# Embedded Ideas and Economic Growth

In the last post I laid out three conditions that could when describing how economic growth worked, and said we had to pick two. In short, I argued that we should pick (1) constant returns to scale in rival inputs, and (2) non-rival ideas earn some part of output. This meant that (3), rival inputs earn their marginal product, had to be done away with.

One particular complaint about my characterization of the issue is that it did not address the concept of ideas "embedded" in people (or things). Something like "the ability to solve differential equations" is a skill that is embedded in some people, and not in others. Once you think about embedded ideas, the argument goes, then you have to consider those ideas "rivalrous". The person who knows differential equations can't be two places at once. The idea of solving these equations is just along for the ride in this persons head, so the idea is rivalrous as well. The strongest form of this argument would then say that it only makes sense to think of all ideas as embedded and rivalrous, and by dropping non-rival idea completely we can maintain the idea that all rival inputs earn their marginal product.

I think this is wrong. Yes, some non-rival ideas or skills are embedded in people or things. I don't have any problem with that. But an embedded skill is still non-rival. Tomorrow someone new is going to learn to solve differential equations and that will have absolutely zero effect on my ability to solve them. I can copy the skill over and over and over, teaching the whole world to solve differential equations, and that will not diminish the ability in anyone else. That's the definition of non-rivalry.

Saying a skill or idea is embedded in a person (or thing) is a statement about exclusion only. People who did not take the right math classes are excluded from solving differential equations. Those of us who know how to do it own an excludable skill. But it is still a non-rival skill.

Non-rival ideas or skills can even be uniquely embedded in a person or thing. Usain Bolt is uniquely capable of running 100 meters in 9.58 seconds. There has never been anyone in recorded history to run 100 meters this fast. Despite that, running a 9.58 is a non-rival skill. If this year Justin Gatlin runs a 9.58, that isn't because he took away the skill from Bolt, which would mean the skill was rival. They could both run this fast; it is a non-rival skill.

Saying a skill is unique is a statement about exclusion, not rivalry. If no one ever again runs 100 meters as fast Usain Bolt did, that doesn't mean running a 9.58 is a rival skill, it means that running a 9.58 is an exceptionally excludable skill. So excludable that it is impossible. But still non-rival.

Making non-rival skills hard to copy doesn't change their non-rivalry. The fact that teaching everyone in the world how to solve differential equations would be very, very time-consuming doesn't make this a rival idea. High costs of time or resources to create copies of skills make those skills highly excludable, but not rivalrous.

World class athletes are still probably the best example here. Roger Federer has a set of highly exclusive - and yet non-rival - skills. It is almost impossible to copy Federer's skill set. I certainly could not, even if I had started training at age 4. But Djokovic and Nadal, after years and years of grueling training and practice, have copied enough of them that they can now beat Federer (sometimes). The skills of playing world class tennis are embedded and highly exclusive. But they are still non-rival.

So what does this have to do with growth theory? The non-rivalry of ideas or skills allows for continuous economic growth. But it is the excludability of those ideas or skills that provides incentives for individuals to create them or learn them.

Romer originally focused on non-rival ideas that were incredibly easy to copy, like software, books, or blueprints. Being easy to copy, these things are not easily excludable, and hence it would be hard to earn rents on them without some kind of protection. Things like patents or copyrights give these easy-to-copy ideas excludability. Those intellectual property rights provide the incentive for people to create new easy-to-copy ideas.

Boldrin and Levine focus on non-rival ideas that are incredibly hard to copy, like the embedded skills of solving differential equations or playing world class tennis. The sheer effort involved in copying makes these ideas highly excludable. The owners can earn rents even without explicit property rights over the idea or skill. Roger Federer doesn't own a patent on world class tennis playing. It's just nearly impossible to copy his skill.

In both situations, growth will arise because of the acquisition of new non-rival ideas or skills. In both situations, that acquisition occurs because the exclusivity of the idea or skill allows them to earn rents on it, and those rents are sufficient to offset the costs of inventing or acquiring it in the first place.

Where I think BL went wrong is in claiming that embedding skills or ideas in people or machines makes them rival. They used that term incorrectly. Embedding makes skills or ideas excludable, even though they are still non-rival. Once they claimed that some ideas were rival, they had to contort themselves into arguing that non-rival ideas don't earn any rents ever to satisfy the "pick 2 of 3" conditions I laid out in the last post. If you want to accuse BL of "mathiness", then it would be because they mis-matched the language (rivalry) with the math (excludability).

For his part, Romer has probably over-stated the importance of monopoly power over ideas. Yes, a patent gives you monopoly power over an idea. And without that patent, an easy-to-copy idea would most likely not be produced. But some ideas or skills are hard to copy, and the people who hold them do not necessarily need a monopoly over them in order to earn rents. Some ideas are hard enough to copy that you can earn rents even though you face some Cournot-style competition from the few others capable of copying you (i.e. Federer, Nadal, Djokovic). Romer doesn't really need strict monopoly power, he just needs rents to accrue to idea owners.

The ultimate point is that the world can make sense with (a) non-rival ideas/skills, (b) that are embedded and highly excludable, (c) with Cournot-style competition among owners of the ideas/skills, and yet still satisfy Romer's conditions that (d) we have constant returns to scale in rival inputs and (e) positive payments to non-rival ideas/skills. (b) and (c) are not incompatible with (d) and (e). But saying that non-rival ideas simply don't exist doesn't make any sense to me.

Last point. Given the last post, we know that such a world would require that rival inputs (raw labor, capital, land) earn less than their marginal product. The rents earned by owners of those embedded non-rival skills have to come from somewhere. How do I square that with the wages earned by someone with an embedded skill, like Federer, or someone who knows how to solve differential equations?

The important point here is to not confuse someone's total reported "wages" with the return earned by their rival input. My total paycheck is some combination of a return to my rival input (i.e. time) and the return to my non-rival, embedded and excludable skills (i.e. teaching 1st-year grad macro). The fact that UH does not separately compensate me for these inputs doesn't mean that my wage is being paid only for rival inputs. Some of my paycheck is rents I earn for providing a scarce, embedded, excludable but non-rival set of inputs. Some of my paycheck is compensation for my rival input, time. What the conditions I laid out last post say is that this compensation for rivalrous time is below the marginal product of my time.