Defense Industry and Threats

International Review of Social Sciences and Humanities Vol. 6, No. 2 (2014), pp. 206-213 www.irssh.com ISSN 2248-9010 (Online), ISSN 2250-0715 (Print) Defense Industry and Threats Cheng-Te Lee (Corresponding Author) Department of International Trade Chinese Culture University 55, Hwa-Kang Road, Yang-Ming-Shan Taipei City 11114, Taiwan E-mail: [email protected] Yo-Yi Huang Institute of Applied Economics National Taiwan Ocean University 2, Pei-Ning Road, Keelung 20224, Taiwan E-mail: [email protected] Kuo-Hsing Kuo Department of International Trade Chinese Culture University 55, Hwa-Kang Road, Yang-Ming-Shan Taipei City 11114, Taiwan E-mail: [email protected] (Received: 27-9-13 / Accepted: 11-11-13) Abstract This paper sets up a dynamic optimization model to analyze the impact of military threats on defense industry. We prove that a rise in the foreign military threats will result in the shift of economic resources from the civilian sector to the defense sector. As a result, civilian sector shrinks and defense sector expands, a phenomenon resemble to so-called ‘Dutch disease’ in the trade literature. Keywords: Defense industry; Threats; Resources allocation; Dutch disease. 1. Introduction The purpose of this paper is to explore the impact of military threats on defense industry. Clearly, military spending is an indicator of the amount of economic resources devoted to military activities. During the cold war period, the East-West struggle has evolved into the arms race, leading to an increase in the worldwide military spending. After the cold war, the military threats reduce and thus many countries accelerate the shift of resources from the defense sector to the civilian sector. Stockholm International Peace Research Institute (SIPRI) Yearbook (1999) states that world military spending has been on a declining trend during the period of 1987-1999. The reduction in world military spending is more than one-third; more International Review of Social Sciences and Humanities, Vol. 6, No. 2 (2014), 206-213 207 specifically the strong cuts have been made in Europe by 55%, America 30%, and Africa 25%. In the meantime, the reduction in military spending has also caused a dramatic wave of defense industry mergers in America in which the defense industry is whittled down from a group of about fifteen companies to the five companies of Lockheed Martin, Boeing, Raytheon, General Dynamics, and Northrop Grumman. 1 As indicated by Markusen and Costigan (1999), the total defense-related employment in the world has fallen by 6.5 million workers during the period of 1987-1995. Obviously, these workers should migrate from the defense sector to the civilian sector. It was not until the 911-event of terrorist attacks, the world military spending rebounded and began to rise on an upward trend.2 Thereafter, the controversial defense programs of European and America are more likely to swim through on a rising tide of national insecurity. Meanwhile, the defense-related employment is expected to accelerate uptrend, corresponding to the phenomenon of return migration from the civilian sector to the defense sector.3 In other words, the military threats will cause the reallocation of economic resources, leading to shrinkage or expansion of defense industry, see Bouthoul (1969). However, what we have observed from the above story is that an increase in the military threats will lead to the expansion of the defense industry and the shrinkage of other civilian sectors or conventional manufacturing sectors, a similar phenomenon of so-called ‘Dutch disease’ in the literature on trade theory.4 Our paper is formally to analyze the above-mentioned interesting phenomenon of the Dutchdisease induced by the military threats. More specifically, we will set up a dynamic optimization framework to analyze the impact of the military threats on the defense industry. The structure of the paper is as follows. Section 2 presents a simple dynamic optimization model. Section 3 presents the comparative static analysis. Section 4 concludes the paper. 2. Model Consider a theoretical model consisting of the home country and the foreign country, and suppose that the home country is a small open economy which is confronted with foreign military threats. There are two sectors in home country: the civilian sector and the defense sector. The civilian sector produces consumption goods (C) and the defense sector produces weaponry (R). The home country derives utility from consumption, and the home weapon stock, and disutility from the foreign weapon stock ( M ∗ ): U (C , R, M ∗ ) . Assume that U (C , R, M ∗ ) is concave and continuously differentiable in its arguments. Following Brtio (1972), Simaan and Cruz (1975), Deger and Sen (1983, 1984), van der Ploeg and de Zeeuw (1990), Zou (1995), and Chang et al. (1996, 2002), the instantaneous utility function U satisfies the following assumptions: U1 > 0, U 2 > 0, U 3 < 0, U11 < 0, U 22 < 0, U12 = U 21 ≥ 0, U13 = U 31 ≤ 0, U 23 = U 32 > 0. Let U i represent the derivative of the utility function with respect to the ith argument. Similarly, U ij represents the derivative of U i with respect to j th argument. The aforementioned assumptions imply that the marginal utility from consumption and home 1 See The Economist (8280 July 2002, pp. 62-63). See SIPRI Yearbook (2006). 3 See The Economist (8242 October 2001, pp. 57-58). 4 The Economist (26 November 1977, pp. 82-83) first describes the phenomenon of ‘Dutch disease’. The phenomenon originally refers to the adverse effects on Dutch manufacturing caused by the natural gas discoveries of the 1960s. 2 Cheng-Te Lee et al. 208 weapon stock is positive and diminishing. In addition, the marginal utility from foreign military threat is negative. The assumption U 13 = U 31 < 0 implies that more foreign weapon stocks reduces the marginal utility of consumption, whereas U 12 = U 21 > 0 states that a rise in the home weapon stock raises the marginal utility of consumption, similarly, U 23 = U 32 > 0 asserts that an increase in the foreign military threat will increase the marginal utility of home country’s weapon stocks. Moreover, the assumption U 13 = U 31 = U 12 = U 21 = 0 implies that the utility function is separable between the consumption and the weapon stocks. The civilian sector and the defense sector employ labor and capital as inputs. Labor and capital are intersect orally mobile. Hence, the production function of the consumption goods is expressed as: Y = F ( L, K ), FL > 0, FK > 0, FLK = FKL > 0, FLL < 0, FKK < 0 , Where L denotes the labor employment and K represents the capital employment in civilian sector. Similarly, the production function of the weaponry is specified as: G ( LR , K R ) , G LR > 0 , G K R > 0 , G LR K R = G K R LR > 0 , G LR LR < 0 , G K R K R < 0 , where LR denotes the labor employment and KR represents the capital employment in defense sector. The production functions are assumed to be linearly homogeneous, and the marginal products of labor and capital are positive and diminishing in both civilian and defense sectors. Let L and K represent the endowment of labor and capital respectively. The full-employment conditions for labor and capital can be derived as: L + LR = L , K + KR = K . (1a) (1b) Following McMillan (1978), the weapon accumulation in the home country is: R&= G(LR, KR) − δR , δ ≥ 0 , (2a) Where δ represents the depreciation rate of the weapon stock. Substituting equations (1a) and (1b) into equation (2a), we have: R&= G( L –L, K –K) − δR . (2b) The household budget constraint can be described as: PF ( L, K ) + G ( L − L, K − K ) = PC + T , (3) Where P represents the relative price of the consumption goods, and T is a lump-sum tax. The objective is to maximize the discounted sum of utility over an infinite horizon with a constant rate of time preference ( ρ ), and 0 < ρ < 1: ∞ max ∫ U (C , R, M ∗ )e − ρ t dt , 0 Subject to equations (2b) and (3). The initial home weapon stock is given as R0. To solve the optimization problem, we specify the corresponding Hamiltonian as following: International Review of Social Sciences and Humanities, Vol. 6, No. 2 (2014), 206-213 209 Ham = U (C , R, M ∗ ) + λ[G ( L − L, K − K ) − δR ] + γ [ PF ( L, K ) + G ( L − L, K − K ) − PC − T ] . (4) Where λ is the costate variable which can be interpreted as the marginal contribution of weaponry to utility. The variable γ represents the shadow price of the consumption goods. Normalize prices so that γ =1. Hence, the first-order necessary conditions for the optimization are: U 1 (C , R, M ∗ ) = P , (5a) P FL ( L, K ) = (λ + 1)G LR ( L − L, K − K ) , (5b) P FK ( L, K ) = (λ + 1)G K R ( L − L, K − K ) , (5c) λ&= ( ρ + δ )λ − U 2 (C , R, M ∗ ) , (5d) lim Rλe − ρ t = 0 , (5e) t →∞ and equations (2b) and (3). Equation (5a) says that the marginal utility of consumption is equal to its price. Equation (5b) implies the equality of the marginal productivity of labor between the civilian sector and the defense sector. Equation (5c) implies the equality of the marginal productivity of capital between the civilian sector and the defense sector. The familiar Euler condition is giver by equation (5d), which governs the optimal choice between consumption and weapon accumulation. The transversality condition is given by equation (5e). Let τ denote the tax rate. The lump-sum tax revenue can be described as: T = τ [ PF ( L, K ) + G ( L − L, K − K )] . (6) The government is assumed to collect its lump-sum tax revenue to purchase the armament and then freely offers internal and external security. Hence, the government budget constraint is: τ [ PF ( L, K ) + G ( L − L, K − K )] = G ( L − L, K − K ) , or G ( L − L, K − K ) = τ 1−τ PF ( L, K ) . (7) Combining (5b) with (5c), we have: FL ( L, K )G K R ( L − L, K − K ) = FK ( L, K )G LR ( L − L, K − K ) . (8a) Solving equation (8a), we have: K = K ( L, L , K ) , And (8b) Cheng-Te Lee et al. Λ= 210 ∂K G K R FLL + FK G LR LR − FL G K R LR − G LR FKL = > 0. ∂L G LR FKK + FL G K R K R − FK G LR K R − G K R FLK (8c) Substituting equations (6) and (7) into equation (3), we have: (9) C=F(L,K). Substituting equations (5a), (8b) and (9) into equation (5b), we have: U 1 ( F ( L, K ( L, L , K )), R, M ∗ ) FL ( L, K ( L, L , K )) = (λ + 1)GLR ( L − L, K − K ( L, L , K )) . (10a) Substituting equations (8b) and (9) into equations (2b) and (5d), we have: R&= G ( L − L, K − K ( L, L , K )) − δR , (10b) λ&= ( ρ + δ )λ − U 2 ( F ( L, K ( L, L , K )), R, M ∗ ) . (10c) Differentiating equation (10a) with respect to time, we get: 1 G LR & L&= [ λ − U 12 R&] , ∆U 1 FL Where ∆= (11a) ψ U 11 ( FL + FK Λ ) ( FLL + FLK Λ ) (G LR LR + G LR K R Λ ) + + = < 0, U1 FL G LR U 1 FL ψ = U 11 FL FL + U 1 FLL + (λ + 1)G L L + Λ[U 11 FL FK + U 1 FLK + (λ + 1)G L K ] < 0 .5 R R R R Substituting equations (10a), (10b) and (10c) into equation (11a), we have: G LR U 2 G LR U 12 1 L&= [( ρ + δ )(1 − )− − (G − δR)] . ∆ U 1 FL U 1 FL U1 (11b) Equation (11b) states how the labor will mobilize intersectorally over time. Therefore, equations (11b) and (10b) describe the transitional dynamics of the economy. In characterizing the steady-state equilibrium of the model, we get that there exists a unique ~ ~ stationary state (i.e., R , and L ), which satisfies L&= R&= 0 . Appendix states the stability analysis of the dynamic system. The phase diagram is illustrated in Figure 1. The point E is a saddle point. The path SS is the unique saddle path. In the next section, we will explore the impact of the foreign weapon stock on the labor employment of civilian sector and the home weapon stock at the steady-state equilibrium. 5 Using the assumption of the linearly homogeneous production function and the relationship of the first-order conditions, we can prove that ψ <0 is hold. 211 International Review of Social Sciences and Humanities, Vol. 6, No. 2 (2014), 206-213 L&= 0 L SS E R&= 0 0 R Figure 1: Stably dynamic system 3. Comparative Static Analysis At the steady-state equilibrium, the economy is characterized by R&= λ&= 0 and L, R, and λ ~ ~ ~ are at their stationary level, in other words, L , R , and λ . From equations (10a), (10b) and (10c), we can derive the steady-state relationships as follows: ~ ~ ∂L ∂R δ =− < 0, (G LR + G K R Λ) ∂M ∗ ∂M ∗ (12a) ~ (G LR + G K R Λ ) ∂R [( ρ + δ ) FLU 13 − G LR U 23 ] > 0 , = ∗ Ω ∂M (12b) ~ A> ∂λ = 0, ∗ ∂M Ω< (12c) Where Ω = −( ρ + 2δ )U 12 FL G LR (1 + FK Λ) + δ ( ρ + δ )ψ + U 22 G LR (G LR + G K R Λ) < 0 , FL A = −(GLR + G K R Λ) FL (U 12U 23 − U 13U 22 ) + δU 23ψ − δU 13U 21 FL ( FL + FK Λ) . Equation (12a) indicates that a rise in the foreign threats has a negative impact on the labor employment of civilian sector. From equation (8c), we also can prove that a rise in the foreign threats has a negative impact on the capital employment of civilian sector. In other words, an increase in the foreign military threats will result in the shift of economic resources from the civilian sector to the defense sector. Equation (12b) states that an increase in the foreign threats leads to more home weapon stocks. Equation (12c) describes that the relationship between the foreign threats and the shadow price of home weapon stocks is ambiguous. However, if the utility function is separable between the consumption and the weapon stocks (i.e., U 13 = U 31 = U 12 = U 21 = 0), equation (12c) definitely indicates that a rise in the foreign threats will increase the shadow price of home weapon stocks (see Chang et al. (1996) and Lee (2007)). Therefore, we get the following proposition: Proposition 1: An increase in the foreign threats will lead to the shift of economic resources Cheng-Te Lee et al. 212 from the civilian sector to the defense sector, and vice versa. Proposition 2: A rise in the foreign threats will lead to the booming defense industry, and vice versa, a similar phenomenon of so-called ‘Dutch disease’ in the trade literature. 4. Conclusions This paper sets up a dynamic optimization model to analyze the impact of the military threats on the defense industry. We prove that an increase in the foreign military threats will lead to the shift of labor and capital from the civilian sector to the defense sector, and vice versa. Namely, an increase in the foreign military threats will result in the shift of economic resources from the civilian sector to the defense sector. As a result, civilian sector shrinks and defense sector expands, a phenomenon resemble to so-called ‘Dutch disease’ in the trade literature. Appendix In order to examine the stability of the dynamic system, we rewrite equations (11b) and (10b) which describe the dynamics of the economy as follows: L&= H ( L, R, M ∗ ) , R&= J ( L, R, M ∗ ) . (A.1) (A.2) ~ ~ Expanding equations (A.1) and (A.2) around the stationary values of L and R , we get:  L&  H L  & =   R  J L ~ H R  L − L   ~ , J R   R − R  Where HL = HR = (A.3) G LR [( ρ + δ ) + U 2 ] >0, U 1 FL G L U 22 1 [( H L + δ )U 12 − R ]<0, FL ∆U 1 JL = − (GLR + GK R Λ) < 0, JR = − δ < 0. Let Hi and Ji represent the derivatives of the functions H and J with respect to the variable i respectively, where i= L, R. The slopes of loci L&= 0 and R&= 0 from equations (A.1) and (A.2) are: ∂L ∂R ∂L ∂R =− HR > 0, HL =− JR < 0. JL L&= 0 R&= 0 International Review of Social Sciences and Humanities, Vol. 6, No. 2 (2014), 206-213 213 Assume that µ1 and µ 2 are the two characteristic roots that satisfy the dynamic system described by equations (A.1) and (A.2), we have: µ1µ 2 = HLJR – HRJL < 0. Obviously, the two characteristic roots of the dynamic system are opposite signs, µ1 < 0 < µ 2 . Therefore, we indicate that the system displays the saddle-point stability and prove that there exists a unique saddle path SS in the dynamic system. However, the slope of saddle path SS is positive as following: [H L − µ1 ν1 HR H R ]νν 1  = 0 ⇒ =− > 0,  2  ν2 H L − µ1 Where [v1 v 2 ] represents the characteristic vector. 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