The solar market and the 2nd-Derivative Paradox

How could equipment sales in an exponentially-growing market be anything but upward? It happens all the time. Welcome to the 2nd-Derivative Paradox. That's my name for the trap that one can fall into when it comes to capital equipment markets. Solar is a great example. It's hard to explain the paradox, though, so bear with me.

Start with installed capacity. If you are a power generator, you think in terms of the cumulative installed generating capacity in the world. This is what the users actually use. The figure shows three scenarios how that might play out, and they all look pretty much the same in this chart. Nice, steep slopes. Note how they all start at the same point and end up at the same point.

Then look at panel shipments. But the solar panel industry isn't interested in what's already out there. It needs to ship new panels every year. The shipments amount to a 1st derivative: the new capacity that's added to the infrastructure every year. Now the differences in the scenarios show through, as shown in the second figure. But the scenarios all show steep upward growth. What's to worry about?

Now look at panel manufacturing equipment. The solar manufacturing equipment industry, and that includes lasers--isn't even interested in solar shipments, but the need for more manufacturing capacity to make the panels. You only need more equipment when you are shipping more panels than before. That amounts to a 2nd derivative of the cumulative generating capacity, and can give wildly different results. New equipment is shipped in all three scenarios, but in the "sustaining" scenario the equipment shipments are flat year after year, while in the "slowing" scenario they start out strong, but then decline. Ouch.

Other traps. Of course we would all like to live in the "growing" scenario. The trouble is, strong positive exponential growth doesn't last indefinitely, no matter what they say. And that's not even considering some ups and downs along the way, like this year. A slight shift in the solar panel shipments wreaks total havoc for equipment shipments.

Other things that juice equipment sales. The same trap exists in other industries, too. But there are other details to consider. First, there is usually some churn in suppliers. Machines also get obsolete. And there is also the early obsolescence forced by things like Moore's Law. These all have to be considered.

Watch that 2nd derivative. Don't get me wrong. I love solar. I had a summer job at TI testing solar cells back in the Jimmy Carter era. We all believe it's going to be a great thing in coming decades. But it's not enough that the cumulative generating capacity will be on a steep upward slope for years to come, because when it comes to manufacturing equipment, it's the 2nd derivative that counts.