Saturday, June 20, 2009

Why the Rich Get Richer, Part 1

Let's say you had a chance to play a game, only once, where the rules were as follows: Flip a coin. Heads, you get $100. Tails, you lose $50.
Would you want to play?
The answer to this question will come from your individual risk preference.
The expected value from the game is:
E(x) = ($100 - $50)/2 = $25
But what does the measure of expected value mean to an individual?
If a sizable sample of people play this game, the mean return will approach $25. But to each person playing this game there are only two possible results; a gain of $100 or a loss of $50. This is the origin of risk aversion. If the player could play again, there would be a chance to reverse any losses, and in the long run this would happen. But with this not being the case, people behave differently, usually in a way that is risk averse.
Now, are there any social conditions that would affect one's behavior in a game like this? It is apparent that a person's wealth would be a determinant. Let's say Person A and Person B are walking home from work. Both A and B plan to pick up milk from the grocery store. They both run into a street vendor who offers them the chance to play the aforementioned game. Person A has $100 in cash in his wallet, and Person B has $50 in his. While the monetary payoff or loss from playing the game is the same for both individuals, Person B may very well feel less willing to play. This is not, I repeat, not because Person B is more risk averse. To say that person B is more risk averse would imply that Person B is making decisions using exactly the same costs and benefits as Person A, when really this is not the case. In reality, the payoffs are different. If Person A were to lose $50, he could still pick up the milk from the grocery store using the $50 he has left. But if Person B were to lose $50, he would lose all the money he has, and not be able to get the milk he had desired. This is an added opportunity cost for Person B, so taking this cost into account, it is only natural that he would be less willing to play the game. And by not playing the game, Person B misses out on an expected payoff of $25.
As it goes for Person B, the same goes for real people with lower wealth throughout the world. And though street vendors offering games with favorable outcomes are not common, equivalent risk/reward situations exist everywhere, and for those with low enough wealth it is far more costly to play these games. Thus the rich have greater freedom to play risky games, and, as the saying goes, get richer. (I shall explore these other "games", such as higher education and changing careers, in a future post.)

No comments:

Post a Comment