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.