DEFENSE SECTOR, ARMAMENTS–LABOR RATIO AND NATIONAL SECURITY

Abstract

This paper analyzes a national defense economy in which the army reduces the risk of attack and damage. The results show that it is important how countries or people feel about damage to military personnel, citizens and wealth from attack. The feeling determines the optimal levels of arms procurement and army personnel. It also affects international trade. It is found that labor (armaments) input into the military sector is not always decreased following an increase of wage (armaments price). The model suggests that conscription affects army expenditure and international trade.

Keywords:

• Military expenditures
• Armaments–labor ratio
• Willingness‐to‐pay for safety
• Arms imports
• International trade
• feeling about damage

Notes

¹A small country model is often used in international trade theory since it is very convenient model to analyze many problems. In this model, the prices of tradable goods are constant.

²It is assumed that capital is not used in the sector. It is said that the share of the procurement and personnel expenditure in the defense sector is very large (Sandler and Hartley, 1995).

³Taking it into consideration is easy. However, basically the results are not changed. Realistically, after the Cold War, the arms trade has become more commercial (Brzoska, 2004).

⁴Some developing countries use second‐hand tanks, which were made long ago in the Soviet Union. In this case, the tanks have small M. On the other hand, newly‐made and expensive tanks have large M. In this connection, it is said the unit price of procurement is increased (Kirkpatrick, 1995).

⁵We can define welfare by using an expected utility function with risk aversion. For example, it is represented as: (1 − P)U(D ₁ +p ₂ D ₂) − PU(D ₁ + p ₂ D ₂ − A*V). For simplicity, I do not treat the expected utility function. A kind of risk‐neutral is used in this paper since I want to focus on the attitude to the victims.

⁶ W _MM = ∂(∂W/∂M)/∂M = ∂(∂E/∂M)/∂M = − [2β _r3pM P′F _M + V(P″(F _M)² + P′F _MM)] A*

⁷ W _LL = ∂(∂W/∂L _A)/∂L _A = E _LL − [2V _LA P′F _L + V(∂P′F _L/∂L _A)]A* = − [2(βρ _1−αρ2)P′F _L + V(P″(F _L)² + P′F _LL)]A*

⁸Where W_ij = ∂(∂W/∂i)/∂ _j (i, j =M, L _{A, W} ), W _LM = −A*[P′F _M(β _{ρ 1−αρ2})+V _M P′F _L +V(∂(P′F _L)/∂M)], W _ML = −A* [P′F _L β _ρ4pM + P′F _M V _LA + V(∂(P′F _M)/∂L _A)]

⁹Although wage is an endogenous variable and it is determined by two prices of traded goods, we assume that there is a technological progress that only raises wage under constant prices.

¹⁰ V _W = β ρ′₁ L _A + α ρ′₂(L ₁ + L ₂) + β ρ′₃ M _PM + α’ρ′₄(K ₁ + K ₂)_{pK > 0}

¹¹Detail is omitted for simplicity.

¹²See footnote 2.

Additional information

Notes on contributors

Kazunori Tanigaki

The author would like to thank Keith Hartley for comments and suggestions which improve the paper. I am grateful to Masayuki Hayashibara and Masayuki Okawa for suggestions.