Domestic Content Protection in a Dynamic Small Open Economy

Domestic Content Protection in a Dynamic Small Open EconomyAuthor(s): Tae-Hyung KimSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 30, No. 2(May, 1997), pp. 429-441Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/136349 .

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Domestic content protection in a dyna:mic small open economy T A E - H Y U N G K I M Korea Institute for International Economic Policy

Abstract. In this paper the long-run macroeconomic effects of content protection policy in a small open economy within the intertemporal optimizing framework are investigated. With the explicit consideration of labour-leisure choice, together with incorporation of investment and its adjustment costs, we focus on the long-run effects on capital accumulation, the current account, and employment, which have been neglected in previous literature. Our results show that a more restrictive content protection policy leads to a lowe:r level of the capital stock, an improvement in the current account, and a decrease in employment.

La protection d'une composante nationale de productiont en dvnamique dans une petite &onomie ouverte. Ce memoire examine les effets macro-economiques a long terme d'une politique de protection d'une composante nationale de production. dans une petite economie ouverte dans le cadre d'une analyse d'optimisation intertemporelle. L'auteur tient compte de la relation d'equivalence travail-loisir, ainsi que de l'incorporation de l'investissement et des couts d'ajustement afferants, et examine les effets a long terme sur I'accumulation du capital, le compte courant, et 1'emploi - elements qui ont e negliges dans la litterature specialisee anterieure. Les r6sultats montrent qu'une politique plus restrictive quant a la composante nationale de la production conduit a un niveau plus bas du stock de capital, a une amelioration du compte coura it, et a un declin dans 1'emploi.

1. INTRODUCTION

Following the early literature on domestic content protection (or local content schemes),' substantial contributions have been made in this area during the past

I would like to thank Philip Brock and Charles Engel for helpful comments and suggestions on an earlier draft of this paper. I aim also grateful to two anonymous referees for their helpful comments and corrections.

I See Munk (1969), Corden (1971), and McCulloch and Johnson (1973). Content protection takes two forms in the real world: it can be specified in physical terms, that is, in terms of volume, or in value-added terms. In physical terms domestic producers of final goods are required to use a specified proportion of domestic intermediate goods. McCulloch and Johnson (1973) termed this as a type of 'proportionally distribuited quota.' In value-added terms, a certain minimnum value of the domestic intermediate good must be embodied in the valuie of the final good.

Caniadian Journal of Economics Revue canadienne d'Econiomique, xxx, No. 2 May mai 1997. Printed in Canada lmprirnm au Canada

0008-4085 / 97 / 429-41 $1.50 ? Canadian Economics Association



430 Tae-Hyung Kim

decade.2 The main focus in the existing literature has been on the implications regarding resource allocation and welfare within a static framework, based on dif- ferent assumptions about the market conditions for the intermediate- and final-goods sectors. Yet little attention has been paid to the long-run macroeconomic aspects of content protection.

In this paper, therefore, some important long-run aspects of content protection are addressed. We investigate the effects of content protection on the capital accumulation, current account, employment, and overall welfare of a small open economy. In the existing literature the effect on investment has been neglected because static trade models abstract from capital accumulation. The effect on the current account - which is especially important for a country facing an external deficit - has been neglected because static trade models assume balanced trade. The employment effect also has been neglected under the assumption of the full employment of labour except by Chao and Yu (1993) and Fung (1994).3

Recently, the interternporal optimizing framework has been standard in analyses of the dynamic behaviour of capital accumulation, the current account dynamics, and the effects of government policy in an open economy.4 This framework is especially attractive in that the behavioural relationships are based on microeco- nomic foundations and derived from the intertemporal optimizing behaviour of the representative agents.

The basic production structure we adopt in this paper is similar to the specific factors model developed by Samuelson (1971) and Jones (1971). Our two-sector model, however, considers the intermediate good as an input in the final-good sector. We postulate a model in which the final-good (exportable) sector, em- ploys capital, labour, and both domestic and foreign intermediate goods, which are assumed to be perfect substitutes. The domestic intermediate-good sector, which is under government content protection, uses land and labour in the production process.5 In this paper, for analytical convenience, we specify the content protection scheme in physical terms.6

2 See Grossman (1981), Dixit and Grossman (1982), Hollander (1987), Vousden (1987), Krishna and Itoh (1988), Richardson (1991), Beghin and Sumner (1992), Chao and Yu (1993), and Fung (1994).

3 Chao and Yu (1993) analyse the effect of content protection on employment in the urban area with the three-sector Harris-Todaro model, and Fung (1994) introduces variable labour supply into Chao and Yu's model and analyses the employment effects of content protection policy, but both models are static.

4 This fiamework has been adopted in recent studies on the long-run macroeconomic effects of tariffs (see Brock 1986; Van Wijnbergen 1987; Engel and Kletzer 1989; Sen and Turnovsky 1989; Roldos 1991; Brock and Turnovsky 1993). The first macroeconomic analysis of tariffs was done by Mundell (1961), based on the static IS-LM model.

5 This type of specific-factors production structure is plausible for the Australian tobacco industry and Taiwan's food-processing industry.

6 If the intermediate and final goods are almost homogeneous, then it is reasonable to specify the content protection scheme in physical terms. For example, the Australian government sets a minimum content requirement of 50 per cent domestic tobacco leaves for cigarettes (see Beghin and Sumner 1992) and the Taiwan government requires the food-processing industry to use a min- imurn of 30 per cent domestic rice (see Chao and Yu 1993). If the intermediate and final goods are almost heterogeneous, then it is reasonable to specify the content scheme in value-added



Domestic content protection 431

The main features of our model are as follows. First, with the explicit consideration of leisure in utility function, that is, with labour being endogenous, employment in our model is endogenously determined through the intertemporal optimizing behaviour of a representative agent. Therefore, both the short-run and the long-run effects of a content protection policy on employment can be examined. In addition, with an incorporation of investment and its adjustment costs, we analyse the effect of an increase in content requirement ratio on the dynamic paths of the capital stock and current account of the economy.7

The remainder of this paper is organized as follows. In section II we develop a simple two-sector model, derive the first-order optimality conditions and the short- run equilibrium conditions, and examine the characteristics of the steady state and dynamics. We also derive the long-run equilibrium conditions for the market value of capital, the stock of capital, and the stock of traded bonds in section II. In section III we focus on the long-run effects of content protection on the capital stock, the current account and the shadow value of wealth as discussed in section III. The long-run responses of employment are also examined in section III. Conclusions are presented in section IV.

11. THE MODEL

1. Analytical framework Consider a small open economy that is composed of a single representative agent who lives forever and has perfect foresight. The representative agent produces two goods: a final-good (exportable) Y is produced using capital, both domestic and foreign intermediate goods (M and M*) and labour (Lx), and a domestic intermediate good (M) is produced with land (T) and labour (L n). We assume that Y can be either consumed or added to the original capital stock and that M is not traded and used in the production of good Y. The production functions of these two goods can be expressed, respectively, by

Y = F(K, MX, Lx), M - G(T, Lill),

where MX = M +M*. Both production functions are assumed to be constant returns to scale, concave, and twice continuously differentiable. Therefore, these production functions have the usual properties of the standard neoclassical production function; that is, FK > 0, FM > 0, FL > 0, GL > 0, and FKK < 0, FMM < 0, FLL < 0, GLL < 0. In addition, we assume that any two factors in the final-good sector are cooperative: the second cross-partial derivatives between two factors are positive,

terms. For example, a minimum of 85 per cent of the wholesale value of domestically manu- factured cars in Australia must be due to the use of domestic intermediate parts (see Vousden 1987).

7 As is well known, whether or not the adjustment costs ol capital exist in this framework does not alter the main results of this paper. That is, without the assumption of the adjustment costs, the dynamics simply degenerate, because any investment or disinvestment can occur instantaneously. It is more realistic to assume that the capital stock adjusts slowly with lags in investment.



432 Tae-Hyung Kim

that is, Fij > 0, where i, j-K, M', Lx and i 4 j. In this setting, therefore, capital and the intermediate input are specific to the production of the final (export) good, land is specific to the production of the domestic intermediate good, and labour is freely mobile between the sectors.

The economy under consideration is assumed to be small in world markets, so that the agent takes the relative price of the foreign intermediate good in terms of the final good as given at P*, where the price of the final good is taken to be numeraire. Since the domestic intermediate good is assumed to be not traded, its relative price, P, is endogenously determined. Throughout our analysis it is assumed that P > P*.8

The government in our analysis plays a simple role: it sets the minimum non- zero content requirement ratio (a) for the use of the domestic intermediate good that is employed in sector Y. This is, we consider M >_ a(M + M*) or M* ?

(1 - a)(M + M*). In this paper, to keep the analysis as simple as possible, we assume that the agent simply fulfils the content requirement ratio, so that the agent is not subject to a penalty tariff of any kind.9 Thus, our focus is on M = ca(M +M*) or M* = (I - c)(M + M*).

It is assumed that the agent allocates one unit of labour between leisure (1), labour in sector Y, and labour in sector M. Thus, the total labour allocation constraint can be written as I + LX + L" = 1.

The agent's capital accumulation behaviour is constrained by k = I where there is no depreciation of capital. In addition, following the literature on the adjustment costs of capital (Lucas 1968; Gould 1968; Treadway 1969; Hayashi 1982; Abel and Blanchard 1983), we assume that the agent has to spend +(I) units of the final good in order to increase the capital stock by I units.10 It is also assumed that 4(I) is an increasing, convex function of I where +'(I) > 0 anid +"(I) > 0. In addition, we assume that O(0) = 0 - /(0). II

The agent is assumed to hold and accumulate traded bonds, b, pay an exoge- nously given world interest, and face the instantaneous budget constraint:

b rb + F(K, Mx, LX) + P[G(T, L'1)- M] - C - I - 4O(I) - P*M*. (1)

Equation (1) shows that the change in traded bonds - the current account surplus or deficit - is equal to the final output minus spending on consumption of the final good, investment, interest payments, and the imported foreign intermediate good at P*.

8 If P < P*, then the final-good sector will employ only the domestic intermediate good. Thus, the economy does not need this policy. If P = P*, content protection cannot affect the allocation of resources (see equation (2d)). These cases are ruled out in this paper.

9 For the government to conduct protection policy successfully, such a policy must impose a penalty tariff on the imported intermediate good if domestic producers of the final good fail to comuply with the content requirement ratio.

10 An alternative assumption that adjustment costs depend on gross investment does not alter the results of this paper.

11 Later, it will become convenient to analyse the steady state of the economy where there is no investment.




The agent derives utility from consumption (C), and leisure (1) - from

Max / e-'[U(C) + V(l)]dt,

where the instantaneous utility function U(C) + V(l) is assumed to be increasing in consumption, non-negative, and concave - makes labour allocation decisions (I, LX, Lm), determines employment of MW, and chooses rate of investment (I) and the rates at which he wishes to accumulate his holdings of traded bonds (b), being subject to the budget constraint, capital accumulation constraint, labour allocation constraint, and the initial stocks of traded bonds and capital (bo and Ko). The current-value Hamiltonian for the representative agent's maximization problem is given by

H =U(C) + V(l) + A[rb + F(K, M.x, L-) + PG(T, Lm)-C- I )

-PaM" - P*(1 - a)M + qI + w(lI 1-- L` - L')]

where A, the costate variable associated with the agent's instantaneous budget constraint, is the shadow value (marginal utility) of wealth (in the form of traded bonds), and q and w are the market value of capital and the real wage in terms of the price of traded bonds.

The first-order optimality conditions are

U'(C) = A (2a)

V'(l) = Aw (2b)

FL(K, MX, L;) = PGL(T, L2) -w (2c)

FM =aP + (1- a)P* (2d)

q=I + +'(I) (2e)

A = A(L3-r) (2f)

q rq -.FK(K, M', LX). (2g)

Equation (2a) is the optimality condition for consumption of the final good (C). This condition shows how the marginal utility of consumption is related to the shadow value of wealth. Equation (2b) shows how the marginal utility of leisure and shadow value of wealth are related. Equation (2c) determines the sectoral allocation of labour by equating the values of marginal product of labour in both sectors. Equations (2b) and (2c) together describe the usual marginal rate of substitution condition in work effort. Equation (2d) says simply that the value of marginal product of intermediate good is equal to the weighted average of the prices of domestic and foreign intermediate goods. The optimal decision rule for investment



434 Tae-Hyung Kim

is described in (2e). This equates the market value of newly installed capital to the marginal cost of investment. Equation (2f) shows how the shadow value of wealth evolves over time. Since both the agent's rate of time preference (3) and the world real interest rate (r) are assumed to be constant, we need 3 = r to ensure the existence of the steady state.12 This implies A = 0 for all t, so that A(t) = A for all t, and therefore C(t) = C for all t. This simply implies that the shadow value of wealth remains constant, and therefore from (2a) consumption path for the final good remains flat over time. Equation (2g) describes the evolution of the market value of capital over time.

Finally, for the intertemporal budget constraint to be met we need to impose the following transversality conditions: lim,,+ e-rAb(t) = limt, ertq(t)K(t) = 0, where: = r.

We are now in a position to complete the description of the short-run macro- equilibrium conditions from the static equations (2a)-(2e), with A(t) = A. These equations can be solved in terms of A, a, P*, K, and q as

C=C(A) CA < 0 (3a)

MX = MX(A, , P*, K) MA > O, Ma < ?, MP* < 0, MK > 0 (3b)

P =P(A, a P*, K) P\ O0, Pa < 0, Pp* < 0, PK > O (3c)

I =1(A, a, P*, K) 1,\ < O, la 5 O, 1P* > O, IK < ? (3d)

L X(Aj a, * K) L) > 0, Lxa , L-P* O, LK ? (3e)

L' =Lm(A, a, P*, K) LE>A , a LP K0, LK>? (3D

I = H(q) Hq > 0- (3g)

Some intuitive interpretations of these partial derivatives shown in (3a)-(3g) may be given as follows.13 An increase in the shadow value of wealth encourages savings, leading to a reduction in the consumption of good y.14 A higher A leads to an increase in employment in both sectors and a decline in leisure, thereby stimulating the production of both Y and MX and increasing the demand for both M and M*. An increase in A may lower or raise P, depending upon how the labour market and the intermediate-good market respond to it. An increase in a leads to a reduction in the demand for Mx, since it initially raises the weighted average price of the intermediate goods, given P and P*. Then it causes the demand for Lx to decrease,

12 If 3 $ r, then it is possible that wealth could go to zero or go unbounded. To avoid these prob- lems, we assume 3 = r.

13 Substituting the above short-run expressions for Mx, P, l, LX, and Lm into (2b), (2c), (2d), and G = aMy, together with I + L + LI = 1, yields the identities that we can use to obtain the above properties of short-run equilibrium conditions described in (3b)-(3f). The formal expressions of the partial derivatives are calculated and available upon request from the author.

14 It is important to note that since we assume the utility function is separable in consumption and leisure, the consumption that remains flat over time with A(t) A responds only to changes in A.




thereby raising the marginal productivity of L'" and the marginal utility of leisure. A rise in the marginal productivity of L' does not necessarily increase the demand for labour in that sector, however, because a reduction in the demand for L' leads to a further fall in the marginal productivity of MW. This causes P to fall, thereby lowering the marginal productivity of L'. Therefore, the effect of an increase in a on Lm is ambiguous. However, if the elasticity of the marginal productivity of MX with respect to a decrease in the demand for LX is sufficiently high so that a price-induced negative effect on employment in the domestic intermediate good sector is sufficiently large -- that is, labour supply is sufficiently elastic - and if the elasticity of the marginal productivity of MX with respect to a decrease in M` is unit elastic or inelastic, then employment in sector M decreases.'5 If P* falls, the demand for M` increases. This causes the marginal productivity of LU to rise, and thereby the demand for labour in that sector to increase. An increase in the demand for MX also requires the production of M to increase given a and P*, however, and therefore the demand for labour in that sector also increases. So, if I I7 _ (LX/LS)(aP/FMCFML), employment in both sectors increases. An increase in employment in sector Y in turn raises the marginal productivity of MX and thereby causes P to rise. An increase in the stock of capital raises the marginal productivity of LX, thereby attracting labour to that sector. It also raises the marginal productivity of Mx, leading to an increase in the demand for MX. Then, given a, this causes P to rise, in turn attracting labour to that sector. If the labour supply is insufficiently elastic, so that a fall in leisure is not enough to increase in employment in both sectors, then the effect on employment in both sectors is ambiguous. If the labour supply is elastic enough to meet an increase in demand for labour in both sectors, however, then employment in both sectors rises.

The dynamic system can be described by substituting the short-run equilibrium solutions (3a)-(3g) into (1), (2g), and K = I using the market-clearing condition for the domestic intermediate-good market - that is, G(T, L'") M = aMx - and ensuring that the transversality conditions are met. We can rewrite these relations as

= rq - FK[K, MX"(A, a, P*7 K), LX(A, r, P*, K)] (4a)

K H(q) (4b)

b = rb + F[K, MX(A, ao P* K), LX(A, ce, P*, K)] - C(A)

- H(q) - OL4H(q)] - P*(1 - a)[M-(A, a, P* K)] (4c)

lim ertb(t) r lim erq(t)K(t) 0 O. (4d) .-00 t-oo

15 Define the elasticity of labour supply (i), the elasticity of the marginal produLctivity of the intermediate goods with respect to L*(ErML), and the elasticity of the marginal productivity of the intermediate goods with respect to M-(cMM), respectively, as

dLS w A PGL (AFM FaM FM

dw (L LS V,I ML.s a nFMd I4M aL , L h EMM UV <M

If |ql -> (L/ILS)(aP/FMI F(X L) and |c1mM I <_ 1, then La .



436 Tae-Hyung Kim

2. Equilibrium dynamics anid steady state We now examine the characteristics of the dynamics q and K around the steady state, demonstrating that the system is saddle-stable. In the steady state the dynamics cease to operate. Therefore, both capital stock and the market value' of capital remain constant at q and K, where q and K denote the steady-state values of q and K.

We first linearize the system consisting of equations (4a) and (4b) around the steady state, in order to analyse the dynamics of q and K. The dynamics can be determined sequentially.'6 A linear approximation of this pair of equations around (q, K), yields

-[FKK +FKM M + FKLL-k'I 1 [ -i-q (5) [K] H'(4) O ]K -K]

where the determinant of the matrix of coefficients in (5) can be shown to be negative. Therefore, the eigenvalues are, say, ,i < 0, /12 > 0, so that the dynamic is a saddle-poinit.

Noting that while the capital stock always evolves gradually, the market price of capital may jump instantaneously in response to new information. The stable dynamic paths for q and K are q(t) = q + (-a, , /,VI - r)(Ko -K)eIIt and K(t) = K + (Ko-K)e "", where al I I FKK + FKMMK + FKLLK< 017 and K(O)<= Ko. These two equations generate the following stable arm:

q(t)- = (-al I/ /t -r)(K(t) - K). (6)

This equation is negatively sloped because p I - r < 0 and a II < 0. For the determination of the current account dynamics, we linearize (4c) around

the steady state to yield

b r(b - b) - H'(q)(q -q

+ [[FK + FMMK + FLLK P*( - a)Mxk](K-K), (7a)

where ?'(0) 0 O at steady state. Next, substituting q(t) =q + (-a 1 /,- r)(K( - K)e"" and (6) into (7a) yields

b =r(b -b) + Q(Ko- K-)e"'' (7b)

where Q FK + FMMK + FLLK - P*(1 - o)Mk ] + H'(q-)(aI /At' -- r) > 0, which can be shown to be positive if 177 ? (LX /LS)(aP/FM6FML). Using b(O) = bo and (4d), together with (7b), we obtain

bo -b = (Q1,v - r)(Ko -K). (7c)

16 These equations are relevant to dynamics only because the dynamics of K and q affects that of b, but not vice versa. Because the system is recursive, the steady-state stock of traded bonds does not affect the rest of the system.

17 Applying Euler's theorem to Y = F(K,MX, L-), differentiating the identity with respect to K, Mx, and L', having the expressions for FKK, FMM, and FLL, and using these expressions, together with the expressions for MK and LK, we can show a, < 0.




Equation (7c) describes the equilibrium relationship between the change in the equilibrium stock of capital anid the change in the equilibrium stock of traded bonds of the economy. It implies that there is a negative relationship between the change in b and that in K, since Q/,L - r < 0.

The steady-state equilibrium is reached when k = b 0 O. Using (4a)-(4d), we have

q= 1, (8a)

r = FK[K, MX(A, a P*, k), LX(A, a, P*, K)] (8b)

rb + F[K, Mx( a P*, K), L(A, a P* K)]

- C(A) - P*(1- a)[Mx(A, a, P*, K)] 0 (8c)

bo -b = (Q/p, l-r)(Ko - K)- (8d)

These relationships will jointly determine the steady-state values of the stock of capital (K), the shadow value of wealth (A), and the stock of traded bonds (b).18

111. EFFECTS OF AN INCREASE IN CONTENT REQUIREMENT RATIO

1. Long-run analysis The focus is now on the investigation of the steady-state effects of more restrictive content protection policy on the economy. Taking the differentials of the steady- state relationships (8b)-(8d), we have

al a12 a13 1 dK blda

[,a2 a22 a23 dK] d2da

a3l a32 a33- -Ldb b3

where

al I = FKK + FKMMK + FKIJ( <0, al2 - [FKMxM +FKLL-A] >0, a13 0

a21 = [FK + FMMx + F L-K -P*(1 - o)MK] > 0

a22 [FMMA, + FLLA - CA P*(j - o)Mx] > 0, a23 -r > 0

a3l = Q/ I-r < O, a32 O = a33 =-1

-[FKMMX + FKLLx] > 0

b2---[ FMM + FlLLa-P*(1-a)Ma + P*MX] > O, b3 0-.

18 (9a) is obtained from (4b) by letting k = 0 and using 0'(0) = 0 (by assurnption). Letting q = 0, together with (8a), yields (8b). (8a) and (8b) exhibit the steady-state properties of the Tobin's q theory of investment: the steady-state shodow value of investment q is equal to one, and the marginal productivity of capital is equal to the world interest rate. (8c) can be simply obtained by letting b 0 in (4c). (8d) is obtained in the previous section by requiring the economy to meet the transversality condition (4d).



438 Tae-Hyung Kim

The steady-state effects of an increase in ax can be given as

dk/doa (1/A*)lbl CA - a2( P*M)] < 0 (9a)

dA/doa (1/A*) [-b2ai1 + b1(a2l + r(Q/ltI - r))] >0 (9b)

db/da -(1/A*)(Q/bLi - r)(b2a12 - b1a22) > 0, (9c)

where A* -a IIa22+ai2[a2l +r(Q/I,t-r)] > 0,19 (b2a12-b1 a22) <0, -b2a 1 > 0, bL [(Q/,i- r)r + a2l] > 0, and (Q/pi - r) < 0.

Equation (9a) shows that the effect of an increase in ax on the stock of capital consists of two terms. The first term, which can be shown to be negative if l ? (L-/LS)(oP/FMf-FML), implies that an increase in the content requirement ratio decreases the capital stock by reducing the demand for MX and shifting labour in the final-good sector into leisure, thereby lowering the marginal productivity of capital. The second term indicates that there is a positive wealth effect on labour supply (Ls Lx + L) and the employment of MX, meaning that the marginal productivity of capital rises and thereby the capital stock increases. Nevertheless, the former dominates the latter, and therefore the long-run level of capital stock decreases.

Equation (9b) demonstrates that an increase in a from an initial non-zero content requirement ratio raises the shadow value of traded bonds (A). This can be explained as follows. The first term with b2 in brackets includes the term that measures the marginal effect of a higher a on the trade balance - that is, (dY/do - P*dM*I/do) - which can be shown to be negative if 1cMVOjI ? I where fM\a =-(aMX/1ao)/(MX/ao) and M* (1 - o)MX. This implies that the direct effect of a higher ax on the production of the final good and the import of the foreign intermediate good is the improvement of the trade balance, thereby lowering the shadow value of traded bonds. A decrease in the capital stock, however, has an opposing effect on A. The second term with b1 includes the term that measures the marginal effect of the decumulation of capital on Y and M* - (dY/dK-P*dM*/dK) - which can be shown to be positive if 177-1 > (LX /LS)(aP/Fm-F,L). This effect of a decrease in the capital stock on Y and M* is to worsen the trade balance, thereby raising the shadow value of traded bonds. As the latter dominates the former, the shadow value of traded bonds rises, and therefore the stock of bonds rises over time, as indicated in equation (9c).

2. Long-run responses of the allocation of labour supply Defining the supply of labour as Ls = Lx + Lm 1 - 1, we analyse the long-run effects of an increase in ax on the agent's labour supply and the allocation of labour supply between two sectors. Using the results obtained in equations (3d)-(3f) with

19 We can show that A* is positive, because -aj a22 > 0, a12 > 0, and [a21 + r(QI- r)] > 0, where r = FK[k,MX(A, a, P*, K), Lx(A, a, P*, K)] and p2_-rl + H'( I)ajj =0.




respect to ca and combining those with the corresponding results for A and K, we have

d LSl/da = Ls + Ls )+ Ls (aK/la) (IOa)

dL' /da - L-Y + L)2 (a/laa) + LK. (K/laa) (lOb)

dLn-I/da =rLm + L)\m(a/a) -+ L'K (GifK/a). ( Oc)

Equations (1Oa)-(Oc) summarize information on how the labour supply and the sectoral allocation response to the increase in a in the long run. The first term in (1Oa) captures the initial direct effect, which leads to a decrease in labour supply if In! >- (LX/LS)(aP/FMfF,ML) and IECAlM I ' 1.20 The second term indicates the wealth effect induced by a rise in the shadow value of traded bonds, which leads to an increase labour supply. The third term, however, shows that as the capital stock decreases, thereby lowering the real wage over time, the long-run employment in both sectors decreases as a result of a higher a. Turning to the allocation of labour supply between the sectors of the economy, we can see that the long-run labour supply to both sectors decreases in a manner such that the total labour supply in (lOa) responds to a higher a in the long run.21

IV. CONCLUSION

In this paper we have investigated the long-run implications of content protection policy within the intertemporal optimizing framework. With the explicit consideration of the labour-leisure choice, together with incorporation of investment and its adjustment costs, we have focused on the long-run macroeconomic effects on capital accumulation, the cuirrent account, and employment, which have been neglected in the existing literature. Our results have shown that more restrictive content protection policy leads to a lower level of capital stock, an improvement in the current account, and a decrease in employment.

The analysis that we have gone through is subject to some limitations and suggests interesting extensions of our analysis. First, one of the assumptions we have chosen - the complementarity of capital and labour, that is, FKL > 0 - could be relaxed and extended to consider how the substitutability of capital and labour would change the results of this paper. Second, the role of the relative sectoral factor intensities, such as relative capital intensities, in the determination of the direction of the dynamic adjustments of the economy could be investigated in the standard Heckscher-Ohlin set-up. Finally, the introduction of tariff schemes in

20 The initial short-run effects of the first terms in (lOa)-(lOc) are discussed in detail in section 11.1, above.

21 It is worth noting that a wealth effect associated with a term with @a/lax) and an additional substitution effect associated with the decumulation of capital (aK/la) in equations (lOa)-(lOc) were not captured in static models in which they assume balanced trade and abstract from capital accumulation.



440 Tae-Hyung Kim

the intermediate-good sector and the comparison of tariff schemes with content protection would be another interesting extension of our analysis (currently being explored by the author).

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Domestic Content Protection in a Dynamic Small Open Economy