Wednesday, November 7, 2007

Ducats Matter!!? Yes, but less and less . . .

Things today are more different than they have ever been. Today's point-and-click information age is in sharp contrast to life, let's say, during the Black Death of the 14th century. In fact, it has been claimed that the Daily New York Times Newspaper contains more information in it than the average individual living in the 18th century came across in a lifetime.

We has seen three major cultural shifts in our recent history. The agricultural, industrial, and technological revolutions have guaranteed one thing: we have more choices now than our ancestors did. For much of recorded history, people did what their parents did: Millers milled, Tanners tanned, Smiths smithed, Cartwrights Cartwrighted, and Mathers mathed. Life was dictated by social structures and physical geography. Few people had the desire or resources to rise about their caste or to travel long distances over rough terrain without the latest Nike "All Conditions Gear." In essence, beyond deciding to skin a rodent before eating it or just eating it with the fur, very little was left to personal liberty. But today, we are free to choose. We are filled with choices, dilemmas, conundrums that our ancestors never had to face. Today, there are a bewildering array of options that we have to choose from. In fact, I panic each time I enter a Starbuck's or Subway. Order a simple "coffee" or a "sub sandwich" and people look at you like you're from a rodent-eating era." Should it be paper or plastic? Plastic or cash? Nike or Reebok? Pizza Hut or Mr. Gatti's? Pepperoni or Sausage? Math or Rotting Cabbage? Essentially, our destiny is in our own hands. Social structures have become semi-permeable membranes through which we can waver between at will. Physical geography is now a course we take in college, not something we blame our pitiful future on. But with all these choices, how do we decide??

The answer, thanks to the Mathers of Olde, lies in mathematics. In 1738, a Dutch polymath, Daniel Bernoulli, son of Johann Bernoulli, and a member of the most prodigious math clan of all time (8 Bernoullis made significant contributions to mathematics, which is almost as many people as MY family has made to Health Science . . . as subjects) came up with the answer.

Bernoulli stated that the wisdom, W, of any decision could be calculated by multiplying the probability that the decision will give us what we want, D, by the utility, or usefulness of getting what we want, U.

To him, decision making was a quan
tifiable experience. Everything was a calculated risk:

W = DU

The first variable, D, is pretty easy to calculate: How likely is it that I will get an A on the math test if I don't study? What are my odds of getting a good job if I'm lazy and stupid? Would I remember to breathe if I was in control of my autonomic nervous system? With a little effort, realistic foresight, and rich parents, we can pretty much figure out how our efforts will actually result in giving us what we desire.

The downside to this, however, is that we cannot accurately determine how we will feel once we get what we desire. Sure, my rich dad got me this "cush" job, but now I'm realizing that I never had to get dressed up in a suit to play video games all day before, and why do I have to play them in this giant, lonely private office. The feeling of novelty usually fades once we have achieved what we desired. The honeymoon will end eventually, usually very quickly. So how can we predict how we will actually feel in the future after our decision is made? Bernoulli reasoned that when projecting the fut
ure, our imagination fills in the gaps of future possibilities by substituting realities from the present. In other words, what we objectively want, is not what we subjectively experience. We are quite good at fooling ourselves.

Bernoulli's brilliance lies, not in his mathematics, but in his psychology of the human mind. We all want more once we have what we have. Wealth may be measured in dollars, but utility is measured in how much satisfaction, pleasure, or comfort those dollars can buy. In this sense, wealth does not matter. What is im
portant is utility: how much pleasure can I get out of the things that money can buy.

This is why the beggar is no more happy than the millionaire. This is why King Solomon was not better off than his servant. When asked how much money is enough, billionaire J.P. Morgan stated, "just a little bit more." To mak
e wise choices, we must optimize our pleasure. Bernoulli came up with a quantifiable way to convert dollars to utility--Brillitant! His idea was called "Diminishing Marginal Utility." He thought that each successive dollar provides less pleasure than the one before it; therefore, an individual (who has spent some of his money on someone to do his calculations) can simply (let's say by a flat fee) calculate his utility of any given dollar by adjusting the amount of dollars he has already spent.

He wrote:

the determination of the value of an item must not be based on its price, but rather on the utility it yields. The price of the item is dependent only on the thing itself and is equal for everyone; the utility, however, is dependent on the particular circumstances of the person making the estimate. Thus there is no doubt that a gain of one thousand ducats is more significant to a pauper than to a rich man though both gain the same amount. The utility resulting from any small increase in wealth will be inversely proportionate to the quantity of goods previously possessed.

So the thousand DUCATS has more value,
or more utility to the pauper than the rich man. But is he any more happy?

We can graph utility against wealth, with utility on a vertical axis and wealth on a horizontal axis. This graph would rise from left to ri
ght, meaning that utility increases with wealth. This translates to the indisputable idea that we like more money than less money. But the graph increases at a DECREASING rate, which is why the curve is concave down. In calculus, Bernoulli was stating that the first derivative is positive while the second derivative is negative.

Bernoulli precisely stated that a change in utility with respect to wealth equals the natural logarithm of the sum of initial wealth plus an increment of wealth divided by initial wealth. For instance, let's say you have $100. What is the utility in gaining another $20? According to Bernoulli, it would be:

ln((100+20)/100) = 0.182

So now you have $120. The next gain of $20 will be worth LESS to you:

ln((120+20)/120) = 0.154

This same gain of $20 is almost insignificant to you if you start with a large amount, say $1 million:

ln((1000000+20)/1000000) = 0.0000199998

At this alarming diminished utility value, it might not even be worth your effort to bend over and pick up a $20 bill if you found it on the ground. In this case, it's probably best to leave it there for the pauper.

Today, we look at Bernoulli's idea and say, "Duuuuuh! Of course we like more money." WE also realize that as we spend more and more time eating at an all-you-can-eat dinner buffet, that we will begin to feel increasingly less satisfied at each return trip to load our plates. His ideas, especially the his ability to reduce his ideas to calculations is what is remarkable, for they have profound implications in the theory of risk management, as I will show you tomorrow.

Until then, enjoy choosing your choices.

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