## Thursday, August 21, 2014

### Reswitching and the Minimum Wage: An Austrian doing Sraffian Economics that is not Bob Murphy

Don Boudreaux walks through an interesting exercise where the minimum wage leads to switching between two production techniques as a possible reason for increased employment as a result of the minimum wage. The logic from Don is as follows:
"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."
First, I want to give kudos to Don for spelling this out when many people (myself included) were confused by a previous post where he said that increased supply from a minimum wage might increase overall employment. Actually that still confuses me and it's not at all what he has here (here it's a demand shock, not a supply shock that's occurring). This provides a sensible (likelihood is another question I'll get to in a moment) explanation of a result that empirical analyses seem to point to - and a result that is not one that is particularly amenable to Don's own views on the minimum wage as policy.

It's also interesting, though, because reswitching situations like this are typically highlighted by left-heterodox economists and Sraffians, most notably during the Cambridge capital controversy. For all Don complains about fairly standard models with turnover, fixed hiring costs, and monopsony power as explanations of the minimum wage, this invocation of reswitching is a much bigger departure from received neoclassical economics.

So what do we make of it? In practice I doubt it's a major contributor to the lack of a disemployment effect in the best empirical analyses. A lot of the studies have focused on low-skill service sector work where the opportunity for this sort of reswitching seems like it would be minimal. It seems like it would be much easier as a manager to make low-skill workers more productive than it would be to change a production process, particularly because the reswitching usually involves a capital-labor substitution of some sort. Add in the fixed costs of making the switch in the first place and it just doesn't seem likely. But if there are any good examples where something like this is going on that would be really interesting and I'd love to hear about it. The result is so anomalous I think it's likely that lots of things are going on to drive the result and this might be part of the puzzle.

1. It's a departure from neoclassical economics (the silliest, insipidly mathematical, descriptivist neoclassical economics) but not really a departure from austrian economics. Samuelson's comment about how all this disproved Bohm-Bawerkian capital theory notwithstanding.

1. Right, I'm saying it's a nice analysis. But if you take Alan Manning's work and you take this blog post, it's not Manning that you're going to accuse of "abandoning basic economic theory".

You know I don't like ANY talk like that, I just find it interesting that Don of all people - who has accused people of ignoring basic economics - goes with something out of sync like this.

I think it's an interesting exercise but I am struggling to think about where this actually happens. The best examples of production techniques that would actually change in response to the minimum wages do so by economizing on the use of labor and using more capital. Don proposes the opposite and I'm sort of groping for a concrete example myself.

2. Isn't the labor component of capital expense relevant too ?

For example: If one introduces an assumption that 60% of capital expenses is labor (that is one stage back in the production process the producers of the capital goods employ that labor) , then after the increase in the minimum wage 1 extra person is employed on the product but there will a reduction of more than 1 in total employment.

1. That's exactly what I thought.

3. That's not really reswitching, that's three factors of production, two of which are labeled "labor".

1. It's a blog post, it's not a fully fleshed out reswitching model, but we've got a change of production technique due to a change in the price of a factor.

4. Reswitching of the sort described here can occur with any input. We Austrian Economists disagree with reswitching when discussing *Capital and Interest*. That's because we know a special thing about the interest rate: it's generally low. In his examples of capital reswitching Samuelson uses a very high interest rate. If a low interest rate is used instead then implausible assumptions are needed to make it work. Garrison describes this in his paper "Reflections on Reswitching and Roundaboutness". Without that special knowledge we can't eliminate reswitching as a possibility with other inputs. I generally agree with Daniel though that it's implausible, but monopsony is quite implausible too. There are other explanations though.

Rob Rawlings is right to bring up capital producing processes. It's the same in the debates about roundaboutness, the *total roundaboutness is the issue, not that within one firm or industry. This can get quite tricky. For problems like this it's necessary to be specific about time, to describe how time is treated carefully. Hayek describes this early on in "The Pure Theory of Capital".

5. While the issue of "reswitching" may be an interesting one to some theoretically-minded economists...has there ever been a historically-documented case of the phenomenon in economic history?

6. Isn't the assumption that the skilled labor has less capital unrealistic.

Skilled labor means they can use complex equipment and techniques and a major determinate of productivity is that skilled labor is more productive. But it is more productive because of both the workers training and experience and the amount of capital he works with. Skilled labor digging a ditch with a back-hoe has more capital than unskilled labor using shovels.

All anonymous comments will be deleted. Consistent pseudonyms are fine.