# Harry Potter and the Residual of Doom

The productivity term in an aggregate production function is tough to get one's head around. When I write down

$$Y = K^{\alpha}(AL)^{1-\alpha}$$

for aggregate GDP, the term ${A}$ is the measure of (labor-augmenting) productivity. What exactly does ${A}$ mean, though? Sure, mathematically speaking if ${A}$ goes up then ${Y}$ goes up, but what is that supposed to mean? ${Y}$ is real GDP, so what is this thing ${A}$ that can make real GDP rise even if the stocks of capital (${K}$) and labor (${L}$) are held constant?

I think going to Universal Studios last week provided me with a good example. If you take all the employees (about 12,000 people) and capital (building supplies, etc..) at Universal Studios and set up a series of strip malls along I-4 in Orlando, then you'll generate a little economic activity between people shopping at the Container Store and eating lunch at Applebee's. But no one is flying to Orlando to go to those strip malls, and no one is paying hundreds of dollars for the right to walk around and *look* at those strip malls. The productivity, ${A}$, is very low in the sense that the capital and labor do not generate a lot of real GDP.

But call that capital "Diagon Alley" and dress the employees up in funny robes, and it is thick with thousands of people like me shelling out hundreds of dollars just for the right to walk around a copy of a movie set based on a book. Hundreds. Each.

This is pure productivity, ${A}$. The fictional character Harry Potter endows that capital and labor in Orlando with the magical ability to generate a much higher level of real GDP. No Harry Potter, no one visits, and real GDP is lower. The productivity is disembodied. It's really brilliant. Calling this pile of capital "Gringotts" and pretending that the workers are wizard guards at a goblin bank creates real economic value. Economic transactions occur that would otherwise not have.

We get stuck on the idea that productivity, ${A}$, is some sort of technological change. But that is such a poor choice of words, as it connotes computers and labs and test tubes and machines. Productivity is whatever makes factors of production more productive. That is pretty great, because it means that we need not hinge all of our economic hopes on labs or computers. But it also stinks, because it means that you cannot pin down precisely what productivity is. It is necessarily an ambiguous concept.

A few further thoughts:

• It doesn't matter what is bought/sold, real GDP is real GDP. Spending 40 dollars at Universal to buy an interactive wand at Ollivander's counts towards GDP just the same as spending 40 dollars on American Carbide router bits (We bought two. Wands, not router bits). There is no such thing as good'' GDP or bad'' GDP. Certain goods (tools!) do not count extra towards GDP because you can fix something with them.
• Yes, you can create economic value out of nothing''. Someone, somewhere, is writing the next Harry Potter or Star Wars or Lord of the Rings, and it is going to create significant productivity gains as someone else builds the new theme park, or lunch box, or action figure. This new character or story will endow otherwise unproductive capital and labor with the ability to produce GDP at a faster rate than before. ${A}$ will go up just from imagining something cool.
• This kind of productivity growth makes me think that we won't necessarily end up working only 10 or 12 hours a week any time soon. The Harry Potter park doesn't work without having lots of people walking around in robes playing the roles. It's integral to the experience. So we pay to have those people there. Those people, in turn, pay to go see a Stones concert, where it is integral to have certain people working (Keith and Mick among others). We keep trading our time with each other to entertain ourselves. Markets are really efficient ways of allocating all of these entertainers to the right venues, times, etc.. so it wouldn't surprise me if we all keep doing market work a lot of our time in the future.
• Long-tail'' creative productivity gains like Harry Potter exacerbate inequality, maybe more than robots ever will. You can buy shares in the robot factory, even in a small amount. But you cannot own even a little bit of Harry Potter. You can't copy it effectively (*cough* Rick Riordan *cough*). So J.K. Rowling gets redonkulously rich because ownership of the productivity idea is highly concentrated.