Pyramid Schemes?

Recently I heard from a friend that there is an easy, legal and moral way to earn money - lot of money - so that you can just quit your job and sit at home while your bank balance swells with time. He perfectly sounded like a tele-marketing agency trying to sell me a lucky stone. So I asked him how it works and he took me to a place on a weekend.

There were some 20 to 30 persons who are just like me brought there by their friends. We were quickly introduced to some one who came in a costly car with latest mobile and dressed like a VJ.  He is an elder member of the scheme they said. They started with how marketing works and how much is spent on advertising blah blah... Then they said that if that much amount spent on advertising is diverted to people who introduce their friends or family to the product, then the introducing person can get good deal of money. And as the people who he introduced in turn introduce more and more people, he will get money endlessly as more and more people join the scheme.

Next they showed us some sort of binary tree. Each person must introduce two persons and they in turn will introduce two persons and so on. So if you have two persons below, when they bring two persons each, then you will have 2 + (2 + 2) = 6 persons below you. According to them, you can fully get your money back apart from taxes if there are some 10 to 16 persons below you. Someone asked what will happen if the person whom I introduce didn't bring new joiners. For that they said "Even if you don't bring new customers, we won't allow the tree to grow asymmetrically. We will ensure that the tree grows in a proper binary tree pattern!"

Suddenly Something came in to my mind. It may be linked to the binary tree they have discussed or the racing flag key chain at the hands of the person sitting next to me. That "Wheat and Chessboard Problem". I remembered my dad saying that story when he first bought me a chessboard. Nothing which doubles in every next step can go indefinitely. This is what we call exponential growth. Here the growth will be limited by the population who can participate in this scheme.

Consider India. We have more than 1 billion strong population. But how many of them are earning members who can buy this? Can we take it is approximately 750 million (this is gross exaggeration as most people won't spend thousands of rupees in questionable schemes)?  So it means that almost all the person including children and bed-ridden senior citizens are joining the scheme. So it all starts with one person. He will have 2 persons below. Let us say this is first level. So at any point of time, the total number of persons in a proper binary tree will be 2^(n+1) - 1, where n is the number of levels from the first person who starts this scheme.

So this tree can grow up to 28 levels in India (when the total number of members will be 536,870,911 or approximately 536 million). Even if all of the existing members hunt for new joiners from the dense forests of Andaman to the dusty deserts of Thar, they won't get enough members to fill the next level of the tree, which will cross the 1 billion mark. So all the people at the bottom most level can not register any profit and turn to their introducer for a refund.

And the beauty of a proper binary tree is that in every level it will have 1 more person than the total number of persons in all previous levels. Mind you! This is not just the immediate previous level but ALL previous levels. For example, in level 4, there will be 31 persons in total. But on level 5, there will be 63 persons in total. That means, 32 new people have joined in level 5. The number of new joiners is greater than the TOTAL of existing members in the scheme! So, there will be more people who will be demanding for a refund than the people who can offer a refund.

Another point to note is, unless you get 2 or 3 levels below you, you will suffer loss. So let us assume that people in level 28 and 27 are after all other people in the scheme for a refund. That is 402,653,184 people who lost their money are chasing 134,217,727 people who introduced them to the scheme for a refund. Hmm... Don't worry! Such doomsday events won't happen in real life. Because the tree won't grow that large in first place. In my opinion, the tree can grow safely up to 10 to 20 levels after which, no matter how hard people try, it will stop growing. At this point you can see in news that thousands are protesting outside police station to punish the people who run the scheme and get their money back.

I was just doing some math in my mobile's calculator when I was awaken by my friend, with a typical toothpaste ad grin, from my numeric trance. He was holding some forms with a pen and asking me to sign it! He was telling that he will pay the joining fee and I can repay it later. I just refused to sign as I had lot of negative feelings about the scheme. But I was surrounded by people who were frantically running for ATMs and signing the forms. I just walked out while he was running behind me begging please. I might have lost a good friendship. But I just saved myself from loosing many other good friends who I might have introduced to this scheme if I had become a victim myself.

So, when things like this come to you by any means, just say "NO!". It may be selling some soap oil or buying a gold coin or marketing lunch boxes. Say no! If you want to invest your money, invest in gold, FD, RD, insurance, mutual funds, SIP, ULIPs, shares, land etc. But don't think that there are shortcuts to earn and multiply wealth. There is no way like that to be rich. Pyramid schemes are banned in many countries. I seriously doubt whether these schemes are legal in India. If more and more people start talking about them openly, sooner or later government will ban them. By joining these schemes you may endanger your hard earned money, reputation among friends and family, job and peace of mind just because you allowed someone to fool you.