# Harry Potter and the Residual of Doom

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

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

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.

## 16 thoughts on “Harry Potter and the Residual of Doom”

1. For lack of a better term, the phrase which has shown up lately in my notes for this is “time sculpting” – when a group decides (or is perhaps hired) to generate unique experiential product!

2. This is not productivity in any meaningful sense. It is rents on monopolistic intellectual property, owned by JK Rowling. If I, or anybody else were allowed to open our own Harry Potter worlds, then the price of visiting them would quickly drop to the same price as the strip malls. The prices would be based only on the price of labour, land and building capital. This is the opposite of productivity in the sense of capital that does things more efficiently, eg a new machine, that costs the same as the old one, that can make twice as many widgets per hour while using ony 80% more materials.

• You’re confusing the distribution of the addition to GDP with the addition to GDP itself. Yes, real GDP goes up. Sure, a big chunk of that goes to JK Rowling in the form of royalties. But another chunk goes out in wages to workers, and the rest to owners of Universal stock.

You’re absolutely right that if you could copy JK Rowling then you could drive down the mark-up that Universal gets to charge on their particular park. But you’d either have to bid up the price of existing land and capital (or induce more to be supplied) to build your own park, which would mean real GDP was higher. Getting rid of JK Rowling’s intellectual property rights changes the distribution of the extra real GDP the theme parks produce, it doesn’t eliminate it.

• The time and money people spend on Harry Potter would have been spent on something else if Harry Potter was never written. If Zorgan the Space Knight had become popular instead, you’d be thinking that Zorgan was responsible for GDP.

• That is false. You are confusing money with output. Harry Potter World at Universal represents higher output given a set of inputs, even if the amount of actual money changing hands never goes up or down. If Zorgan the Space Knight had become popular instead, and there was Zorgan land, then sure, that would have raised GDP instead. That doesn’t mean that Harry Potter World did *not* raise GDP.

3. Your last two bullet points are quite thought provoking. Thanks for sharing!

4. This is a great illustration of an idea which is often portrayed in too arcane of a fashion for the lay-person to easily grasp. Thanks so much for sharing this! 🙂

5. I don’t know. As a metaphor for how Labor & Capital combine to make things of different value, than sure. But as you described it, I have a hard time believing that this is generating increasing returns to Real GDP. Wouldn’t the patrons of Diagon Alley buy something else with their $100? Wouldn’t that be an equal sized contribution to Real GDP? What you’re talking about seems like a redistribution of Real GDP from other sources to Gringotts, not a fundamental change in achievable Real GDP. This seems like a problem of scale. When looking just at the GDP of Orlando, then putting in Diagon Alley seems to be a multiplier for Orlando’s Real GDP. But I am not so sure if you think about it in terms of the US. • No, they wouldn’t. Because without Universal that patron wouldn’t have$100, they’d have $99 (or something less than$100). It’s a circular flow. So the payments you make to Universal become wages and earnings for workers and capital of Universal, who spend that on other stuff….which ends up paying my wage which lets me go to Universal. So it’s absolutely good for the entire US. This is not a zero-sum game.

• (I’m a different Ben but I agree with the original Ben’s post.) Just because money is a circular flow doesn’t mean that we have infinite money to spend on consumption goods. We can’t non-zero-sum our way out to a world where everyone has written a million-selling fantasy novel that has its own amusement park. If everyone just writes novels that everyone else buys then that comes at a cost to the rest of our consumption spending. Harry Potter World only adds to the circular flow if people are keeping their money in their mattress otherwise (or there is slack demand for some other reason).

It’s all about input costs relative to output. It makes sense to think of discretionary consumption goods as a zero sum game so long as the cost of producing those goods stays constant and resources are not slack (both of which are debatable in the HP case, but not really the point made in the original post). Consumption goods are competing for a limited share of national budget that can only be as large as the our economy is productive. If book publishing technology improves so that it’s cheaper to write or read books then that is technology improving (or if somebody writes a really popular book that increases the economies of scale of the writer). But if somebody just writes a new book that replaces another popular book, and an amusement park just builds a new area to replace an old decrepit area, productivity is not increasing. New ideas and investment that have resources diverted toward them only add to productivity if they actually increase output relative to input.

If you’re going to argue that HP and associated amusement parks are a higher quality good than people would otherwise be able to purchase with their discretionary income, and that marginal gain in quality is a productivity improvement, then I suppose that’s fine. But these are only marginal improvements and they are entirely subjective. (and since they’re marginal, it’s misleading to refer to Harry Potter World as something conjured out of nothing, when in fact it’s something conjured out of the resources that would have gone to the next best investment)

People can exchange money in a circular flow all they want, be it at home or at a strip mall in Orlando, but it doesn’t actually increase our residual unless costs go down or output goes up.

• But output does go up. Output is the value of goods and services produced, and the value of them has risen because we organized some capital and labor as “HP world” rather than “a strip mall”. Or, if you like, the cost of “pretending to be Harry Potter” has fallen in that it is cheaper for me to visit Orlando rather than build a castle in my back yard. Either way, the real value of goods and services has gone up.

The circular flow of *money* is not the same thing as the circular flow of *real goods and services*. You can get more flow of G and S without changing the flow of money at all. The price level simply changes.

6. Couldn’t we see the Harry Potter universe as just a certain form of capital? And we are only including it in ‘productivity’ in this case because we haven’t found a good way to measure it’s value as capital?

• Sure. But that’s true about nearly everything. Is software “capital” or is it “technology”?