The Utility of Wealth and the Distribution Of Income

I’ve Been Poor, and I’ve Been Rich. Rich Is Better!

but by how much?

Every summer I spend two weeks camped out at the Pennsic War with ten thousand fellow historical recreationists. Cooking is over a campfire, I sleep on a rope bed in a pavilion, spend evenings telling medieval stories around the fire. It is fun, tiring, and educational.

One of the lessons is how rich we are. All of us. On the drive home to California — Pennsic is in Pennsylvania — we enjoy the luxury of heated motel rooms, hot and cold running water, toilet and shower in a bathroom attached to the room we sleep in, restaurant food cooked for us. Returned home we are back in our, by contrast luxurious, usual lives.

Most medievals were poorer than we can well imagine but not all. With enough servants, in antiquity slaves, life could be almost as luxurious as it is for a modern. You do not need hot running water if you have servants to heat your bath, electric stoves if you have cooks, a gas furnace and thermostat if there is someone else to split logs and keep up the fire. They did not have modern medicine or entertainment as diverse and convenient as movies, television, and recorded music, but the routine problems could mostly be taken care of by other people.

The Uses of Wealth

Contrast the advantage to being rich then with the advantage now. Ordinary people may not eat at fancy restaurants but they eat very nearly the same food as the rich. Even the modern poor, though they have access to a lower variety and quality of food than the rich, do not starve to death in famines. A poor medieval, even an average medieval, sometimes did. The median American sleeps in a heated room, is unlikely to share it with his children. The typical medieval peasant shared an unheated one room cottage with his family. Being rich in America today gives you a more pleasant life than the median American lives, substantially more pleasant than the life of an American at the tenth percentile of the income distribution. But even someone at the tenth percentile probably has a color television, very possibly a car — not as large screen a television or as new a car as the rich American, but closer to both than no television and no car.

The Distribution of Income

One of the things I do at Pennsic is story telling, largely from Medieval Arabic sources. One of the things I notice is the level of income inequality that the society they are set in takes for granted. In one, a vizier giving alms to a poor woman carelessly specifies the amount in gold instead of silver, two hundred dinar instead of two hundred dirham. That is enough to persuade her that she is now too rich a woman to remain married to her poor husband. In another a prince orders his vizier to get him five hundred thousand dinar for a project he has decided on, in a third a wealthy man plans to offer the caliph a three million dinar bribe.

I do not know if any economic historian has calculated a Gini coefficient for the medieval world but I am pretty sure it was a world where the difference in wealth between the average person, probably a peasant, and the richest person he interacted with was substantially larger than it is in the world I live in.

And I may know why.

Life a Gamble

Should you go to law school? If you are very lucky you end up a partner at Cravath or Kirkland, making several million dollars a year. If you are moderately lucky you graduate, pass the bar, get a job at a respectable firm, a hundred and fifty thousand a year for sixty hours a week. If you are a little less lucky you fail the bar exam or pass the bar but cannot get a job as a lawyer, end up ninety thousand dollars in debt and with no better job prospects than you had three years earlier.

Should you train as a computer programmer? It’s cheaper than law school and you should be able to tell if you are good at programming pretty quickly. If you are, you can expect to earn upwards of a hundred thousand a year, twice that and more if you are really good, but some of it may have to go for Silicon Valley rents. And there is the risk that AI will replace you.

Should you marry your girlfriend? You get along tolerably well, both want children. Her parents, on the other hand, and her sister, and her unfortunate taste in books and music, and her political opinions … . if you break up with her and go back on the market you might do better — there are a lot more fish in the sea. Or you might end up single, childless, facing the future alone.

In all of these gambles, both the odds and the payoffs depend on what other people in your situation are doing. If a lot of smart college graduates go to law school, your chance of ending up with a multi-million dollar income go down. If a lot of people train as computer programmers, jobs will be harder to get and pay less. If other men marry the first reasonable match who will have them and you let your girlfriend go in the hope of trading up, you may find that there are not as many fish left in the sea as you expected.

Life is a game of repeated gambles. You don’t get to choose what bets you are offered, do get to choose what bets you make.

The Utility of Wealth and the Distribution of Income

You are choosing between two alternative careers. The easy one gives you a certain income of a hundred thousand a year. The hard one, another four years of school working seventy hours a week, eighty thousand in student loans, might give you two hundred thousand, might not. On a hundred thousand you can live a pretty decent life. Two hundred thousand would be better, vacations in Europe instead of New England, a bigger house, sometimes flying first class instead of tourist, a better life — but not much better. Unless the odds of winning are pretty good you play safe.

What matters is not how much money you get but what it buys. The more useful a high income is, the greater the risk you will accept for the chance of getting one. The greater the risk you and others are willing to accept for that chance, the greater the competition and the worse the odds of winning. Just like law school.

In the modern world, where a two hundred thousand dollar life is not that much better than a hundred thousand dollar life, people take risks, bear costs, in the hope of getting a higher income only if the odds of winning are reasonably good; we end up with a world where the number of people at an income level declines only gradually as the level rises. In the medieval world, where the difference in lives was very much larger, people were willing to compete for the high income slots even when the odds of winning them was low.

I am sure that is not the whole story. Another part is the distribution of abilities, the income distribution changing with changes in that distribution or in what abilities matter. If, as often claimed and perhaps true, inequality is increasing in the modern world, the explanation might be the decreasing importance of broadly distributed physical abilities, increasing importance of more narrowly distributed mental abilities. That is another part of the story.

This post is the part I got from two weeks a year playing medieval.

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