Why do some sports stars retire at their peak?

Sports stars like the Cubs' Carlos Zambrano may be responding to what economists call the 'income effect.'

Pat Sullivan/AP
Chicago Cubs starting pitcher Carlos Zambrano rubs his hand after trying to make a barehanded catch on a ball hit by Houston Astros' Brian Bogusevic in the second inning of a baseball game Saturday, Oct. 2, in Houston. Zambrano, a sports star at the peak of his pitching career, has said he'll retire when his contract runs out in 2012.

The law of supply says that when the price of a good rises, all else equal, the quantity supplied of that good also rises. Applied to labor markets, the more people are paid, the more they work. There’s no surprise there. But there is a case where the law of supply seems to be violated in labor markets: the case of the backwards-bending supply curve.

The economist models the decision to work as a trade-off between working and leisure. Work and leisure are substitute uses of a person’s time, and his income is the implicit price of taking leisure. As a person’s income rises, it becomes more costly not to work, and the person responds by working more. This is the substitution effect of an income increase.

But leisure can also be thought of as some kind of a normal good. As a person’s income rises, all else equal, he would respond by taking more leisure. This is the income effect, and it at least partially offsets the substitution effect.

In a person’s mind, the income and substitution wage a constant battle. When the law of supply holds, the substitution effect outweighs the income effect. But as a person’s income rises past some threshold, he feels his income is sufficiently high to allow him to, in effect, “purchase” more leisure time, and he responds by working less. Past this threshold, the income effect outweighs the substitution effect.

Off the top of my head, I can think of a couple of examples where a star athlete has retired while still at the top of his game, and men who may be examples of the backwards bending supply curve: Tiki Barber and Barry Sanders.

Another one has recently reiterated his desire to retire at the end of his current contract is the Cubs’ Carlos Zambrano (fyi, the link also contains embedded audio for a vlog, so readers may want to turn down their speakers).

Enjoying his best run of pitching in more than two years, the always-controversial Carlos Zambrano said after winning his ninth game of the season Wednesday that he will retire when his contract ends after the 2012 season.

“I told you the other day, this will be my last contract,” Zambrano said. “This will be my last contract. I won’t be playing anymore. I don’t want to play anymore. Life is short. Sometimes you miss things with your family, like very important people, like my daughter. Sometimes you miss things in life because of baseball that you shouldn’t miss. I want to be there any moment for my daughter and my family. Baseball takes a lot of time away from us.”

If he follows through on his current plan to retire, Zambrano (aka Z and The Big Z) will no-doubt be criticized by fans and in the media. But this decision is really nothing new. Is Z the first person to take early retirement? Besides, who can criticize a man for wanting to spend more time with his family after his contract runs out especially one as wealthy as The Big Z?

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