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# Minimum-Wage Minutia

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Three e-mail correspondents and a commenter have asked me to clarify a specific claim that I make in this post [2] – namely, that it’s possible for a hike in the minimum wage to increase overall employment even while it decreases the employment of those workers it is ostensibly meant to help (namely, low-skilled workers).

I do so below.  First, however, I want to express regret that I did not focus that post more appropriately.  My point there is that trends in overall employment cannot be used to test the economic argument against the minimum wage because that argument is that the minimum wage reduces the employment prospects only of low-skilled workers.  (I assume throughout what is empirically the case, at least in the U.S. – namely, that the legislated minimum wage never comes close to being as high as the median wage.)  Talking about trends in overall employment when the question involves the employment consequences of minimum-wage legislation is to talk about an irrelevant fact.  What matters is the employment of low-skilled workers.

Anyway….  Suppose that the two lowest-cost options for Acme Co. to produce Q amount of output X are as follows (and reckoned on an hourly cost basis):

1)  10 hours of low-skilled labor combined with 50 dollars of capital expenses;

2) 11 hours of skilled labor combined with 30 dollars of capital expenses.

If the prevailing hourly wage for low-skilled workers is \$7.25, then Acme Co.’s hourly production costs will be \$122.50 if it goes with option 1.  (\$72.50 for ten hours of low-skilled labor plus \$50 of capital expenses.)  If the prevailing hourly wage for skilled workers is \$8.41 or higher, then Acme will use option 1; it will produce X using low-skilled rather than skilled labor.  (If Acme employs 11 skilled workers at \$8.41 per hour, and uses with these workers \$30 of capital every hour, Acme’s hourly production costs are \$122.51 – higher than the total costs of hiring ten low-skilled workers at \$7.25 per hour along with \$50 worth of capital each hour.)

Now let the minimum wage be raised to (say) \$8.41 per hour.  If Acme continues to produce Q amount of X each hour by employing ten low-skilled workers, along with \$50 worth of capital, Acme’s hourly production costs would rise from \$122.50 to \$134.10.  (Ten low-skilled workers at \$8.41 per hour = \$84.10; adding \$50 of hourly capital expenses sums to \$134.10 per hour.)  But by instead employing 11 skilled workers at \$8.41 per hour, along with \$30 worth of capital, Acme’s hourly production costs will rise only by one cent, to \$122.51.  Raising the minimum wage in this example causes Acme to fire (or not hire) the low-skilled workers and instead to employ the skilled workers.  Overall employment at Acme rises, and might rise for the economy as a whole if the now-artificially higher demand for skilled workers entices enough skilled workers, who would not have been in the labor force, into (or back into) the labor force.

I understand that the above is no general-equilibrium analysis.  Yet it is certainly possible, if not likely, that raising the minimum wage can cause overall employment to rise even as it cruelly shoves many low-skilled workers into the ranks of the long-term unemployed.

Again, though, my main point is that overall employment trends are irrelevant when discussing the merits or demerits of minimum-wage legislation.

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