Private provision of public goods

Maybe I am writing this too early in the morning to see what I am missing here. I really mean that . I feel like I must be missing something. Alex Tabarok argues at Cato Unbound that he has a private solution to the problem of public goods. The setup for his example is that there is a bridge that will cost $800 to build and will provide $100 benefit to each of ten people.

Now consider a dominant assurance contract. An entrepreneur agrees to produce the public good if and only if each of 10 people pay $80. If fewer than 10 people donate, the contract is said to fail and the entrepreneur agrees to give a refund bonus of $5 to each of the donors. Now imagine that potential donor A thinks that potential donor B will not donate. In that case, it makes sense for A to donate, because by doing so he will earn $5 at no cost. Thus any donor who thinks that the contract will fail has an incentive to donate. Doing so earns free money. As a result, it cannot be an equilibrium for more than one person to fail to donate. We have only one more point to consider. What if donor A thinks that every other donor will donate? In this case, A knows that if he donates he won’t get the refund bonus, since the contract will succeed. But he also knows that if he doesn’t donate he won’t get anything, but if does donate he will pay $80 and get a public good which is worth $100 to him, for a net gain of $20. Thus, A always has an incentive to donate. If others do not donate, he earns free money. If others do donate, he gets the value of the public good. Thus donating is a win-win, and the public good problem is solved.

The first part makes sense. If you do not think that others will donate, then it is clear that you should donate and get the refund plus the bonus. My problem is the second part in which he seeks to show that a person always has an incentive to donate by arguing that he also knows that if he doesn’t donate he won’t get anything, but if does donate he will pay $80 and get a public good which is worth $100 to him, for a net gain of $20. Thus, A always has an incentive to donate. Economists generally define a public good as one that is non-rival and non-excludable. Non-rival means that your consumption does not diminish the benefit that I gain from the good. The non-excludable part means that once the public good is provided it is very costly to exclude people for consuming it. Fireworks displays provide a relatively obvious example.  The problem with Tabarrok’s argument is that if it is a public good A can use it even if he does not pay. If he believes enough others will contribute, his choice is between contribute $80 and get $100 benefit (net $20) or pay nothing and get $100 benefit (net $100).  If he does not get to use the bridge because he did not contribute that mean the good is excludable. Thus at least in this example the public good problem appears to be solved by assuming it away.