Thursday, June 16, 2011

Positive Externalities Part 1: The Subsidy Solution

In this post on public investments in science, Stravinsky asks how "the government internalizes benefits of funding basic research". I'm not sure saying that the government internalizes the benefits is the best way to phrase it. Remember when we say that costs or benefits are "internal" or "external", these reference internality or externality to the market transaction. You can think of public solutions to externalities as a way of finding another allocation process besides the market which internalizes some of the benefits that were previously external. From the perspective of the person enjoying the benefits or paying the costs, the benefits are always there, after all! The question is - are these people at the table making the allocation decision? In many market transactions they are not. The idea is that in a democratic polity or any other democratic social institution they have a chance to be, so there may be a plausible improvement.

Economists usually talk about three solutions to a positive externality: public subsidy, public provision, and the reassignment of property rights. [UPDATE: So as I'm thinking about it, there's an extremely important fourth solution that I'll go over too - in addition to public provision, there is of course direct public demand. We can think of this as a price response (subsidy), two quantity responses (supply and demand), and an institutional response (property rights allocation)]. I'm going to try to discuss each of these in turn, and I'll start with the subsidy, which is presented here:

Here you have the basic positive externality. Market transactions can be expected to converge towards the point where marginal benefit equals marginal cost (the far lower left yellow circle marks this equilibrium). That's where private net benefits are maximized. The problem is, if there are substantial externalized benefits, that's not where total (i.e. - private plus social) benefits are maximized. I've shaded the deadweight loss region of the graph in gray, and you can think of an externality like a tax imposed by the property rights regime. Now, there are some social benefits enjoyed, of course. I've shaded in green the social surplus and in red the private surplus.

One solution is to subsidize private purchasers of the good in question. I've marked this subsidy with the dashed line. We can think of it as a lump sum ("we'll give you $X to go towards Y") or you can think of it as a percentage ("we'll pay X% of the cost of Y"). Either way, it will shift the quantity demanded and the price charged out to a new equilibrium along the marginal cost curve (if demanders are being subsidized the situation has not changed for the suppliers, so we are still on the MC curve).

One argument against public solutions for externalities that I am always shocked so many smart people are impressed by is this banality that "the government doesn't know where the equilibrium is". Of course it doesn't. Has anyone said it does? I think drawing an optimal subsidy or tax to deal with an externality on paper has given people the false impression that those who support these public investments think the government knows where the marginal social benefit curve meets the marginal cost curve. I've never claimed that, and I cannot recall anyone else claiming that. So to avoid that confusion, I've drawn several potential new equilibria (also in yellow dots), none of which fall on the intersection of the marginal social benefit curve and the marginal cost curve! Four words you have never seen written on this blog are "the government is optimal", and you never will see those four words written.

So the government is not optimal. That is so obvious it doesn't need elaboration. The point is, though, any public solution to the left of the intersection of the marginal social benefit and marginal cost curve is an improvement on market allocation. Allocation is still efficient because we are still using the market to economize on decentralized knowledge about who can produce and use the good most efficiently (i.e. - we are still on the MC curve). And it's also closer to being welfare maximizing. This is an unambiguous improvement.

It becomes more ambiguous if we move to the right of the intersection of the marginal social benefit and marginal cost curves. Past that point marginal cost exceeds total marginal benefit, which means net social benefits are declining. I say this is "ambiguous" rather than bad, because the net social benefits at a point to the right of the intersection of the marginal social benefit and marginal cost curve may still be higher welfare than the market solution. But of course this is not the territory we want to be in. But if clear social benefits are modestly subsidized, there's no good reason to run away from this option. If we think about "robust political economies", both the market alone and the government alone clearly fail to pass the robustness test in the case of positive externalities. Both are incapable of fully dealing with the incompleteness and imperfection of human decision makers. This really shouldn't surprise economists. Anyone who clings to a corner solution should immediately raise red flags - the "economic way of thinking", as it's been called, alerts us to the fact that corner solutions are rarely sensible or robust. Experience shows us this as well. Societies that rely heavily on government allocation repeatedly fail, and societies without a robust government to meet social needs fail to emerge or develop into mixed economies over time (it only took a matter of years to move from the Articles to the Constitution).

Next I'll do public provision, and then I'll do the rearrangement of property rights. Not sure when exactly - I'm going to be out of town a lot of this weekend, and working on the engineering labor supply paper as well.


  1. You write:

    One solution is to subsidize private purchasers of the good in question. I've marked this subsidy with the dashed line. We can think of it as a lump sum ("we'll give you $X to go towards Y") or you can think of it as a percentage ("we'll pay X% of the cost of Y"). Either way, it will shift the quantity demanded and the price charged out to a new equilibrium along the marginal cost curve (if demanders are being subsidized the situation has not changed for the suppliers, so we are still on the MC curve).

    The issue here is that the allocation may be efficient in the sense you point out, but where it fails is in the allocation to the most efficient producer. The problem is that since the money is being doled out by the government, the government has to either decide who the most efficient producer is, or rely on signaling such as lobbying or other "connections". This is how we got the Bush subsidy of ethanol that not only wrecked the farm industry, but held back energy efficiency progress. One can argue that the firms that have the money to lobby are necessarily the most efficient firms or they would not have the money to lobby, but I think that argument has too many other factors at play to be able to use that defense. larger companies are slower to change generally, and the most efficient solution could come from some small producer who is innovating at a faster rate.

  2. It seems to me it depends on exactly how it's being subsidized, right. If it is the government handing money to certain ethanol producers this obviously raises serious efficiency problems. If it's some sort of refundable tax credit on all ethanol production, that doesn't seem so bad (presuming ethanol is even something we want to subsidize, of course). You could also think of subsidizing the consumers (which was more what I had in mind in this case). Gas retailers or refineries (I'm not sure where along the line the ethanol gets added) could be given a credit for the ethanol that they purchase.

    It doesn't seem to me you're picking winners in this case. You're moving along the market's marginal cost curve but the point is you are still on the market's marginal cost curve. It only seems to pose a problem if you design the subsidy very poorly - if the subsidy is essentially writing a check to a specific party. That isn't the way to go.

  3. Yes, I overlooked the method of subsidization to an extent. I'd be curious, however, to know the dollar difference between handing checks out and the methods you propose. My guess is that your methods are less politically tractable and the vast majority of subsidies are handed out as lump sump checks to individual corporations.

    The problem I state, in part, still stands though. However we want to subsidize it, under Bush, we still would have ended up with subsidies to ethanol and money is still diverted away from more efficient alternative fuels.

    I'm not entirely against subsidies, but I'd like to see more subsidies like the X prize rather than targeted subsidies that are controlled by special interests.

  4. Apologies for becoming one of those annoying libertarian X prize rehashers:)

    3 posts! Can you tell I'm done with comps?

  5. Nothing annoying about promoting the X prize, or any prize fund!

    Prizes are a great way of leveraging private solutions to collective action problems precisely because (1.) they don't require that much collective action in the first place, and (2.) you get a lot of activity (i.e. - innovation) for a single payment.

    Of course the logic works for public or private, but if libertarians can get on board that's great.

    A lot of the very early public science and technology investments in the United States were actually prize funds rather than broader subsidies (although there were those too).

  6. I wasn't very clear. Here's my confusion:

    So you've got an externality. It's a problem. Markets don't want to solve it because there's no money in solving it. So government needs to solve it. Except there's no money in solving it for the government. So it won't solve it.

  7. It's not clear to me why we would expect government to be a profit seeker, and thus why we would expect there being money in it to mean anything.

    Indeed - if government were profit seeking, I bet it would be considered a lot more efficient by most economists! Then again, you use this advantage of the state as a means of pursuing social ends.

  8. I'm still not being clear, so let me say it as plainly as possible: what incentive has the government to fix externalities? I can't imagine winning an election on the slogan, "I read a microeconomics textbook!"

  9. I would say that even taking into account everything we know about public choice, maximizing social benefits that are left unsatisfied by the market and minimizing social costs that are imposed by the market seems to be a reasonably good election strategy.

    In certain corners of the blogosphere this may not apparent, but making public investments in science and education and these sorts of things actually help politicians in elections in a lot of cases.

    Is that a guarantee? No, of course not. This is the whole reason why we're suspicious of government allocation, after all. This is the whole reason why we like markets so much - because the incentive structure is much clearer. But that doesn't change the reality of these externalities and the public solutions at our disposal.

  10. I'm ambivalent towards public funding of science (fuggin uncertainty, amirite?) and totally against public education, so those are hardly persuasive examples. Taxing pollution or the use of antibiotics seems more obviously desirable to me, and I'm damned if I can see why politicians would want to do those things. Public opinion might change--there are definitely a lot of people who want something done about these problems. But right now the incentives aren't there, and there's no particular reason to expect them in the future.

    I'm not just suspicious of government allocation--I don't think they'll allocate, period. They're more concerned with important things like harassing Mexicans and conquering the Middle East.=.

  11. Stravinksy,

    My (amazingly profound) take is that the relative incentives of Government vary widely according to the externality at hand... However, one example that may prove interesting to you can been seen in (surprise!) climate change, which broadly involves both negative and positive external effects.
    - Negative, in the sense that emissions anywhere stand to affect us all equally. (Actually "equally" is not true, of course, but just go with it...)
    - Positive, in the sense that technology developed by, say, one country in combating emissions stands to benefit everyone... provided that it is sufficiently diffused.

    This latter issue is commonly referred to as the "knowledge externality" or "R&D failure". The interesting point, however, lies with the idea that the positive externality could be leveraged against the negative one.

    As I'm neck deep in thesis deadlines, I'll simply leave you this link to have a look at. (Or, here's another comment thread that you may -- or may not! -- find interesting/convincing.)

  12. I get how economists can try to estimate the cost of pollution. But how do you measure the benefits of undiscovered technology?

  13. dkuehn:

    This basic principles model doesn't do justice to the true complexity of the problem. You need to note the *many* implicit assumptions that go in to getting that result.

    Most importantly, has it been assumed that the other goods in this presumably GE model are themselves not characterized by some kind of externality?

    A more appropriate model would be a general equilibrium model where:

    1. The consumption/production of many of the goods (if not all) would be characterized by either a positive or negative externality.

    2. We wouldn't place any special structure on the utility/production functions to conveniently get rid of inter-dependencies.

    Under these more realistic assumptions (although the model would still not incorporate changing preferences/technologies, etc.), we would need to not only look at the graph for Y, as you have done, but also the graphs for A,B,C,D, their production may change given a subsidy in Y. And as A,B,C,D,....each also have negative or positive externalities, we would need to also know the magnitudes of these changes - magnitudes which will depend on assumed functional forms and parameter specifications.

    Thus, the planner *not only* needs to have some idea of where the yellow dot is on the graph for Y - itself a difficult task - but where the yellow dots will now fall for a tremendous number of other goods as a consequence of the subsidy for Y - then he could calculate the net effect. We're talking about a practically infeasible task, since even small errors in the functional/paramater specifications could produce completely opposite results - not to mention the time complexity of obtaining the comparative statics in a GE model is exponential.

    And this is still all under the assumption of no dynamics, particular market institutional forms, etc.

    You talk about appreciating complexity on here and then you use this basic stuff to make an argument for neutralizing externalities?

  14. edarinew -
    I'd agree probably every good has some externality associated with it. And as I've written in the past, every good has important inter-temporal externalities associated with it even if it wouldn't otherwise have an externality associated with it. There clearly needs to be some sort of demarcation of what is substantial and what isn't - and what we value and what we don't.

    As for your GE discussion, you seem to be misusing the very real issues around complexity and dynamics to avoid having a conversation. There's no hope of ever modeling the complexity of the real economy. Science is about parismonious explanation. None of the issues you raise - to my knowledge - negate any of the more basic points here.

    I don't just talk about appreciating complexity - I talk about complexity. And the point is this: simple decision rules and organizing principles can produces order and structure at a macro level that could not have been anticipated from the beginning. That's the source of market equilibrium, and it's also how non-market institutions evolve to address issues like externalities.

    I'm not sure exactly what your concern is here. You seem to just be pointing to the words "general equilibrium" and "complexity" without sufficiently communicating what you think the implications are for this discussion.

    Recognizing general equilibrium effects and complexity we can either:

    (1.) think through issues, make observations and have people review, think more deeply on the issues in response, observe more, etc. etc., or we can

    (2.) determine it's all just terribly complicated and conclude we should just talk about ideas like "complexity" without actually thinking through specific questions and problems that we could at least start to approach a solution on.

    I'm opting for the former - I think that's the more fruitful route. If I were on a search for The Truth I might opt for the latter and get very depressed. Since I'm just trying to understand what's going on better, I'll opt for the former.

  15. Now - practically speaking, the implications of your concern are that we should always be cautious in actions we take, and we should only address the highly consequential (or less risky) options.

  16. I'm clearly not communicating the essence of my post - it wasn't addressed.

    Maybe a couple of questions will help me get closer to your stance.

    I get that if you're trying to understand some phenomenon, the simpler the model, (without losing anything essential) the better. And in so far as this only extends to the understanding of the principle *as such* I am in agreement.

    But if we want to *actually implement* a policy -eg a subsidy - are you saying that parsimony is better? Are you saying that we shouldn't feel obligated to model reality as closely as we can? And if so, how can we possibly legitimize a given subsidy? If we have no idea about whether it improves the situation, why should we even consider the policy - surely not on the basis of some small toy model?

    Moreover, are you suggesting that there's some sort of mechanism in place that would drive a subsidy towards the "optimal" subsidy? If so, what's the mechanism?

  17. "presuming ethanol is even something we want to subsidize, of course"

    Dear god no. Not only will you burn through it faster than gasoline, but this corrosive crap will also damage both big and small engine machinery. It is truly a joke to consider this junk biofuel, which deliver negligible energy output compared to input, a viable source of alternative energy. Of course I'm only speaking my own experience and that of others. Take it as you will.

  18. I tend to agree, Anonymous (although granted only because I've always heard what you say here). My point was just to clarify that I was discussing the nature of dealing with subsidizing a positive externality rather than endorsing ethanol as a legitimate positive externality.


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