by all parts, and no reassembly can bring them any value !

Remember this : this is a true story, and the man who invented the solution did not know what a mathematical model was and did not have any degree at all…

[P.S: added Dec 4 (3:40PM CST): It's a riddle. One could make the point that this type of business model is not robust. All the countries in the world revise their own laws in order to effectively plug holes such as the one presented here. The ever growing sophistication / complexities of the tax systems in most countries reflects this adaptive behavior. If this system were robust it would be common business practice by now. It may have worked in some countries in the past however. The most important take away from this riddle is that the definition of the price of an item is indeed a difficult problem for which modeling is going to be tricky for a long time]

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