Wednesday, February 2, 2011

Populations models and Minimum wage

I'm holding off on my Liberty vs Utilitarianism post for which I needed the definitions in my last post.  I also wanted to subtitle this post "How to convince a liberal engineer that minimum wage is bad".

Walter Block has many of his talks and guest appearances on the Mises Torrent (should try to add a link for that).  For the second time now, I've heard him debate this hack, Jared Bernstein, on minimum wage.  At the beginning of one of these debates, Walter lays out the logical conclusion that 1) it is not an employment law, namely it doesn't say that so and so must be hired, but it is inherently an unemployment law, it says it is illegal to hire someone below some dictated amount.  And 2) it increases employment higher than it would other wise be. This second point is what I want to focus on and the wording is very important.

Bernstein comes back with something like, "if Walter's simplistic theory actually were true then this would be a closed and shut case, but it isn't.  When you look at the data, moderate increases in the minimum wage do not result in more unemployment".  Walter explains that he has failed to uphold ceritus paribus (all things being equal) and wonders why Bernstein is so stingy with the raise, why not raise it to $10,000/hour?  Bernstein replies in his ad hoc style with "that's over the top".

Now, why is Bernstein willing to admit that raising the minimum wage to $10,000/hour would cause massive unemployment but raising it to $7/hour would have no effect except to raise the wages of the poor?  Let's put aside all the games economists play with the numbers such as not including those who stop seeking employment, or looking at immediate rather than long term effects, or not seeing the redistribution from low skill, low pay jobs to high skill jobs (which are not held by the same people).

Bernstein does not understand simple differential equations.  Take population models, our first introduction to stability, eigenvalues, and systems of first order, non-linear equations.  The rabbit and fox model is a favorite.  This will be easier if you remember what the time dependent plots look like, but you'll be able to follow either way.  Now, if the fox population increases, does the rabbit population decrease?  Answer: Just as with an increase in minimum wage, not necessarily.  Why?  Because the interaction term, or the rate at which foxes eat rabbits, in the differential equation (i.e. -a*x*y where x is the population of foxes, y is the population of rabbits, and a is positive coefficient) might be small compared to the intra-action of rabbits, the rate at which they multiply (b*y or is it b*y^2?).  An increase in the fox population may still give an unbounded population of rabbits.  It may, however, cause the rabbit population in the area to disappear if the increase in foxes is large enough or it may shift the equilibrium.

The market is very complex so I could go on for pages as to why you may not see an increase in unemployment, the easiest being inflation: inflate the money supply, raise the price of everything including labor.  But let's return to the importance of Walter's wording.  Ask the above question slightly differently, would an increase in the fox population cause the rabbit population to be smaller than it otherwise would be?  Yes, since "a" is not zero and neither is x nor y, this term necessarily pulls down the rabbit population.  In non-math terms, if one fox eats one rabbit then the rabbit population is smaller than it otherwise would be, ceritus paribus.  Is this contradictory to what I wrote above about an unbounded rabbit population?  No, because there is a time component.  Instead of rabbits increasing at the rate y=exp(5*t) it may increase as y=exp(1*t).  Either way an increase of foxes, or in our case in minimum wage (or the number of politicians who are akin to foxes), is detrimental to the rabbits.  And minimum wage is detrimental to those with small marginal revenue products who are also known as the poor.

Walter responded to Bernstein with, "I do agree with Jared on one thing, that this is a closed and shut case, you can't argue with the logic".

2 comments:

  1. I think I may have to take some more time with understanding your post, but I thought I'd put my assumptions out there to evaluate (as if I were some fellow off the street):

    Minimum wage is good, because it separates people into categories of "employed" and "unemployed," rather than having masses of people being somewhere in the middle or possibly categorized as "the working poor" (working while living in grinding poverty).

    In our society, being "unemployed" means you might fall into a "safety net" and be retrained or redirected (this is not always the case), whereas a person of the working poor may continue in desperation at their "real wage" job until emergency strikes and they are wiped off the face of the earth.

    And so, although "real wages" could raise employment in a population, there could be real disaster for people in this gray area of "working poor" where no one may know their desperation.

    (This way of thinking takes for granted the existence some sort of governmental or ngo assistance for the unemployed)

    I write all this without censoring myself, simply recording my own free flowing assumptions.

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  2. Ryan, if I understand your comment, the minimum wage is a "weeding out" process where low skilled, dangerous, or "impoverishing" jobs are raked from the market. It forces companies to invest in capital improvements and automation, making them more efficient.

    Without minimum wage to kick them out of the work force(coupled with government programs) the working poor would just keep going to their unfullfilling, low-wage jobs not realizing there are unemployment and retraining opportunities for them.

    The logic is kind of there; it may be true that unemployment by minimum wage is a net benefit to SOME people. This will be the topic of my upcoming posts, but why do we need to resort to government regulation of the price floor for wages... or more accurately, the price hurdle?

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