The Arithmetic Fallacy

by Russ Roberts on March 28, 2005

in Myths and Fallacies

Suppose you want to create jobs in your society.  Does it seem logical that to create more jobs, you need to restrict the effort of the people who already have jobs?  Well, sort of.  If it currently takes 100 people to do a certain task, then cutting their work effort in half would then require 200 people to get the job done.

The logic at first glance seems pretty appealing.  On a certain level, it seems undeniable.  Yes, there might be problems in monitoring how hard people work.  But you can see the surface appeal of the basic proposition.  It’s just basic arithmetic.  Half of 200 is 100.

Doubts start to creep in when you wonder about whether the amount of work being done would stay constant if you had to pay twice as many people.  And then there’s the question of wages.  Would they simply fall in half?  After all, there are costs related to having another employee regardless of how much they work—record-keeping and maybe other fixed costs.

Maybe cutting work effort in half wouldn’t double the demand for labor after all.  Maybe it would reduce the demand for labor.  For example, if you weren’t allowed to cut wages in half, then legislation that cuts work effort in half would actually make workers less attractive.  It would create an incentive to find different methods of production that use machines instead of labor.

What seemed so obvious at first to be undeniably true because of arithmetic—cutting the amount of work effort in half would seem to require doubling the number of workers—actually turns out to be false.  So what would you call this fallacy?  The arithmetic fallacy.  Or maybe the vertical demand curve fallacy.  Or maybe the Ceteris isn’t Paribus Fallacy.

Whatever we should call it, the French seem to have discovered.  After a five year experiment, they have repealed the mandatory 35-hour work week which by putting a ceiling on hours of work was supposed to have increased the number of jobs in France.  The AP reports:

French lawmakers effectively abolished the country’s 35-hour work week
Tuesday by allowing employers to increase working hours — and pay — as
the country struggles with high unemployment and stagnating living
standards.

President Jacques Chirac’s government has tried to sell the reform
to voters as an opportunity to "Work More to Earn More," but many
remain unconvinced.

Work more to earn more.  What an intriguing idea!

Many French workers have become accustomed to their longer holidays and
regular weekdays off, and a recent survey by polling agency CSA showed
that 56 percent of salaried employees oppose the reform — although
jobseekers, retirees and unskilled workers approve.

Yes, they would.

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