Is National Defense a Public Good
October 29, 2002
This excerpt is part of a chapter of a text I am writing on market failure.
Is national defense a pure public good? We can divide this question into three parts. (1) Is national defense a good? (2) Does it have the characteristic of jointness? (3) And, does it have the characteristic of non-exclusion. We consider each in turn. In order to save space we denote national defense as ND.
Is National Defense a Good?
The very idea of national defense should stop us from answering this question too quickly. A pure public good must yield benefits to everyone. Not everyone in a nation, but everyone in general -- in the world. Obviously an effective ND by one nation does not benefit the people who live in another nation and who feel threatened by the first nation's ND. Thus, when people say that ND has the characteristic of jointness, they mean that it has this characteristic for the people who live in a nation to which the ND is supplied. We might say that they assume that is a "pure national public good." We could define this as a good for the citizens of a given nation.
But this does not totally remove the ambiguity. If you were an ordinary French citizen in 1944, your country would have been occupied and under the rule of Nazi Germany. You probably would not have benefitted from Germany's supply of ND against the Allies. Or if you were a citizen of Granada in 1983 or Haiti in 1994, you would probably not have benefitted from your nation's defense against U.S. troops. If you are a citizen of North Korea today, it seems doubtful that you benefit from your nation's ND.
The essential point is that some residents of a nation may prefer to live under the rule of the very military force or political regime that they expect to replace the one that is currently providing ND. If this is true, ND will not even be a good for those people. It may be a bad. The claim that ND is a pure national public good assumes that all the citizens of nation regard defense against a particular enemy as a benefit.(1)
The Jointness Characteristic
Let us now ask whether ND has the characteristic of jointness. Jointness means that additional consumers can be added without increasing the cost of production. The marginal cost of adding a consumer to any given quantity is zero. If 100,000 people are now enjoying ND, the cost of adding one more must be zero.
It is easy to confuse a low marginal cost with a zero marginal cost. Suppose that there is a constant marginal cost of $10. Under this circumstance, if 100,000 consumers are consuming the good, the cost of supplying them will be $1,000,000. To add one more consumer is only $10. This seems very small compared with the $1,000,000 already paid. However, it is not zero. In fact, it is exactly the same as the average cost of supplying the other 100,000 consumers. For jointness to exist the marginal cost of adding a consumer must be zero.
For ND to have the characteristic of jointness, at least one of the two following conditions would have to be present. First, it would have to be possible to add consumers to a given geographical location at zero cost without diminishing the level of defense offered to others who are already there. In other words, there would have to be zero congestion costs. Second, it would have to be possible to expand defense to cover additional areas in which additional people live at no additional cost. The second condition does not seem to be realistic. It seems evident that conventional ND cannot protect an additional geographical area without additional cost. This fact is evident in countries like Indonesia and The Phillippines, which consist of numerous islands. In the United States, the defense burden increased substantially when Hawaii and Alaska were added as states. However, the first condition does seem to be present, at least within limits. For a given geographical area, additional people can be added, within limits, without increasing the cost of defending the total population by conventional means. However, beyond some point, as more and more people are added to a given area, congestion occurs. Even if the cost of producing ND stays the same, when we account for all of the costs of adding people, we must conclude that the marginal cost is not zero.
The Non-Exclusion Characteristic
Does ND have the characteristic of non-exclusion? The answer seems to be a flat "no." Since ND is supplied to a geographical area, it is a simple matter to bar someone from entering that area and partaking in the benefits of ND. The costs of exclusion are not zero. National borders would have to be policed, identity cards issued, visitors screened and monitored, and so on. However, exclusion seems possible at a reasonable money cost.
Suppose that someone refused to pay her share of the tax burden for ND. Then she could be exiled. Her passport could be taken away and she could be forced to leave the country.
Technically, then, exclusion is possible and can be achieved at relatively low cost. One complicating factor is that the government may contain a constitution that prevents the exile of a citizen who refuses to pay a price for ND services. For constitutional reasons, exclusion may be impossible. Nonexclusion in this case in not due to the technical nature of the good but to the structure of the government.
National Defense as a Natural Monopoly
If ND is not a public good, is there some other reason for market failure? The answer seems to be yes. ND seems to be a natural monopoly. To see why, let us try to imagine a country in which ND is supplied through the market economy. We assume that the suppliers of ND all have national loyalty and would never use their weapons against other citizens. Thus, there is no chance of civil war. If we assume otherwise, market supply would be impossible.
We might assume at first that ND-supplying firms would compete in the market for customers, not unlike movie theaters now compete. There is jointness, so each firm would want to gain as many consumers as possible. In order to enforce exclusion, each firm would have to choose a particular part of a nation in which to offer its services. Thus, consumers might have a choice between living in the Northeast and buying from the NEND company or living in the southwest and buying from the SWND company. NEND may charge a higher price but offer a higher quantity while SWND charges a lower price but supplies a low quantity. If the cost of supplying a given quantity of ND was higher in one part of the country than in another part, we might imagine that the fee that consumers would have to pay would be lower for a given quality in the part where the cost is lower. If a consumer was dissatisfied with the high price of ND in his jurisdiction, he could move to a lower-priced jurisdiction. Thus the nation would be divided into national defense zones.
Now it is evident that for this system to work, the government would have to agree to allow each ND firm to exclude any resident from the national defense zones who refuses to pay its ND fee. Otherwise a person who refused to buy national defense services at all could not be excluded. We might suppose that a person who chooses not to pay an ND fee at all would either be expelled from the country or be sent to a place in the country that was not defended and thus vulnerable to attack.
We have noted that there appears to be a relatively high measure of jointness in demand. This means that additional consumers can be added to a given area at zero marginal cost (or at least at a lower marginal cost than the consumer before him).. Suppose that you currently lived in the Northeast and that you paid the same price for ND services as someone like you who lives in the Southwest. The Southwest company could add you as a customer at a zero or relatively low cost. It could afford to reduce its price to you below what you were paying and, at the same time, reduce its price to its existing consumers. Thus, it would have an incentive to undercut the price to you offered by the Northeast company. Of course, it would have the same incentive to reduce price to all the Northeast company's customers. In practical terms, it would try to attract citizens to its national defense district. We might expect under these circumstances that companies from different districts would compete by offering discounts to newcomers from other districts.
The situation we are describing is very much like that of the theory of competing public utility companies -- the natural monopoly. In the public utility theory, a utility company can increase its scale and reduce long run average costs. If two firms of equal size are making normal profit, one can increase its size and reduce its costs. Thus, it can reduce price and make higher profit because it will be able to attract customers away from the other firm. The only feasible long run outcome is one in which a single firm supplies all of the consumers. The ND industry we have in mind is similar, except that there are congestion costs beyond some point. To see the similarity, assume at first that there are no congestion costs. Imagine two adjacent ND regions each of equal size and population. Since the marginal cost of adding one more consumer is nearly zero, each ND supplier would offer special discounts to consumers who shifted from the other supplier. As in the case of the theory of public utilities, the only situation compatible with equilibrium is one in which only one firm supplied the ND.
For one firm to supply ND services to all consumers, all the consumers would have to move to the ND firm's district. But as more and more people moved in, congestion costs would increase. Moreover, the marginal congestion cost would rise. The arrival of each new resident would cause a higher congestion cost than the resident before her. Possibly, there would be a point at which the marginal cost of supplying a citizen in her existing district would be the same as the marginal cost of supplying in the new district plus the marginal congestion cost. If so, long run equilibrium would require more than a single national defense supplier.
Let us suppose that such a point is not reached. In other words, suppose that all the ND of all of a country's citizens is supplied from a single district. The supplier would be a monopolist. Consider now the situation faced by a monopolist supplier. We have assumed that the marginal cost of defending additional space is positive and that there may be a crowding problem. In view of these characteristics, the firm might well provide a range of qualities of national defense. It might offer discounts to consumers who are willing to live together in a relatively small geographical space, while it charged a higher price to individuals who lived in less densely populated areas. This would encourage denser populations, although other advantages of living in less dense areas, such as less crowding (or perhaps farm profits) would probably exist to compensate some people for the higher price of ND.
Of course, if there was only one ND firm, it would be inclined to charge a monopoly price, or range of monopoly prices depending on location. We have seen that Pigouvian economists have recommended several solutions to the natural monopoly problem: marginal cost pricing, average cost pricing, and government control. In each case, there is a serious incentive problem. Regulated firms and government agencies have little incentive to control costs; and regulators are at a distinct disadvantage in knowing whether cost-inflating methods of production are being used. Also, it is difficult for regulators to give the natural monopolist an incentive to invent. We would expect the same results from a regulated ND natural monopoly.
If we relied on regulation, we could expect substantial inefficiency. But if we allowed the monopoly to be unregulated, the supplier of national defense would get very rich. Moreover, the monopolist would probably exclude consumers even though they valued national defense at a higher price than the cost of adding them as consumers. The reason is the difficulty that the supplier of ND would have in discriminating one consumer's demand from another's. A possible solution is to grant a limited-time franchise in supplying national defense and to require national defense suppliers to bid for that franchise. For example, we might give a national defense supplier a five year contract to supply under specific conditions. We would invite many firms to bid for the contract.(2)
The Problem of Regulating a Natural Monopoly in Defense Services
The goal of our discussion of ND has mainly been to determine whether the free market supply of ND would entail some kind of market failure. In order to make our exercise conform to the theory of market failure, we assumed that anyone was free to form a ND firm and that ND firms would remain loyal to the nation. In everyday life, it seems unreasonable to expect that the citizens of a country would allow market supply. First, since the competing firms must have control over massive firepower, their competition might turn warlike. The owner of one ND company might say to consumers of another company's service "If you continue to buy your ND from another supplier, my company will attack you and prove to you that the other company cannot defend you as well as we can."
Even if there was peaceful competition among ND companies, there is an overriding reason why citizens would prefer government supply to the alternatives. It is that one who controls the ND monopoly may use it to his own advantage. Realistically, how can a government that lacks control over ND regulate the ND monopoly? If a government regulator decided that the chief of the armed forces charged too high a price for his services and should be imprisoned, how could he enforce his decision? Moreover, what would prevent the chief of the armed forces from simply appropriating whatever property that he wanted? The owner of a monopoly ND company could presumably earn more money by simply taking it away from citizens than by protecting citizens against foreign aggressors. Thus it seems that the reason why governments supply ND is not that ND is a public good. It is (1) that ND is a natural monopoly and (2) citizens would be afraid that if a private company controlled the monopoly, the owner of the company might use his power to overthrow the government.
1. In defining national defense, people often confuse the defense of life, limb, and property with the defense of the nation state, or government.(See Hummel, 1990, p. 94-98) A person may demand the first without demanding the second. He also may demand the second without demanding the first. For example, some people speak of sacrificing the individual for the defense not of other people but for the defense of the national government. In this text, we define national defense as the defense of life, limb, and property.
2. See Demsetz, 1966.
Demsetz, Harold (1966). "Some Aspects of Property Rights." Journal of Law and Economics. (October).
Hummell, J.R., "National Goods Versus Public Goods: Defense, Disarmament, and Free Riders," The Review of Austrian Economics, Volume 4, 1990.
Copyright (c) 2002
J. Patrick Gunning
Professor of Economics/ College of Business
Feng Chia University
100 Wenhwa Rd, Taichung
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