Perpetual motion machine, Perpetuum mobile, 3D illustration. 3D model is accurately made according to drawings of Leonardo da Vinci

Jubal Harshaw at the blog GrokInFullness had an excellent post last month on the minimum wage that I had missed. (HT2 Jonathan Meer.) It’s titled “The Minimum Wage as a Perpetual Motion Machine.” Here are the second and third paragraphs:

I worry that an elasticity of less than 1 can be abused by people who try to calculate the net benefits of increasing the minimum wage. I’ve seen a few studies that try to do this. They will take some estimate of the elasticity of demand from the empirical literature, count up the costs to the losers (those who lose their jobs) and the benefits to the winners (those whose wages increase) and cheer the net social benefits of the minimum wage.

Try this on for size. Let’s increase the minimum wage by 10%, which will reduce total employment of affected workers by only 1%. (Assuming -0.1 as the elasticity of demand for low wage workers.) The net effect is a benefit, because the gains to the winners are larger than the losses to the losers. Total compensation changes by (1 + 10%) * (1 – 1%) = 1.09, in other words a 9% increase. (The first term is the increase in wages per worker, the second term is the decrease in the total number of workers. Multiplying these together should give you the change in total compensation. Try it with some actual values for the minimum wage and numbers of workers to convince yourself.) Okay. So let’s keep going. Let’s raise the minimum wage by 100%. Net benefits to the affected workers are (1+100%)*(1-10%) = 1.8. An 80% increase! To boot, maybe there’s some way the winners can compensate the losers, such that everyone’s take-home pay increases! A 200% increase would yield an even bigger 140% increase! This isn’t literally a perpetual motion machine; it maxes out at a 450% increase in the minimum wage, then the net benefits start coming back down. But the notion that someone could take the logic of small increases and extrapolate them this far is alarming. It implies that there’s something fundamentally wrong with this approach. That fundamental error is present even for small changes, but the smallness allows minimum wage advocates to paper over it.

He goes on from there. The whole thing is well worth reading.

I’ll point out, though, that even if the problem he identifies with the way of thinking above were not a problem, there would be another huge problem: the cost/benefit analysis looks only at a subset of winners and losers. The other two groups that lose are employers and consumers of the products that the employers produce. And in case you think they don’t count (I disagree with you), remember that many of the products produced by low-wage workers are bought by low-wage workers.