Why The Rich Get Richer, Part 2: The Danger Zone

Just as for any other asset, the marginal utility of money is a decreasing function. But the marginal utility of money inevitably decreases at a slower rate than any other asset because money can be used to purchase all other assets. Compare the marginal utility of gaining money to the marginal utility of gaining carrots. At a certain point, one can have too many carrots, especially since, as perishable goods, carrots cannot even be converted to cash once they go rotten. But money never rots, and can easily be converted into whatever one desires. So the marginal utility of money will only approach zero once one has literally satisfied all desires, including the desire for unconventional things like giving to charity. Nonetheless, there are important conclusions to be drawn from the fact that the marginal utility of money decreases.

To understand the concept of the individual's decreasing marginal utility of money, consider the difference between Person A with $4000 in the bank, with $1000 rent payable due in a week, and Person B with $500 in the bank, and $1000 rent payable due in a week. If Person A suddenly received $600 in income, he would have many choices of what to do with his money, including saving it. If person B received $600, $500 of this would most likely go towards rent, and the remaining $100 would go towards other essential items such as food.

My subjective judgment is at work here, but I am sure that many will agree with me when I say that the opportunity costs of not getting the extra $600 would be greater for Person B than for Person A. There are extra costs for Person B that would be incurred by not receiving the $600: in not making rent, or in the health costs of malnutrition. Also, at very low levels of wealth, the loss of money adversely affects one's ability to make money in the future. For example, if someone loses his front teeth because he can't afford to see a dentist, he will probably make less of a good impression at a job interview. This is a hidden opportunity cost that people with low levels of wealth must face.

This helps to better illustrate the same phenomenon presented in part 1. It is clear to me that the net benefit of making an investment is not a linear function in relation to one's level of wealth. This is because there are extra costs that naturally arise when one's wealth is at a certain low level. There are unavoidable items, such as basic food, shelter, clothing that everyone must obtain to survive, live with some dignity, and be able to produce wealth in the future. Then there are avoidable items, like MP3 players, which are biologically of a second priority, and do not affect someone's ability to produce wealth in the future. At a certain level, one's wealth will be used exclusively for unavoidable items. (Though people suffering from addiction and mental illnesses may avoid these items in favor of others.) It is apparent that the cost of being without food for a week would be greater than the cost of being without an MP3 player.

All types of investments can be a problem for people at lower wealth levels. As we have seen, if one accepts that the marginal benefit of having money is a decreasing function, one must accept that those with lower wealth will face greater marginal costs involved in any given investment. The marginal benefits of investments will also be greater at low wealth levels, but in smaller proportion than the costs. For everyone, there lies an economic danger zone, at the point where basic needs cannot be sufficiently satisfied by one's funds. All wealth from $0 rising up to the edge of this danger zone must be in a liquid form to satisfy current essential needs. Even risk free opportunities for profit would not be taken by rational people who simply cannot afford them because of the need to maintain a certain balance of liquid wealth. To escape the perils of the danger zone, and make profitable investments, such as those in vocational training, or a new car to help a job-search, one may resort to borrowing, but clearly there are extra marginal costs involved with this, e.g. interest due. Those with sufficient wealth can better avoid borrowing.

Those with enough money to avoid the danger zone are free to take greater risks and reap rewards for doing so. Thus, the rich get richer.

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.)

Marginal Analysis of Senior-itis

We have all probably heard of "senior-itis", the phenomenon of High School or College Seniors losing interest in the outcome of their classes. It's likely that the phenomenon is largely caused by simple boredom, but marginal analysis seems to shed some light on this phenomenon. Early in a scholastic career, each grade affects GPA greatly. With the completion of each class, however, the effect of each grade on GPA decreases. This will continue to the point that in the senior year, GPA may not even budge in response to one's grades. In economic language this is a decrease in the marginal benefit of getting a higher grade in a class. Thus the return from an investment in studying time decreases, and students may find it reasonable to decrease their studying to a new equilibrium. Obviously, students will not want to incur the cost of repeating a class due to failing, and this is a separate issue. Thus the new equilibrium will always be above a failing grade, no matter how small the marginal change to GPA will be, but it will decrease to lower levels as more courses are completed. This little bit of economic analysis may partially explain why bored high school and college seniors might aim for C's in their classes.