# Embedded Ideas and Economic Growth

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

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.

## 19 thoughts on “Embedded Ideas and Economic Growth”

1. If non-rival ideas are non-excludable, would it imply zero returns? If only excludable non-rival ideas earn positive returns, could the growth models that assume price-taking remain valid (after tweaking them to make it clear that constant returns apply only to inputs and excludable ideas)? Just trying to work out what your latest post implies. Thanks.

• Yes on both questions, I believe. If non-rival ideas are non-excludable, then anyone can copy them at effectively zero cost. So the instant I invented a new idea, you’d copy it and undercut my price, and others would keep entering the market until profits went to zero. Thus my incentive to invent in the first place disappears.

Yes, the models of price-taking can make sense with CRS on rival inputs. For them, the excludability is driven by being hard-to-copy. I may not have a patent, but you can’t copy my product without a lot of effort (it may take years). Thus I can keep earning P>MC for a while, providing incentives to invent.

2. Concerning incentives to invent new varieties of goods, recall that an existing variety may be easy to copy but still not be copied. If inventing a new variety costs the same as copying an existing variety, then it always is better to spend your money on inventing the new variety. You would have to split the market with the incumbent if you copied his variety, whereas with a new variety you get a niche all to yourself. There still must be some monopoly power to generate the excess profit necessary to pay for the original sunk cost. The point here is that varieties can be perpetually invented even though there are no trade secrets and no patents, leaving rival producers able to copy existing varieties.

Patents are effective in markets where imitation is much cheaper than invention. However, they also work in markets where imitation and invention cost the same. That’s because patents effectively prohibit not just exact copies but also very close substitutes. Courts would judge the very close substitute to be essentially the same as the original and judge it to be a patent infringement.

• John – good point. I think that gets to the issue here – there is no single right market structure for ideas. Some ideas would benefit from copyrights or patents, some ideas don’t need them because they are so hard to copy anyway. What’s the *optimal* amount of protection? Where do we draw the line? No idea.

3. The strange thing is that new ideas and inventions occurred before patents, etc. I think your last point that there is no single right market for ideas is closer to reality!

4. I agree with the bottom line but at some point if something is “incredibly difficult to copy” then calling it non-rival isn’t useful. Usain Bolt’s skill isn’t a recipe. Let’s say, contrary to fact but helpful to your argument, that with time and effort that anyone can duplicate the running fast skill. In this case, it’s the time and effort that really *are* the skill and these are rival. Your point that Bolt and Gatlin can both have the skill so it isn’t rival doesn’t work because there is no spillover–it’s not the same skill. Gatlin didn’t get anything from Bolt he didn’t copy the skill or get any benefit from Bolt he just engaged in the same production process. One might just as well say apples are non-rival because two farmers can both have an apple if they invest the same time and effort in growing apples.

• I think you are lumping “excludability” in with rivalry. Just because it takes time to acquire the skill doesn’t mean the skill is rival, it just means that it is hard to acquire, i.e. exclusive. Spillovers are not equal to non-rivalry. Spillovers just mean that something isn’t very exclusive.

But something can have no spillovers (it’s literally impossible to copy) and yet still be non-rival. Music, meaning a recipe for what notes to play in a certain order, we could probably agree, is non-rival. If I play it, I don’t use it up or keep you from playing it. So on December 8th, 1980, John Lennon has a great melody idea, and he is the only person in the world who knows it because he just thought of it. He’s killed later that day. This melody had no spillovers. No one ever heard it. No one will ever be able to copy it from Lennon. It’s still non-rival.

Maybe the apple example works best. *An apple* is rival. The inputs to apple production are rival (soil, labor, water, sunlight, etc.). But the characteristics of a Pink Lady (a personal favorite) that make it desirable (texture, taste, etc.) are non-rival. If I open an apple orchard, I can grow apples that are identical *in characteristics* to yours. The fact that you worked really hard to grow those apples using your rival inputs doesn’t mean that I cannot also work really hard to raise an apple with those same characteristics. The fact that the actual apples you produce are rival, and the apples I produce are rival, doesn’t change the fact that they have the same non-rival characteristics.

• Hi I understand Pink Lady is really a brand name. There is no property right in the variety itself. Others can grow the same Appel, but just can’t call it Pink Lady. I guess a trademark is non-rival but excludable. Cheers.

• Careful – the trademark is not non-rival. The characteristics of a Pink Lady apple are non-rival. The trademark is a way of making those non-rival characteristics excludable.

• Aristotle>>Plato.

5. “What the conditions I laid out last post say is that this compensation for rivalrous time is below the marginal product of my time.”

Dietz, that’s right. It’s too bad (for me only, I guess) that you didn’t follow through by stating that, because of this, it is perfectly valid to model this as a competitive equilibrium, contrary to the claim made by Romer.

• David – sure, for ideas that are “naturally” excludable, it can make sense to think of them being provided even though they take their output price as given. And practically, we could argue about whether some ideas *should* be provided without market power or with market power (i.e. patents).

But in defense of Romer, because of the presence of *some* non-rival ideas that are *not* naturally excludable, and the fact that those ideas earn some rents, then there must be some market power in some markets in the economy. The whole economy cannot be modeled with competitive equilibrium given the presence of those ideas.

• Perhaps I misunderstand, but I thought you agreed that if a non-rival idea is non-excludable, it earns zero returns. That said, there are people who write poetry or music for non-monetary reasons. So even non-excludable and non-rival ideas can be created. Beethoven symphonies are no longer excludable but people still benefit from his work.

6. Dietz,

I’m afraid I disagree with you: there is no defense of Romer’s personal attacks against the academics in question.

In my original post, I noted that Romer should have attacked the assumptions that these authors were making and why their world view was not the best way to think about growth. He did not choose to critique their ideas in this legitimate manner. Instead he chose to impute motives to them. It was a shameful display.

7. Tennis fan here: I think I may disagree with your claim that Djokovic and Nadal have copied a subset of Federer’s skill set. Instead they have developed their own skill sets – Nadal’s topspin, Djokovic ultra-fitness – that counter RF’s set.

• This is a tough case of definition. They’ve mastered the skill of “beating RF”, which they did not previously have. But yes, Nadal’s particular shot-making is unique to him, for sure. It isn’t the best analogy.

8. I suddenly get a thought: if the payoff of rival input is less than its marginal product, how would the price forms? By what kind of rule?

• Supply and demand, same as always. It’s just that the demand curve for labor/capital is lower than it would be with perfect competition.