Private investment and government protection

Hurricane Katrina did massive damage because New Orleans and the Gulf Coast were not appropriately protected. Wherever natural disasters threaten, the government—in its traditional role as public goods provider—must decide what level of protection to provide to an area. It does so by purchasing protective capital, such as levees for a low-lying city. (“Protection” also consists of prohibiting projects that raise risk levels, such as draining swamps.) We show that if private capital is more likely to locate in better-protected areas, as would be expected, then the marginal social value of protection will increase with the level of protection provided. That is, the benefit function is convex, contrary to the normal assumption of concavity. When the government protects and the private sector invests, there may be multiple Nash equilibria due to the ill-behaved nature of the benefit function. Policy makers must compare them, rather than merely follow local optimality conditions, to find the equilibrium offering the highest social welfare. There is usually considerable uncertainty about the amount of private investment that will accompany any level of protection, further complicating the government’s choice problem. We show that when deciding on the level of protection to provide now, the government must take account of the option value of increasing the level of protection in the future. We briefly examine but dismiss the value of rules of thumb, such as building for 1000-year floods or other rules that ignore benefits and costs.