The structure of the defense industry and the security needs of the country: a differentiated products model

Abstract

This paper models the interactions between the defense needs of the USA and Western Europe, which produce several heterogeneous defense goods, and the defense industry market structure. The results show that net defense costs of the USA and Europe are lower when the number of defense firms in each arms‐producing country is small and when the world prices of the defense goods are high. The model predicts that the increase in world prices will crowd‐out countries in the developing world from the market for modern weapon systems and may force them to develop and use ‘cheap and dirty’ weapon systems.

Keywords:

• Defense industry
• Security levels
• Net defense cost
• Industry profits
• JEL codes: H56; H57; L11; L13

Notes

† Corresponding author. E‐mail: [email protected]

We are grateful to I. Ben Israel, P. Dunne, G. Fethke, M. Garcia‐Alonso, S. Golde, K. Kagan, P. Levine, O. Setter, I. Tov, the participants of the Seventh Annual Conference on Economics and Security at the University of the West of England and the University of Bristol, and two referees for many valuable comments and suggestions.

Bolks and Stoll (2000) choose the ratio rather than the difference of arms stocks in analyzing naval arms races. Smith (1980), who developed an econometric model for Great Britain's defense expenditure, points out that the ratio, rather than the difference, between US defense expenditures and those of the USSR is statistically significant in the model. Hirshleifer (2000) discusses the characteristics of the measures of security and points out when each should be used. These two security measures may yield very different interpretations. To clarify this point, consider two cases in which, for the sake of simplicity, we assume that tanks are the only available weapons: (a) one country with 10 tanks and another, clearly stronger one, with 110; (b) one country with 3900 tanks and the other with 4000, which is stronger, but not by much. The difference measure does not distinguish between these two cases of a difference of 100 tanks. The ratio measure does. Generally, the two measures yield similar interpretations when the ratio measure is large (ten, for example); that is, when one country is much stronger than the other (the US and Iraq in 2003, say). However, they may yield substantially different outcomes when the ratio of the weapon systems stocks between the two rivals is closer to one.

This set‐up permits the use of the same model to analyze changes in the policy of the arms‐producing countries when ‘new rivalries’ (Afghanistan or Iraq versus the US, for example) develop.

Clearly, this decision rule may be viewed as a proxy for welfare maximization subject to the availability of the country's resources. However, this decision rule emphasizes the strong connection between the country's defense expenditure and that of its potential enemies, and the seemingly small correlation between defense expenditure and other government expenditures (on education, welfare, health, etc). A priori, it is not clear which decision rule is a better approximation of reality.

See Levine and Smith (1995, 1997, 2000), and Garcia‐Alonso (1999, 2000) for models of arms races among the countries in the ‘rest of the world’.

Following Garcia‐Alonso (1999), Levine and Smith (1995, 1997, 2000) and Blume and Tishler (2001), we assume that suppliers in the two producing countries know the aggregate demand functions of the recipients (countries in the rest of the world), can discriminate between recipients through export licenses and the like, and know how the military capability of the recipients will affect their own security (see Garcia‐Alonso, 2000; Levine and Smith, 2000, on the optimal policy of security restrictions on exports by the producing countries).

We shall also comment on the solution of the model when the defense firms sell the defense good to their own government at a price that is equal to their marginal cost plus a mark‐up (see Blume and Tishler, 2001 on this issue). Furthermore, we assume, as is the case in reality, that the governments of the producing countries do not altogether prohibit, or tax, exports. The interplay of market structure and government trade policy, whereby governments simultaneously and non‐cooperatively choose whether or not to tax or provide subsidies for their firms, is found in Balboa et al. (2004).

Since the model exhibits a single equilibrium, in the static analysis we use the measure ‘net defense cost’, which is not part of the government's objective function. See Miyagiwa (1991) for a similar measure.

Extending the model to several countries would complicate the presentation but would not change the nature of the results.

In the sixth section we extend the model to include N and K defense firms in countries A and B, respectively.

In the model, we assume that the defense goods exhibit a similar quality. The definition of security is somewhat different when the defense goods produced in country A are different in quality from those produced in country B. This extension can be handled as follows. Denote by λ the quality of the defense good produced in B relative to the one produced in A (that is, A's quality equals 1). Expressions (1a) and (1b) become S _A  = x ^A _A /(x ^W _A  + λx ^W _B ) and S _B  = λx ^B _B /(x ^W _A  + λx ^W _B ), respectively. It is straightforward to extend the model to allow each country to exhibit a different perception of the quality of its defense good relative to the defense good produced by the other country. The results of the model without differentiated qualities are similar in nature (although somewhat less complicated) to those of the model with differentiated qualities. To simplify the analysis and presentation, we proceed to analyze differentiated defense products with similar qualities.

The nature of the results does not change when marginal costs are increasing. An interior equilibrium may not exist when marginal costs are decreasing.

If the products are quality differentiated, where λ is the quality of the defense good of country B relative to the quality of the defense good of country A (that is, A's quality equals 1), equation (7) becomes: x ^A _A  = λD ₁ S ⁰ _A /(λ − λD ₂ S ⁰ _A  − D ₃ S ⁰ _B ), x ^B _B  = D ₁ S ⁰ _B /(λ − λD ₂ S ⁰ _A  − D ₃ S ⁰ _B ), where D ₁ ≡ Ã ₁ + λ ₁ > 0, D ₂ ≡ Ã ₂ + λ ₂ < 0 and D ₃ ≡ Ã ₃ + λ ₃ > 0.

If the defense goods are quality differentiated, we obtain: x ^A _A  = D ₁ S ⁰ _A , x ^B _B  = D ₁ S ⁰ _B /λ, where D ₁ ≡ Ã ₁ + λ ₁ > 0.

The demand by the rest of the world can be similar to the demand by the private sector in Miyagiwa (1991). The separation between the world price and the size of the governments' commitments under MU, and the (mostly positive) effect of the size of these commitments, under WP, on the world prices are also obtained by Miyagiwa. We thank a referee for pointing out these similarities to us.

Eventually, in April 2001, General Dynamics acquired Newport News Shipbuilding.

The simulation results in Figure 6 assume, in addition to the symmetry assumption, that: (i) the relevant parameters of the demand functions of the rest of the world for the defense goods in A and B are identical (in other words, a _i0 = b _i0 ≡ a ^N ₀ > 0 ∀i, a _ij  = b _ij  ≡ α ₁ ^N  > 0 ∀i ≠ j, a _ii  = b _ii  ≡ a ^N ₁ < 0 ∀i). (ii) C _Ai  = C _Bi  ≡ C, c _Ai  = c _Bi  ≡ c > 0 ∀i, and (iii) target security levels in the two countries are equal (S ⁰ _A  = S ⁰ _B  ≡ S ⁰). Figure 6 is based on a particular set of parameter values. Clearly, other sets of parameter values would yield different numerical results. However, very extensive experiments, using different sets of parameter values, yielded the same pattern of results as in Figure 6.

In theory, full cooperation between A and B can prevent exports of the defense goods to the rest of the world, yielding zero defense expenditure in A and B (zero procurement). This solution is not possible here since we assume, as is the case in reality, that A and B do not cooperate.

On these estimates see Kirkpatrick (1995) and Golde and Tishler (2002). The calibration results described here are not too sensitive to the use of other reasonable values of the rates of change of the price indices of the defense goods, or to the number of defense firms in each arms‐producing country.

See Mantin (2001) for details.