Question: What is the Objectivist point of view on positive externalities? Is charity truly the only moral way to fund projects whose costs are less than anonymous benefits?
Perhaps the real question is, wouldn't self-interest encourage me not to donate, as long as enough other people do?
Answer: According to L.H. Rockwell, Jr. (founder and president of the Ludwig von Mises Institute) externalities can be subjective, as costs and benefits may well be viewed differently by different people. They occur in the natural course of economic activity and there is no need for any sort of governmental intervention to "correct" them. (Nor is there any certainty that the government could accomplish this). I'm afraid I am unfamiliar with views of the Austrian School and Ludwig von Mises, so I cannot comment on their specific treatment of the matter. (I suggest you write to the Mises Institute at firstname.lastname@example.org if you have a more specific interest in the Misean view of the matter).
If the actions that create the externality are actions taken in a free environment and in good faith, then the indirect benefits to others are not unjust to those that bore the cost. As long as those who bear the costs reap the benefits they wanted, their investment is a worthwhile one to them (or they would not have financed the projects in the first place). In this case, some may be reaping benefits without paying, but they are hurting no one. (It is a far worse scenario when those that are paying are not allowed to reap benefits.)
Objectivist ethics hold that rational self-interest (which may often be indirect) is the correct basis for all action. Thus these projects are financed by people who think that it is in their self-interest to finance them. If the patrons see a benefit, direct or indirect, in their funding of such projects then it is in their interests to donate to them. If they do not see a benefit then there is no valid moral reason for them to do so.
Therefore charity, or a voluntary means of payment for financing a project should invariably hold some sort of benefit for the payer himself. Voluntary payments are the only moral way to fund such projects, because forced payments can never be justified. (Force sunders the valuer from his ability to choose what to value.)
To force payment without consent is not only a violation of rights, it destroys value rather than creating it.
If other people are donating amply to a project that you think is beneficial, then it may be in your self-interest to not do so. As a matter of principle, most Objectivists (or even most rational people) would see it in their long term self-interests to finance such a project. But if the project is carrying on without your support, then you may want to avoid paying for it. In the logical course of events the people who would benefit most from such a project would find it in their self-interest to pay. And if no one finds it in their self-interests, then the project should probably not be undertaken to begin with.
Objective value only exists through the free exercise of an independent, rational judgment. This is true of economic value and money prices as well. The market price is nothing other than what customers are willing and able to pay and what producers are willing and able to accept. If a project lacks funding, or if a product can’t find a market, the only way to prove that it is really a “public good” with positive externalities is to demonstrate that fact through a contractual arrangement by which people agree to pay in order to have or create the benefit. To force payment without consent is not only a violation of rights, it destroys value rather than creating it.