As first noted by Olson (1965), the voluntary provision of public goods among large groups is expected to result in underproduction relative to the efficient level as first defined by Samuelson (1954) due to the large transaction costs involved. Being nonexcludable, consumer free-riding leads market provision of goods such as national defense to fall short of efficiency. In "A Note on the Market Provision of National Defense" Leeson, Coyne, and Duncan (2014) rightly observe that since there are also nonexcludable benefits of national aggression, it, too, must be considered a public good that will be underproduced. They conclude that if the underproduction of aggression is relatively severe enough, then the level of defense that is achieved through voluntary provision may be efficient after all. However, their reasoning is not adequately dynamic.
It is the threat of national aggression by foreign powers that makes national defense desirable to consumers. The efficient level of defense is determined in part by the potential level of aggression that consumers face and their estimation of the probability of being attacked; the efficient level rises and falls directly with their perception of the threat of aggression. As the threat of aggression falls, the decrease in risk will drive down consumers' demand for defense, resulting in a reduction in its efficient quantity; this effect favors the authors' thesis.
Yet, their argument rests on the level of voluntary provision remaining constant as demand for defense falls. Willingness to contribute may also fall as the threat of being attacked and thus the cost of free-riding falls; in a scenario where the threat of aggression is halved, an individual may offer only half his original contribution. The incentive consumers have to offer less than their true willingness to pay remains. This process will prevent the efficient level of defense from being achieved as the threat of aggression falls. Free-riding may even increase exponentially as the threat is deescalated from, say, nuclear first strike and 10 percent chance of death to limited conventional war and 5 percent chance of death.
If national aggression by foreign powers is less than it otherwise would be due to nonexcludability, it is this level that consumers consider in determining the level of national defense they demand. If the nonexcludable benefits of national aggression suddenly became excludable, the demand curves for defense would shift...