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An Application of the Backwards Bending Supply Curve

2010 October 7
by Phil Miller

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?

5 Responses
  1. Yvan Kelly permalink
    October 7, 2010

    On a related matter, when I was scouting for the Sonics, George Karl told me to never bring in a player who had “won the lottery.” He said when people who win the lottery are asked what they are going to do next, most reply that they’re quitting their jobs. Being drafted in the NBA, according to Karl, was like winning the lottery. He didn’t want a player that was going to shirk because of the size of their pay check.

  2. October 9, 2010

    Definitely a fascinating phenomenon, and I think we actually see this everyday to varying degrees — every team in every sport has a “Haynesworthless” (aka a player who has all but given up on the field because his bank account is fat).

    I think we see this in the business world all the time. When Bear Stearns was buzzing in 2007, CEO Jimmy Cayne hit the golf course and bridge tournaments 5 days a week. He probably felt he had “purchased” enough leisure time. (http://online.wsj.com/article/SB119387369474078336.html)

  3. October 10, 2010

    2 words: Bjorn Borg.

  4. zlionsfan permalink
    October 10, 2010

    Jim Brown is another excellent example: he retired at 30 (one year before Barry, two years before Tiki) from a team that was regularly contending for championships. From what I understand, there was no question that he could have played for a number of years … he was the league MVP his last season and was first or second in the league in pretty much every category that applied to running backs.

    Of course, each RB ostensibly had a different reason to retire. In Brown’s case, he wanted to act. I’m not sure how much money he made in his respective careers, although it wouldn’t surprise me if he made much more as an actor. It’s certainly true that then, as now, the cumulative damage that football players suffer on the field affects not only their future earnings as a player but also their earnings (and quality of life) off the field; this was probably a factor in the decisions of all three players.

    The irony in Sanders’ case was that he was reportedly tired of playing on losing teams, yet the Lions were more successful during his career than at any other time in franchise history outside of the ’50s: six of their nine Super Bowl-era playoff appearances occurred during Sanders’ career. Maybe he should ask Jeff Backus and Dominic Raiola about playing on losing teams …

  5. Greg Pinelli permalink
    October 17, 2010

    All this so called “law” proves is that some people are not inanimate goods…little things like values keep creeping into the picture. Then there is the entire issue of players being paid exaggerated amounts who are past their prime and never again produce even to the mean, let alone above it. I am beginning to think that a better case can be made for the inverse of this “law..” The more you pay a player the less you will soon get of the “good” you paid for.

    I must say I am mystified by Mr. Kelly’s post..how many undrafted players are there in the NBA who have a snowballs chance in hell of making it?? Does he possibly mean drafted No. 1???

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