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"And the marginal cost of communicating the idea to the n'th person very probably will be greater than the cost to the first person of figuring out the idea, if n is large enough."

That's probably the last sentence I'd ever expect a *blogger* to type...

Have a good time!

Nick, aren't you putting skills and ideas into the same pot? The economics are quite different, no?

This is an area where the internet has been so powerful. It's become so much cheaper to share ideas. A scientist can put up his ideas and data on the internet and anyone in the world can read them virtually for free 24/7/365. The same for downloading vast software programs, and so much more. It's not 100% free, but it's amazingly close, compared to any other time in history. And this has really changed what's efficient and maximizing of total societal utils, especially since in a modern economy idea goods are so much more important than they have been in the past.

It might help to get specific. Name an idea that, let's say, anyone in the discussion here could use (i.e. not too technical). Then we can all try to use the idea, see how that works, then we can more intelligently discuss the economics of the value of the idea versus the cost of getting/using the idea. What would be a typical example of a general, nominally economically non-rival idea, in other words, that we could focus on.

I think the problem you're pointing at is that, crudely stated, ideas aren't for everyone.

Thinking more on this, I think you are conflating (non)accessibility with rivalry. An idea may be inaccessible to someone for any number of reasons, from intellectual (unable to comprehend it) to economic (can't afford a tutor). What is NOT one of those reasons is: other people are using the idea. That's all that non-rival means.

See also: the movie Ratatouille as to its (final) take on the motto/aphorism "Anyone can cook".

Romer was pretty hard on this post. I don't see that you've even addressed *rivalry* so much as the *difficulty* (of unlimited copying) of ideas. And the idea that ideas don't really exist would be, well, blatantly self-nullifying, eh?

Sorry for going on and on, but made another connection around "comprehension" and the fact that "idea" is itself an idea. So what if someone is unable to comprehend the idea of "idea" itself. One would think that would blatantly disqualify that person from even engaging in any type of discussion whatsoever. But evidently they are around. How best to identify such "zombie" debaters, out them, and disqualify them? Hmm. Romer's anti-mathiness campaign might be one way. Also, the internet term "troll" comes to mind, as do Paul Krugman's identifications of "zombie ideas". (Maybe the trouble is that those aren't ideas (and/or aren't treated as ideas by their pushers) in the first place. A misnomer.)

Or even if non-rival in conception, failing to be so in implementation.

A point that needs to be made here is that with knowledge/ideas OR skills, it's not just a matter of sharing with one person causes an increase in the input by one, but that the spread is exponential. I.e. ten becomes twenty becomes forty, etc. With this doubling, you would need exponentially diminishing returns to scale in order to not have the growth accelerate. This is why ideas spread like wildfire and are generally impossible to stop. The internet helps to accelerate this, but even without the internet you have extremely rapid growth.

rsj, The rebuttal to the "wildfire" metaphor is that there can be (are) bigger frictions than that for (most) ideas. Sparser fuel (fewer "listeners") if you will, due to intellectual and interest deficits. But also lower "heat" and "wind" for valuable ideas as there is profit motive in "keeping them close" (NDAs for instance).

For example, the idea of rivalry and non-rivalry of goods. That has been around for quite some time, but I never encountered it until now in some fifty years of intellectual life, including education through grad school. Because of course my field of education was not economics. Let alone examples of "hard" ideas like Relativity and Quantum Mechanics that only a small minority of folks understand completely.

Maybe "slow burn" or "smolder" is a better metaphor? (Also notice that the ideas that do tend to "spread like wildfire" are rumor and gossip, i.e. stuff that tends to be inaccurate or outright false.)

The cost of spreading an idea can be the cost of smacking down the bad ideas that surround/attempt to refute the good idea. Example CO2 emissions and climate/ocean hwalth. An un-currated internet is a terrible place to learn about those.

"The cost of spreading an idea can be the cost of smacking down the bad ideas that surround/attempt to refute the good idea."

Or the cost of smacking down the good ideas that refute that bad idea.

I think "idea" is too broad here. The original issue of non-rival goods is really about digital media, patents, software, and other goods with zero cost of reproduction that fall under the rubric of intellectual property. These goods play a *huge* role in our economy -- it's what all the TPP fuss is about. Non-rival goods have eclipsed rival goods in the production process -- more than half of the market value of SP 500 firms consists of intangibles. Romer's point is not an obscure technical "gotcha".

That is the economically relevant distinction -- intellectual property versus physical capital, not the broad notion of an "idea", which can be anything from "all men are created equal" to how spectral analysis can help train deep learning algorithms.

I think rsj's post comes closest to the issue of debate. Abstractions of anything to the limits allow for "almost" any interpretation of the meaning of the abstraction. To wit: An idea is an abstraction for human thoughts and imagination. They exist within a single set of synapses in one brain and this can have no value unless and until communicated AND in such a manner of communication that they have some meaning to the person receiving the communicated thought. Interpreting the meaning is likewise within a single set of synapses within the thought processes of each person to whom the original thought is communicated, but which invariably is modified by the person's own thoughts and other synapses holding other pieces of thoughts not inherent in the originators.

This leads to some form of exponential gain of what the original thought actually entailed as a function of n persons to whom communicated. The assertion therefore that an idea is a singular is without merit unless it remains uncommunicated at all. Thus there is never just a singular idea as communicated. By simple extension then how can non-rivals of anything ever exist? To be a non-rival of anything it must exist as an exact duplicate in the interpretation by more then one person, which I will submit is only theoretically possible in an alternate universe.

Therefore the entire economics notion of "non-rival" is a figment of fertile imagination with no reality, and hence every good is therefore a rival good / service ... it's just a matter of degree at any given point in time by any two interpretations of what the "idea" or 'non-rival' means to each. Economists will have to dis-abstract their marginal value equations by several orders of magnitude to have any real world value.

If you want an example, pick binary codes and read up on the origins and history... quite the example of how what can be by some considered a 'non-rival' idea or good has in fact had a huge and forever rival basis since it's earliest forms as n increased exponentially with communication of the idea.

Disagree as to "too broad". Non-rival refers to ANYTHING whose use by one party does NOT prevent (nor deter) its use by another party. Language, math, assembly line, specializing one's labor force, computer programs, ANYTHING. Sorry, but this is a theory discussion. Trying to limit the meaning (of non-rival) will only lead to confusion, as already seen in comments above regarding economies of scale.

@Longtooth, What is this concept of "synapse" that you keep going on about? It has no direct or usable correlate in any of my thoughts. Can you possibly explain it so that I will have the identical concept that you are trying to communicate? Or is it hopeless. Hello? Are you still there?

Agree with some other commenters that the definition of "idea" may be too broad. I'll suggest a special case.
In the US, the test for insider trading requires the investor to have traded on "material, non-public information". What's "material" is defined as information that a "reasonable investor" would determine alters the total mix of information available about the company (I'm not a lawyer but I think I've got this right). In reality, the materiality of a piece of information to an investor depends on what else the investor knows. To an unsophisticated investor, knowing that Company A ordered 10 containers of Part B from a supplier may mean nothing, while to someone super-informed, that information might have tremendous value. In production, knowing a new technique to cram more transistors on a piece of silicon means nothing to me (I have no way to act on it), but there's a handful of chipmakers to whom that information is extremely valuable. If you're in the business, you should already be receptive to the kind of idea that can reduce your costs. If you are not, and your competitors can use that information to outcompete you, you won't be in business for long.

Thinking about this some more, I think this is the key point: "But is it really the same good, as we move along that MC curve?"

If it costs more to teach the same idea to some students than to other students, we can't really call it the same good. And we wouldn't call it "price discrimination" for example, if we charged an increasing price for teaching the same idea as we moved along the horizontal axis. And competitive profit-maximising teaching firms would indeed charge different prices, if they were allowed to, and had the information they needed to do so.

We want to be able to define rival vs non-rival in terms of the cost of providing n people with z units of the good. With a pure rival good, the cost depends only on nx. With a pure rival good, the cost depends only on z.

I notice that Paul Romer slags me off for my metaphysical musings in this little post, but hasn't (as far as I can see) addressed my counterexample to his post in my previous post. And he is pissed that I used words, not math? I don't get it. Perhaps he is pissed at my counteraxmple.

Another metaphysical point: take the standard common resource fishery problem. Uncaught fish swimming in the ocean are a scarce good. I find I need to talk about "unthought ideas" being a scarce good just like uncaught fish. (Like in the "rush to invent" idea.) But "ideas that nobody has thought of yet" have a very dubious metaphysical status.

Cost of acquisition is quite distinct from the cost of replication. Once someone writes down their idea or codes their program and puts it on a server for download, the replication costs are more or less zero, but the cost for someone to start using the idea or the program vary by individual, and in some cases are infinite because the individual does not have the ability to comprehend it. Non-rival and anti-rival goods are very important in our present day economy and not well understood, in my opinion. Anti-rival goods are especially influential.

@louis, You too are conflating general non-usability with rivalry. Rivalry is one specific TYPE of non-usability only -- non-usability BECAUSE someone else is using it. Like a personal computer. Not like a computer program. Nor like inside information.

@Nick, Romer has a whole paragraph addressing your previous conterexample (for some value of "addressing"):

1. Marshallian Intuition One type of reaction involves a recitation of some Marshallian intuition about rents or quasi rents and a request for clarification about what this intuition misses. My suggestion is that if you are stuck, try approaching the problem from a new angle. In this case, a good way to do so is to work through the logic of the proof based on Euler’s Theorem and try to see whether its assumptions fit the example you are considering. Even if you are “crappy at math” give it a try. The theorem requires little more than calculus. You may have fun discovering why specific Marshallian intuitions fail to carry over to a full equilibrium context where things have to add up.

As to ideas that nobody has thought of yet, isn't that the very DEFINITION of innovation? And isn't it a historical fact that it has occurred? I don't understand the objection.

Jeff: Thanks. Aha! Yes, that does look like it's a response to me previous post, even though I don't see a link. Not really much of a response though. Sure, the marginal products add up to more than total products under IRS. But my post was a counterexample to what he said about taking prices as given. Those are not the same thing.

On the "ideas that haven't been though of yet": that's not intended as an *objection* to anything. But I find it philosophically interesting that we need that concept. Because, metaphysically, it is very weird. And there ought to be a way to talk about the "rush to invent" problem without talking about "unthought ideas". Maybe by talking about the external costs that one inventor imposes on other inventors, just like one fishing boat imposes an external cost on other fishing boats.

What is underlying my point there, and this post, is that we want to try to define rival vs nonrival goods in terms of cost functions, to try to avoid these sorts of metaphysical questions about whether two goods are the same goods, or what things exist.

@Nick, Agree about avoiding unnecessary questions, thanks. As to the "puzzle" about non-rival nonetheless having cost: After some cursory research, I am seeing that "fixed costs" aren't to be counted in marginal cost. And isn't bringing something non-rival on board a "fixed cost" for any individual producer? Maybe that's the (accounting) trick to all this. Of course, as you note, the "same" non-rival good may have different "on-boarding costs" for different producers. In the extreme case I am picturing something like a million-dollar six-sigma/TQA/whatever training course being sold to some company that hasn't the internal conceptual ability to ever use it at all. As you seem to be conjecturing, maybe this zero-cost stuff doesn't add up at the macro level? Curious now whether that really rebuts anything Romer is saying though.

Nick: Very interesting question!

We usually say that ideas are nonrival because I can use the Pythagorean theorem without affecting your ability to use it, which is quite different than if I were to use your car.

But as you point out, people aren't born knowing the Pythagorean theorem, and have to be taught it. As a society, we expend quite a lot of resources on teaching people such things.

Given that it's costly to transfer ideas, in what sense is this any different from your car? Why can't we talk about the pattern "Pythagorean theorem" existing in your brain as "your Pythagorean theorem", analogous to "your car"? It's costly to replicate your idea of the Pythagorean theorem in someone else's brain, just as it's costly to replicate your car in someone else's driveway.

I think the difference is quantitative: the cost of replicating ideas is generally much lower than the cost of coming up with the idea in the first place. Thus a greater share of the cost of producing an idea is in the act of invention, and less in the act of teaching/learning. By comparison, while the idea of a car is certainly nontrivial, its production is a greater share of its costliness.

Richard Serlin:

This is an area where the internet has been so powerful. It's become so much cheaper to share ideas.

But since this hasn't produced an explosion of growth and idea generation, this suggests that a lot of the cost of spreading ideas is the cost of uptake, and not just availability. i.e. you now can google something instead of going to a library, but you still have to work through difficult material to understand it!

In fact, one could argue that the internet has had a greater effect on the RELATIVE costs of different types of information. i.e. we're now awash in memes and clickbait that gets shared on social media, but there's been little increase in the creation and dissemination of high quality difficult to understand ideas. If anything, there may be incentives for decreasing the production of such.

jonathan: thanks. I think I agree with "I think the difference is quantitative: the cost of replicating ideas is generally much lower than the cost of coming up with the idea in the first place."

And then we can quite reasonably define "pure non-rival" as the limiting case, where the cost of replicating is zero. And then apples would become pure non-rival too, if we had a costless duplicating machine. Apple trees are a duplicating machine, but take labour land and time, and we usually ignore the cost of the original apple, because it's trivial (unless it's some fancy new variety).

Jeff: "Curious now whether that really rebuts anything Romer is saying though."

Nothing in this post was really intended as a rebuttal of anything Paul Romer was saying. It's just me musing about the definition of "non-rival" good, and whether ideas fit that definition.

(Though I do think there's an important distinction between Increasing Returns to Scale at the level of the individual firm vs at the level of the whole economy. Like the point luis(?) was making in comments on the previous post. We could double the economy by doubling either the number or the size of all the existing firms, and we won't always get the same results either way.)

Nick - looking through the comments, I'm coming back to one of my old points about public goods - that the more one abstracts, and strips away concrete specifics, the more something starts to look like a public good. Hence the discussion of e.g. skills and ideas above.

To make things more concrete, take the example of language. Languages are just big collections of ideas (e.g. the idea that this particular object is "rhubarb"). Substitute "language" for "ideas" in your post, what changes? One thing that changes is that the answer to this question: "And can you separate the activities of research and teaching (communicating research)?" becomes a fairly easy and obvious yes. Also languages don't have a single inventor, single light-bulb-switcher-on-er, the way ideas do in your post.

Frances: the example I like is money (or monetary system). In some ways it's like language, in that you want to use the same money as the people around you, and there are positive spillovers and externailties. But in other ways (of course) it's like a private good.

Speaking of concrete, I'm having trouble matching the terminology to even the simplest little toy production thought experiment.

I can buy empty small boxes at 0.50 per. I can buy small shiny balls at 1.50 per. I can sell boxes with balls in at 3.00 per. (All price-taking.) A worker can produce boxes with balls in at the rate of one every 3 seconds.

What is the marginal product of the boxes?
What is the marginal product of the balls?
What is the marginal product of a worker?

(Note: all inputs are rival so far; will introduce non-rival later.)
Little help for this non-economist on just the basic terminology? Thanks in advance.
(I am having particular trouble with the phrase in Vollrath "receive output equal to their marginal product" as it applies to boxes and balls. What are boxes and balls receiving exactly?)

Everyone is as stumped as I, eh? I'll take a stab. Given that you can't increase the *rate* of production by just adding boxes or balls, and that all online examples seem to be marginal product of *labor*:

MP of boxes: 0
MP of balls: 0
MP of worker: 1200 ball-in-box per hour

Is that about right?

Also not clear is whether MP can/should be expressed in value rather than product, and if so whether it should be net not gross. Assuming yes to both:

MP of worker: 1200.00 per hour

How'm I doing? :-)

You really using "cottage" as a verb?

Jeff: that's the joint inputs case. One worker plus one shovel dig one hole per hour. Q=min{K,L}

MPL and MPK are either 1 or 0 or undefined. We define a composite input of one worker plus one shovel. That composite input has a marginal product of one.

Robert: Typo. I think only Brit gays use "cottage" as a verb.

Hey Nick! I must say you do an excellent job of 'communicating' here. After reading this I have a much better idea of what 'rival' means.

It inspired this post

On researching new ideas vs. teaching old ones http://diaryofarepublicanhater.blogspot.com/2015/06/on-costs-of-research-vs-teaching.html

It seems to me that the larger and wider the audience you want to reach if it's a really difficult idea the more costly communicating it will be.

If most people don't understand economics a large reason is that most people don't have any desire to.

If I might venture totally off subject, I believe you are also from England. I was but came to the states when I was 3.

In all the debate over what Cameron's re-election means it occurs to me is that the main thing it means is that it's only a matter of time till Scotland leaves. If so that would actually be great news for the Conservatives as Scotland has 1 Conservative MP in the whole country.

@Nick, Thanks re joint inputs. That still leaves a very awkward units problem in this very basic representative case. To wit, don't I have to express the balls and boxes input as a *rate* in order to sensibly combine it jointly with worker? Q=min(box rate, ball rate, #workers) where the "equality" condition for the "min" is 1200/hr == 1200/hr == 1, respectively?

And the answer to my 3 questions is then: MP(1200,1200,1) = 1200 ball-in-box per hour?

(No wonder it's so easy to obfuscate with economics math; this seems terribly awkward already for such a simple case.)

In particular there is no defined MP for a worker alone in this factory, and so the so-called "real wage" is undefined in this case?

And back to one of my previous questions: What does it mean then for the input unit (1200/hr boxes, 1200/hr balls, 1 worker) jointly to "receive output equal to their marginal product"? How is the output (pay?) divided up among the 3 components? And if it is all considered to go to the worker, isn't it counter-intuitive that "real wage" is dependent on management's ability to supply raw materials at certain rates?

Nix my last question above. I see now that this is just an example of "diminishing returns of labor" (too much labor for the raw materials).

And, I think I see the answer to my "divide up" question as well: boxes and balls get their cost, worker gets the rest. 3600.00/hr --> (600.00/hr, 1800.00/hr, 1200.00/hr). Yes?

So, cutting to the chase: non-rival input.

First a slight aside. For purposes of all the below, assume any supply rate is achievable. If my supposition above that supply *rate* has to be the input (correct me if I'm wrong), all the pedagogical price-taking examples I've seen about "any amount can be supplied at that price" have to be supplemented with "at any rate" as well. That seems to be a serious gloss, as real-world delivery capacities are a very different thing (economically, technologically) than real-world quantity capacities.

Anyway, the factory has an "ideas man" Steve. Steve sees that part of the 3 second ball-in-box process is opening the box first and wonders if that could be "specialized". He has a worker try just opening boxes using both hands and finds that the worker can do that at a rate of 1 box per second. Lo and behold, he also finds that it also takes a "specialized" worker only 1 second per to put balls in open boxes if that's all the worker has to do. So all workers are immediately paired up and achieve a rate of 1 ball-in-box per second per 2 workers. Supply rates are costlessly increased as above, and we have a new joint input and production function: MP(3600 box/hr, 3600 ball/hr, 2 workers) = 3600 ball-in-box per hour. The new MP value breakdown goes 10800.00/hr --> (1800.00/hr, 5400.00/hr, 3600.00/hr(for 2)).

Steve's "idea" has increased average worker productivity by 50% (+600.00/hr/worker). What and when should Steve be paid? Technically the total value of the idea is +600.00/hr/worker * #workers * #hrs in the *total remaining operating life* of the factory. (I know someone who was once a worker who put in a suggestion at a company whose name starts with "I", suggestion value projected at something like $1M overall. He got an umbrella I think.)

As Vollrath said though, it doesn't matter how much or when Steve is paid, if Steve is paid *anything* out of the firm's revenue, other workers CANNOT be paid their full MP share of 3600.00/hr/pair (and/or 1200.00/hr before the change was implemented). *Somebody* will "take a hit" *somewhere* (relative to their MP). (Of course workers may be more than happy with an hourly rate significantly more than before, even if not the full MP. The proverbial win-win. Maybe that's why such worker-Steve "cooperation" is not called "competitive" equilibrium?)

Jeff: "In particular there is no defined MP for a worker alone in this factory, and so the so-called "real wage" is undefined in this case?"

Good question. No.

Draw an MP curve for the joint input. That's the demand curve.

Draw the 2 supply curves for the two inputs, then add them up vertically to get the supply curve for the joint input. Equilibrium is where the demand and supply for the joint inputs cross. Drop a line down from that equilibrium point, to determine wages and shovel rents, on their respective supply curves.

Like this picture, only in reverse: http://worthwhile.typepad.com/worthwhile_canadian_initi/2012/08/joint-demand-and-joint-supply.html

If the supply curve exists....

Yeah, both demand and supply are assumed infinite ("curves" are horizontal lines at their respective prices) in this example (for simplicity), so "cross" is N/A.

Actually, that condition is the definition of "price-taking environment", isn't it?

@Nick, So coming back to Romer's Marshallian comments (on previous post), I think I am in a position to fill in the answer to what he meant. You and Jonathan took on most of it -- Romer really does mean (full) competitive equilibrium == ALL rival inputs get their MP. Farmers (land) were not getting full MP because (if) they were paying something to some inventor.

As to your question "but aren't taxes similar?" Absolutely, which is why there is ALL KINDS of tax avoidance work being done by companies, especially large and/or multinational ones. (Farmers in your example would be constantly seeking to get out of paying "innovation fees" as well.) Equilibrium means there are no such pressures consuming non-productive effort.

And as to labor's wage vs. paying the "ideas men", isn't that precisely what the (arguably non-productive) labor union movement was all about? "We don't care about no past inventions, you need to pay us what we earn for you TODAY [our MP], or it's STRIKE, STRIKE, STRIKE." Non-equilibrium in'it?

Besides the differing ideas regarding what "competitive equilibrium" might mean, there also seems to be some daylight between what Romer means by "monopoly" and what your example describes. Innovators competing for the identical market, regardless of whether their ideas are each unique (patentable), could be taken to mean "no monopoly" unless/until there is a clear winner. If a top dog emerges, he/she is the (only) monopolist.

I see a potential objection: the other competitors WERE "the" monopolist for a while (before the next better idea appeared) and each of them was still limited in what they could "charge": one ton of wheat per acre per year. But wait, just as in my little ball-in-box example, "price taking" necessarily includes the presumption (unrealistic as it may be) of *unlimited supply*, in this case of acres (land). And thus the monoplist is also *unlimited* in what he or she can charge.

In other words, Romer was being a bit loose (mathy?) when he wrote "unable to influence the price that users have to pay", when he should probably have written "unable to influence the price that the market has to pay". There is only one idea for sale to the market (pearl of great price), whose price the innovation-monopolist seller can set at anything he or she wants. Let's say monoplist wants 1,000,000. As it is worth more than 1,000,000 to the market as a whole, there will be comers. Monopolist just says "as soon as I have 1,000,000 worth of pledges from comers, I'll cut off the sale/auction and we'll all go to the Sheraton to swap goods and sign NDAs".

«Innovators competing for the identical market, regardless of whether their ideas are each unique (patentable), could be taken to mean "no monopoly" unless/until there is a clear winner. If a top dog emerges, he/she is the (only) monopolist.»

If there are many innovators, each of them with a different idea, could be considered monopolistic competition (well, I suspect that in pratice the concept of "monopolistic competition" only makes sense if, not only the products are heterogeneous, but also the preferences of the consumers are heterogeneous)

I'd guess ideas are mostly rival. It takes a lot of underlying human capital for an individual to test or deduce the idea as truth. I suppose many people can learn most ideas that are now known as truth. Some won't be smart enough or have enough time, but mostly the problem is many individuals don't seek to better themselves for god knows whatever reason.
For example, Martin and Harper have espouse large cap business tax cuts for political reasons. Gordon has taken up the cause for ideological reasons. But a nation with lower R+D spending and immobile industries like defence, petro, natural resources, healthcare, finance...can't accrue foreign competitors. Another example is Bombardier. They makes the finest lane on Earth using advanced materials, but the airlines like to procure from the big 2 and don't appreciation low GHG airplane innovation. The industry itself seems more a cartel devoted to an old World Bank platform opening up of trade. The nuclear power industry is also just a naval and Cold War subsidy. These industries don't stand on their own an should be taxed more to fund industries that are efficient.


A very nice reply to the boorishness displayed by Romer. I have my own reply here: http://andolfatto.blogspot.com/2015/06/competitive-innovation.html

I think you'll enjoy the cartoon. :)

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