Quality versus quantity in arms races.

• Author: Hirao, Yukiko

1. Introduction

   Many defense analysts note that the U.S. military has a bias toward too high a level of quality [3; 8]. In contrast, the Soviet Union before the breakup used to have a substantial lead over the United States in terms of the number of conventional weapons. Most European nations also put more emphasis on cost minimization than on maximum performance. Gansler [3, 305] states as follows:

   Whereas the Americans emphasize the objective of maximum performance in each individual weapon . . ., the Europeans set out to minimize cost and risk in order to achieve an acceptable defense posture within their limited resources . . . Thus, one would expect to see lower-cost, lower-performance systems coming out of the European model--and a detailed investigation comparing aircraft-system developments in the United States versus the four countries of Europe confirmed this expectation.

   Some defense analysts maintain that the United States can achieve more effective defense by acquiring a larger quantity of less state-of-the-art weapons. As the potential enemies change and regional conflicts become more likely in the post-cold war era, it is important for us to examine national defense.

   The U.S. emphasis on quality over quantity is attributed to several factors. First, the United States has a superior technology in defense. Second, the military procurement process, unlike the free market system, does not motivate a supplier to produce at a minimum cost [3, 143-69]. Rogerson [10] offers a theoretical explanation for the military's bias toward quality. Noting that the military, as an expert agency, is delegated the choice of quality by the government (the principal), he shows in a single-country, agency framework the conditions under which the military chooses a level of quality that is excessive relative to the first-best benchmark case. The goal of this paper is to extend his analysis to a two-country arms race model. We study how an international arms race and organizational structure between the government and the military in each country affect the equilibrium choice of quality and quantity.

   Following Rogerson [10], we assume in a one-period, two-country model that the type of weapons (defense quality) must be determined prior to quantity, and that the choice of quality is delegated to the military in each country. In the second stage, the governments decide the number of weapons to buy. In this setup, the military uses the choice of quality as an instrument to influence both its own government (the effect discussed by Rogerson [10]) and the rival government.

   The first effect is referred to as "the agency effect" and the second as "the strategic commitment effect". We find that overall, the military's choice of quality will tend to be too large relative to the benchmark case if the country has a more efficient defense technology, a higher marginal cost of improving quality, and a lower marginal cost of output expansion. Since the marginal cost of arms production typically falls with output, it implies that a country with a superior technology that produces arms on a large scale tends to have a bias toward quality. This result seems to be in accord with the observed international differences in military procurement. It has an implication for empirical analysis.

   In addition to Rogerson, this paper is naturally related to the literature on arms races [4; 5; 6; 7; 11]. While the literature is growing rapidly, the papers cited above do not address the issue of quality versus quantity. Except for John, Pecchenino, and Schreft [7], most of these papers treat each country as a single decision-maker. Rogerson [10], on the other hand, does not explicitly consider international rivalry.

   Our paper is also closely related to Dixit's contest models [1]. Dixit shows that if one of the players in a contest can choose his effort before his rival does, then he will commit to a higher level of effort than in a simultaneous game if he is favored to win. This strategic commitment effect is present in our setup. Additionally in our model, the military's incentive to influence its own government's quantity choice works in the opposite direction from its incentive to influence the rival government: On the one hand, the military of the more powerful country wants to commit to a higher quality than in the one-stage game to force the rival nation to reduce the quantity of their arms. On the other hand, it wants to choose a lower quality so as not to trigger its own government to contract the number of weapons. And vice versa for the weaker nation. Overall, the strategic commitment effect will dominate the agency effect if the stakes of the conflict are high.

   Yet another strand of literature related to our work is the one that considers the effect of agency contracting on oligopoly [2]. In contrast to this literature, however, we posit that the agents (the military) move before the principals (the governments) do. We also differ from the other analyses in that we focus on quality-quantity choice.

   Section II sets up the model. Its features are discussed in section III. Section IV concludes briefly.

2. The Model

   Preliminaries

   Consider a one-period arms race between two nations. If country i (i = 1, 2) acquires [x.sub.i] units of weapons at quality level [q.sub.i], its military preparedness (the defense level) is given by [f.sup.i]([q.sub.i], [x.sub.i]). The cost of acquiring defense is [C.sup.i]([q.sub.i], [x.sub.i]). Denote a partial derivative [Delta][f.sup.i]/[Delta][q.sub.i] by [Mathematical Expression Omitted], and likewise for [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted]. We interpret quality and quantity as the...