International Trade and Renewable Resource: Endogenous Property Rights

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1 International Trade and eneable esource: Endogenous Proerty ights bstract: This aer examines trade atterns and elfare outcome under endogenous roerty rights The most interesting result is hen facing a loer rice for resource good, the small economy may exort resource good and imort manufacturing That is trade atterns are affected not only by the roerty regime in lace, but also the change of roerty regime With sitch of roerty rights, trade ill alays be benefit to an autarkic enforced economy, hereas the autarkic oen-access economy suffers elfare loss in some secial case Trade sanctions may make things orse Key ords: Endogenous roerty rights; International trade; eneable resource; Proerty rights; Trade sanction 1 Introduction Economists are interested in hether trade causes deletion of reneable resources and immizerisation Many facts have shon there is a relationshi beteen orld resources and trade ccording to Global Forest esource ssessment 005, deforestation continues at an alarmingly high rate-about 13 million hectares er year (F, 006) t the same time, orld forest roducts trade has gron raidly in volume and value fuelled by orld economic groth and falling trade barriers (Zhu et al, 001) With a regression analysis, Ferreira (004) also argues oenness is a significant redictor of deforestation under oen access Nevertheless, several researchers hold oosite vieoint Burgess (1993) has stated that only 6% of total troical roundood roduction enters the international trade, and in addition, timber trade can lead to greater net returns for forestry investment, making sustainable management of forest more attractive than deforestation Loez and Galinato (005) find that trade has no significant effect on forest cover in Indonesia and Malaysia With regards to elfare, the over-exloitation may result in long run elfare losses, hich have been described in Bron (1995) and Loez (1997) Chichilnisky (1993, 1994) and Brander and Taylor (1997a, b, 1998) have formalized this anecdotal evidences and develoed theoretical model to demonstrate that oening of trade can cause over-exloitation and reduce elfare under oen access, hereas the enforced economy alays gains from trade Hannesson (000) and Jinji (006) have extended their basic model from diminishing returns to manufacturing and endogenize the carrying caacity resectively The former concludes that oening u for trade may result in gains from trade even under oen-access diversification, hile the latter shos free trade may increase forest stock in resource-exorting countries 1 ll above aers assume that roerty rights are exogenously and remain unchanged before and after the oening of trade 1 For valuable overvies on trade and reneable resources, see Barbier and Bulte (004) and Bulte and Barbier (005) 1

2 More and more economists, hoever, have emhasized that in any given economy, the roerty rights regimes should be modeled endogenously See Hotte et al, 000; Kar (005), Margolis and Shogren (009) Coeland and Taylor (009) argue olicy analysis based on the assumtion of a fixed degree of roerty rights rotection may lead to serious error In addition, they suggest that securing those rights is the result of a cost-benefit analysis on the art of the rivate oner If there are costs associated ith roerty enclosure, onershi ill be claimed only as long as the benefits from exloitation exceed the costs of enclosure (Hotte, 005) This is the focus of this aer This aer is based on the classical model develoed by Brander and Taylor (1997a, b) We consider the effects of endogenous roerty rights on trade atterns and elfare outcome for a small oen economy n aarently closely related aer is Francis (005), in hich the fixed cost of enforcement is ostulated such that the decision of resources oner is binary: either to enforce the roerty rights erfectly by aying the fixed cost or not to enforce it at all, ie oen access While Francis (005) mainly focuses on the effect of trade on the change of roerty rights, e focus on hat the trade atterns and elfare ill be under the above effect To analyze trade atterns, e give the recise conditions that determine the roerty rights under autarky, hich is not mentioned in Francis (005) lso, e sho the effects of trade interventions The main results are as follos The most striking consequence is that although facing a loer orld rice for the resource good (comarative disadvantage in resource sector), this economy may exort resource good and imort manufactures under endogenous roerty rights The economic logic behind this is a shift of suly function of resources good, triggered by regime sitch, hich is referred to as effects of regime sitch on trade atterns In addition, the choice of regime in autarky is endogenously determined by the cost of enforcing roerty rights L There exists a critical value L, hich is fully deendent on arameters of national characteristic, such that the autarkic economy adots enforcement if 0 L L, hile oen access is referred if L L L Similarly, there also exists a threshold rice, such that it is indifferent beteen the to regimes after trade Furthermore, the autarkic enforced economy must enjoy higher trade elfare even trade induces regime sitching to oen access Conversely, the autarkic oen-access economy may suffer elfare loss after trade even though regime sitches from oen access to enforcement This ell-knon immiserizing effects of resource enforcement ill haen under some secial conditions Finally, trade sanctions such as imort ban or consumers boycott may result in Francis (005) reorts trade atterns and elfare in a secial case here the autarkic rice under oen access and enforcement are the same It ill haen hen the curve of S and S intersect (See Figure 1 and in this aer) This aer, hoever, analyzes the cases here the above to curves doesn t intersect, hich is more general

3 some unexected consequences, hich make things orse lternatively, internalization of external effects from resources may be more effective The remainder of the aer is organized as follos Section sets out basic model Section 3 investigates the endogenous choice of roerty rights regime in autarky Section 4 considers the small oen case Section 5 examines effects of trade sanctions Section 6 contains concluding remarks Basic model 1 esource dynamic Within a given country, the stock of the resource at time t is denoted by S t The natural groth rate of the resource,g, deends on the existing stock The net change in the stock at timet is the natural groth rate, G St minus the harvest rate, H t ds / dt G( S( t)) H ( t) (1) We omit the time argument hereafter s is usual in the revious studies, e assume resource groth is given by a secific functional form of the logistic tye: 1 / G S rs S K () The variable K, referred to as the carrying caacity, is the maximum ossible size for the resource stock The variable r is the intrinsic or uncongested groth rate See Brander and Taylor (1997a) for more discussion about Eq Production and suly The country roduces and consumes to goods H is the harvest from a reneable resource M is some other good, hich e refer to as manufactures Good M is treated as the numeraire hose rice is normalized to 1 side from the stock of the reneable resource S, there is only one additional factor of roduction, labor,l Manufactures are roduced using labor as the only inut Using L M used in manufacturing, e can rite to denote the labor M L M (3) s the rice of good M is 1, it follos that labor's value of marginal roduct in manufacturing is 1 Therefore, the age in manufactures sector must equal 1 if manufactures are roduced n the other hand, the harvest of the resource is carried out according to the Schaefer roduction function, hich is ritten as follos, (4) P H SL H here L H is the amount of labor used in resource harvesting and is a ositive constant, measuring the roductivity of labor, ith suerscrit P denoting roduction Productions in both sectors are carried out by cometitive rofit-maximizing firms 3

4 under free-entry s in Brander and Taylor (1997a), e mainly focus on the analysis of steady state, here the steady state is defined as a situation in hich the resource stock, S, is stationary By definition, the steady state harvest of resource is P H G( S) rs 1 S/ K (5) Combination Eq4 and 5 yields steady state stock S 0 or S K 1 L / r (6) s shon in Brander and Taylor (1997a), a ositive steady state solution exists if and only if r/ L We assume this condition holds throughout the aer With the full emloyment 3 condition, given byl LH LM L, e have H / 1 / P M L L r S K (7) Dividing Eq 5 by Eq 7 allos us to obtain the steady state relative suly of the harvest to manufactures as a function of the steady state stock S : P P H / M [ rs 1 S/ K ]/[ LL r/ 1 S/ K ] (8) In order to kee our analysis from becoming excessively taxonomic, hoever, e focus our attention on economies that are diversified in steady state, hich also imlies 4 that 1/ K Furthermore, as Brander and Taylor (1997a,b) have shon that the ossibility of one country secializing in good H can be ruled out by assuming r/ L, hich is ostulated in resent aer 3 Utility, consumtion and demand Identical households are assumed reresentative household is endoed ith one unit of labor and is assumed to have instantaneous utility given by the folloing Cobb-Douglas utility function: u h m 1, here h and m reresent individual consumtion of goods H and M, resectively Taste arameter is strictly beteen 0 and 1( 0 1 ) Let denote the rice of good H The instantaneous budget constraint is given by hm I, here I is the household s total income, hich includes age income and rents from resources, if any ggregate demands for goods H and M are given by 3 L 0 hen the economy chooses an oen access regime This condition is also adoted in Eq7 and 8 4 More recisely, if 1/ K, then the marginal value roduct of labor in the resource sector, hich cannot exceed K, must less than 1 In this case, labor is orth more in manufacturing (here its marginal value roduct is 1) than in harvesting and no resource good ould be roduced 4

5 D H D IL/, M 1 IL (9) here the suerscrit D indicates variables in the demand side Thus e can rite the relative demand of the harvest good to manufactures as: D D H / M / 1 (10) Furthermore, making use of the indirect utility function, elfare is given by U CIL/ (11) herec 1 1 and is a constant 3 Endogenous choice of roerty rights in autarky 31 To management regimes The folloing analysis is concerned ith one single oner of resources as a reresentative of many identical oners of resources He tries to maximize the steady-state rents from resources Folloing Francis (005) and Jinji (007b), e assume that the roerty rights can be erfectly enforced by hiring a fixed number of orkers, L, here 0 L L Therefore, the decision of resource oner is binary: either to enforce or not to enforce the roerty rights In other ords, the management regime of resources is either rivate roerty rights or oen access In case of enforced roerty rights, rents in resource sector,, are given by H L L (1) H here is the age in resource sector and the suerscrit stands for variables under enforced roerty rights In case of diversification, the age in resource sector must be 1 because of freely mobile labour Maximizing Eq 1 subject to Eq 4 and Eq 6 yields the otimal solution for a given as: / 1/ (13) S K Using Eq 5, Eq 1 and Eq 13, e arrive at the steady-state suly of resource goods and maximized rents under enforced roerty rights: / 1 1 / 4 (14) H r K K K / 1 / 4 r K K L (15) n the other hand, hen the oner of resources decides not to enforce the roerty rights, it means the oen access regime is adoted, hich requires current-eriod rents for the reresentative harvester to be zero This yields / S, here suerscrit 5

6 refers to variables under oen access Under the conditions of diversification and freely mobile labor, the folloing equation is obtained: S 1/ (16) Substituting Eq 16 into Eq 5 gets steady-state roduction of H under oen-access: / 1 1/ (17) H r K The reresentative oner acts to maximize the rents from resources In case of oen access, the rents in resource sector are zero That is, if the regulated resources generate ositive rents, then enforcement is referred therise, oen access is referred 3 Endogenous choice of roerty rights in autarky Differentiating Eq 15 ith resect to yields / 1 1/ K rk /4 Note that 1/ K under diversification Therefore, for any 1/ K that / 0imlying is strictly increasing in Setting 0 in Eq 15 allos us to obtain 5 /, it follos L r L L r L Kr (18) Equating the domestic suly of resource good ith domestic demand gives L / r/ K 1 K 1 / 4 K (19 ) We can then obtain autarkic rice under enforcement regime, the above equation 6 : L r L L rk 1 here 0follos 7, as the solution to (19) r 4r L L 4 L L For any 0 L L, In addition, it holds 8 that both and autarky rice under enforced roerty rights, exceed1/ K, hich imlies that if the, exceeds, then the oner of resources chooses to adot a regulatory regime By contrast, if, it follos 5 Proofs are resented in the endix 6 Proofs are resented in the endix 7 Proofs are resented in the endix 8 Proofs are resented in the endix 6

7 that 0, imlying resource regime ill be oen access Combining Eq18 and Eq19 derive the critical value 9 ofl that makes 4 / L r r L (0) Thus, e have established the folloing result: Proosition 1 Given L r r 4 L /, the choice of roerty rights over resources in autarky is endogenously determined by the cost of enforcing roerty rights, L If L is small such that 0 L L, then the economy is under enforcement therise, if L is high such that L L L, then the economy is under oen access For the roof see the endix B Proosition 1 imlies the roerty rights of resources is entirely endogenous in autarky, not given exogenously as in Brander and Taylor (1997a,1998) and Chichilnisky (1993, 1994) and the cost of enforcing roerty rights lays an determinant role If L is smaller than L, that means the enforced economy generates ositive rents, then enforcement is referred, and vice-versa ccording, e refer to 0 L L and L L Las the lo cost of enforcement and high cost of enforcement case resectively Furthermore, Eq 0 shos the critical value L is entirely determined by the arameters of an economy, hich reresent national characteristic Differences across countries in r,,, L may lead to different L, leading to Corollary 1 Corollary 1 i n increase in, and L ill increase L ii n increase in r ill decrease L For the roof see the endix B With Corollary 1 in hand, it is found that in autarky, an imrovement in harvesting technology may be an effective artifice to manage resources 4 The Small en Economy 41 Endogenous choice of roerty rights in free trade We assume the small country is at initial autarkic steady state, then becomes oen to trade For a small oen economy the orld rice is exogenous and indeendent 9 Proofs are resented in the endix 7

8 of the choice of regime s e have roosed in section 3, for any 1/ K strictly increasing in With the definition of, ie 0 roosition can be given Proosition / Given, is, the folloing r L L r L Kr, the choice of regulation regime for a small oen economy is endogenously determined, hich deends on the divergence beteen and In detail, if, then the oen economy is under enforcement therise, if, then the economy is under oen access Proosition is similar to Proosition 4 in Francis (005) little imrovement is e oint out the critical value of, ie Combination Proosition 1 and shos the resources regime is endogenously determined both in autarky and oening to trade We analyze the model using relative demand and suly constructs because it is very useful for determining trade atterns by looking at the difference beteen its relative suly and demand curve Brander and Taylor (1997b) secify the comarative location of relative suly and demand curves in the case of L 0, in V hich the relative suly in conservationist country is denoted as S given by Eq 7 of their aer Denote the relative suly under enforcement as S, given by Eq 8 V By comarison of exressions beteen S and S, it can be shon that their nominators are the same, hile the denominator of S is strictly smaller than that V V of S as L 0 Thus, given L fixed, the locus S must lie to the right of S locus and is alays uard sloing Furthermore, the relative suly curve under oen access, S, and relative demand curve D kee the same as hat Brander and Taylor (1997b) have shon Figure 1 and illustrates the tyical relative suly and demand curves 10 From Proosition 1, it is useful to consider the case of0 L L (lo cost of 10 Note thats may exceed S 1/ for any rice K, imlying there is no intersection beteen them 1/ for K Hoever, reasonable restrictions on function forms can ensure an intersection as deicted in the diagram Meanhile, the case that S exceeds S 1/ for K is essentially equivalent to those in case of severe overuse, hich ill be discussed in the folloing section ccordingly e exclude the ossibility 8

9 enforcement) and L L L (high cost of enforcement) searately The former corresonds to the case of an autarkic regulated economy Conversely, the latter imlies oen access regime What e are most interesting in is hether and hen the resources regime ill sitch from one to the other, and hat the effects of the sitch on the small economy 4 Lo Cost of Enforcement ( 0 L L ) In this case, the autarkic economy is under enforcement at rice When trade oens, if, then Conversely, if, it is aarent that to different ossibilities arise, and The above three cases ill be discussed one by one 41 Case i : and Caseii : With Proosition, it follos that an enforced regime is referred for the oen economy in casei andii Thus, the resources regime remains the same in autarky and free trade In Figure 1 and, the intersection of the relative demand curve and relative suly curve under enforcement shos the regulated autarky rice of the resource good, In casei, the small oen economy trades at a fixed orld (relative) rice for the resource good in excess of the autarky rice,, then reading off the corresonding quantities on S and D e find that since its relative suly of the resource good to manufactures exceeds its relative demand, it ould exort the resource good and imort manufactures in free trade lternatively, if trade oened at a orld rice belo this country s autarky rice it ould exort manufactures and imort the resource good, hich corresonds to the caseii Conventional isdom of trade theory suggests that in small oen economy case, a higher orld rice for resource good imlies the country has a comarative advantage in the resource good and ill exort this good under free trade Conversely, a loer rice orld rice for resource good means a comarative disadvantage in resource good and ill imort this good Hence case i and ii can be said to suort this conventional isdom 4 Caseiii : Unlike the above to cases, the oening of trade ill change the roerty rights regime from enforcement to oen access as described in Proosition s exlained in Brander and Taylor (1997b), there are to sub-cases, ie severe overuse and mild overuse The former refers to o, hile the latter 9

10 imlies o Fig 1 Trade atterns under endogenous roerty rights in severe overuse o In severe overuse, s shon in Figure 1 ( is denoted as 1 in this case), the relative demand at orld rice, D( 1 ), exceeds the relative suly, S ( 1 ) Therefore, the economy imorts resource good and exorts manufactures in free trade o In mild overuse, if, similar to the exlanation in case of severe overuse, this country imorts resource good and exorts manufactures at the steady state trading equilibrium Figure illustrates this case here is denoted as o lternatively, if, a striking consequence is resented as Lemma 1 Lemma 1 In the case of lo enforced cost, resources regime may sitch from enforcement to oen access after oening trade, hich is a race-to-the-bottom-like result lthough facing a loer orld rice for the resource good (comarative disadvantage in 10

11 resource sector), this economy may exort resource good and imort manufactures, in hich the conventional isdom of trade theory is reversed For the roof see the endix B The striking result oes to a sitch of relative suly function induced by the regime sitch from enforcement to oen access In Figure, the transition of relative o suly function is deicted by the arros t orld rice 3, the regime sitch results in a corresonding change, ie shifting the relative suly out from S ( 3 ) to 3 S ( ), here S ( 3 ) D( 3 ) hile S ( 3 ) D( 3 ), imlying this economy is an exorter of resource good desite aearing to have comarative disadvantage in resource good We refer to this as effects of regime sitch on trade atterns Fig Trade atterns under dynamic roerty rights in mild overuse 43 Welfare Effects With regard to the elfare imlications for trade, Brander and Taylor (1997b) have shon that, in mild overuse, the regulated country gains from trade hereas the oen access country has loer utility from in free trade In severe overuse, both countries enjoy higher steady-state elfare Hoever, all the above conclusions are based on 11

12 the assumtion that roerty rights over resources are fixed in autarky and free trade Proosition 3 describes the general roerties of elfare for an oen economy General means it holds for any cases, no matter hat the cost of enforcement Proosition 3 i If an oen economy is under enforcement, elfare, U, must be decreasing for any feasible rice belo UT has a minimum at, and increasing for any rices above In other ord, ii If an oen economy is under oen access, elfare, U,must be decreasing for any feasible rice above1/ K iii The elfare function of an oen economy must be continuous at any rice 1/ K For the roof see the endix B T T Fig 3 Steady-state utility for an autarkic enforced economy 1

13 By Proosition 3, e obtain figure 3 The flat line labeledu reresents the steady-state utility of an autarkic enforced economy The other line reresents steady-state level of utility under free trade as a function of the orld rice of resource good for this economy The rices1/ K,, marked on the horizontal axis are ivotal rices for this case When oening for trade, orld rices less than ould lead the small country to sitch from enforcement to oen access With case ii of Proosition 3 in hand, the steady-state utility must be monotonically falling for any rice in the range of1/ K and t orld rice above, caseiof Proosition 3 is valid In this range, steady-state utility is U-shaed and minimizes steady-state utility case iii of Proosition 3 ensures the continuity of elfare function Figure 3 shos that the oening of trade must imrove its elfare, even though roerty rights regime sitches to oen access after trade Note that this result can not be regarded as the case of trade creates standards gains described in Brander and Taylor (1997b) since roerty rights regime are different, although the elfare imlications for trade in this aer are the same as those in their aer lthough suorting the vieoint such as unrestricted trade imoses loer standards (Daly, 1993), our model suggests that this regime sitch can not be regarded as an excuse to restrict free trade, since trade alays imrove elfare in above case To some extent, anti-free-trade environmentalists have aid excessive attention to the negative effects of trade on environment We no consider the case in hich the small country has a high cost of enforcement 43 High Cost of Enforcement ( L L L) 431 Trade Patterns In this case, the autarkic economy is under oen access at rice We do not examine the case here, imlying the economy adots oen-access regime before and after oening of trade, since it has been analyzed by Brander and Taylor (1997a) If, free trade induces regime a shift in regime aay from oen access to a regulatory regime and e have Similarly to the discussion in 4, 13

14 in the mild overuse case, it holds that, hich is denoted as 4 in Figure It shos that the relative suly at orld rice, S ( 4 ), exceeds the relative demand, D( 4 ) Therefore, the economy exorts resource good and imorts manufactures in free trade lternatively, in the severe overuse case, o if (corresonding to 5 in Figure 1), similar to the analysis in case of mild overuse, this country exorts resource good and imorts manufactures at the steady state trading equilibrium n the contrary, if, a striking o counterintuitive consequence is resented as Lemma Lemma In the case of high enforced cost, resources regime may sitch from oen access to enforcement after oening trade, hich is a race-to-the-to-like result lthough facing a loer orld rice for the resource good (comarative disadvantage in resource sector), this economy may exort resource good and imort manufactures, in hich the conventional isdom of trade theory is overturned Furthermore, as long as trade induces a sitch of regime under high cost of enforcement, the economy must be an exorter of resource good For the roof see the endix B s described in 4, this counterintuitive result due to a shift in relative suly function aay from S to S, induced by regime sitch, hich is called as effects of regime sitch on trade atterns again Lemma 1 and Lemma are summarized by Proosition 4 Proosition 4 lthough facing a loer orld rice for the resource good (comarative disadvantage in resource sector), this economy may exort resource good and imort manufactures no matter hat the regime is in autarky, thus the conventional isdom of trade theory is reserved In other ords, trade atterns are affected not only by the roerty regime in lace, but also the change of roerty regime 43 Welfare Effects of Trade Liberalization It is useful to consider the case of and In the former case, by Proosition 3, hen orld rices are ranged from1/ K to, the small oen economy is under oen access thus the steady-state utility must be monotonically falling dditionally, for rices above, this economy adots enforced regime and trading elfare is monotonically increasing, hich ensures that there exists a threshold rice, such that steady-state utility in free trade exceeds that in autarky 14

15 for See Figure 4 Moreover, this economy ould suffer elfare loss for orld rices located beteen other ranges and, hile enjoy higher trade elfare for rices in Fig 4 Steady-state utility for an autarkic oen-access economy ( ) The elfare effects of trade in the case of can be established by similar analysis as illustrated by Figure 5 Like the case of, the utility locus has a U shae and reaches the minimum at Hoever, in the case of, the autarkic oen-access economy must gains from trade for any orld rices above1/ K To summarize, elfare effects of trade are ambiguous for an autarkic oen-access economy Even though regime ould sitch from oen access to enforcement, gains from trade can not be guaranteed, either, hich is ell knon as immiserizing effects of resource enforcement in Hannesson (000), Hotte et al (000) and Emami 15

16 and Johnston (000) Furthermore, it is demonstrated that this immiserizing effects ould haen only hen orld rice for resource good is in the range of the case of and in Fig 5 Steady-state utility for an autarkic oen-access economy ( ) 5 Trade sanctions and olicy imlications Trade sanctions may be in the form of imort ban on resource good exloiting from ill-managed resources or consumers voluntary boycott of those good Similar to Jinji (006), e consider trade sanctions as an instantaneous decrease on the orld rice of resource good, and assume that the small oen economy is in a trading steady state The folloing roosition describes the effects of trade sanctions Proosition 5 Suose a small oen economy is initially in a trading steady-state equilibrium, a trade sanction may result in i a sitch of regime over resources from enforcement to oen access, ii a transition of trade atterns from imorter to exorter or 16

17 vice-versa, iiia loer trade elfare relative to that ithout sanctions, and iva smaller resource stock and a higher outut of resource good For the roof see the endix B Proosition 5 states trade sanctions are not alays effective tools of resource management, hile they can even make things orse, in the sense that the inefficient exloitation and overuse increase, hich is the oosite of hat the initial goal of olicy instrument itself Moreover, it can be said to suort the vie ut by some researchers, eg Vincent (1990), ho declares 11 that Don t boycott troical timber It is orth noting that an outcome identical to that arises ith trade sanctions might occur if external benefits of resources could not be fully internalized, ie, the rice of resource good is underestimated To see this, according to Proosition 5, the underestimated rice may induce the oen economy adots oen access regime, hereas it might choose enforced regime if these externalities are fully internalized Without loss of generality, e refer to resources as forests Usually, forests rovides various non-commercial values, such as carbon sinks, biodiversity and ater-retention services, hich do not enter into the decision of rivate due to market failure, thus making a distinction beteen the rivate and social returns of forests esearchers have long been aare of the lack of roerty rights and externalities are to main reasons for excessive deforestation Secure roerty rights could be established and enforced to eliminate the oen access roblem Even hen roerty rights are established, forested lands rovide external benefits that do not accrue to the oner, government forester, or other decision maker (von msberg, 1998) What e find, hoever, is externalities of resources increase the likelihood of oen access That imlies externalities have dual effects on resource deletion The first one is direct effect, ie the undervalued rice of resource causes excessive conversion from forest land to others use, see Barbier and Burgess (1997) The second is indirect effect, ie externalities increase the likelihood of oen access and exacerbate the common-roerty issue Furthermore, the above sights exlains to some extent hy develoing countries here externalities of resources are not or not fully internalized, tend to adot oenaccess regime, hereas develoed countries exhibit oosite tendencies in the real orld 1 With regards to olicy interventions, Chichilnisky (1994) oints out roerty-rights olicies may be more effective Given the above discussion, e further suggest that internalization of external effects from resources may be an effective instrument to enforce roerty rights and mitigate the common-roerty issue 6 Concluding remarks This aer has examined atterns of trade and elfare outcome for a small oen economy ith endogenous and dynamic roerty rights The threshold 11 Vincent (1990) argues that an imort ban ould reduce the rofitability of forestry and hence encourage the conversion of forestlands to other uses This aer, hoever, shos an imort ban may cause regime sitch to oen access such that resources stock decreases Hence, e have different economic logics 1 For data on the states of resource management standards in develoing and develoed countries, see table 1in Jinji (007a) 17

18 value, L and, are obtained to endogenously determine the roerty rights in autarky and free trade, resectively Then, a surrising conclusion that defies common isdom comes out, i e hen facing a loer orld rice for resources, the small country may exort resource good and imort manufacturing, resulting from a shift in the suly function of resources good induced by regime sitch, hich is referred to as effects of regime sitch on trade atterns The elfare effects of trade are notably different The autarkic enforced economy alays enjoys higher elfare regardless of trader atterns For the autarkic oen-access economy, hoever, gains from trade can not be ensured, thus the immiserizing effects of resource enforcement ould haen under certain conditions In addition, trade sanctions hich are rimarily aimed at rotecting resources may cause orse consequences, hereas internalization of the external effects from resources may be more effective There are some additional lines of research that could be ursed The starting oint of this aer focuses on the small oen economy natural extension is to consider a to-country model ith endogenous orld rice ecalling that L lays an imortant role in determining roerty rights in autarky and free trade, hence some interesting results may be obtained if e consider a to-country model ith different L Moreover, the set-u of fixed enforcing cost simlifies the roblem and avoids unnecessary comlications since it makes the choice of regime binary: either enforcement or oen access Hoever, Francis (005) argues that the cost of regulating the resource ould be linked to the level of harvesting efforts Meanhile Hotte et al (000) models this cost as an increasing function in the enforcement level Therefore, it ill be more general to allo intermediate levels of roerty rights and a variable enforcing cost such that different levels of roerty rights can haen simultaneously in one country, hich is more realistic These interesting issues seem to arrant further research endix : Proof for section 3 Proof for the value of and 1/ K Setting Eq 15 equal to zero yields to roots 1 r L L r L / Kr, r L L r L / Kr It can be roved that K hile K that 1/ K r/ Kr 1 1/ 1/ To verify this, recalling, therefore the relationshi of 1 and 1/ K is identical to 18

19 comare L L r L and zero Square oeration shos that L L r L L r L , imlying L L rl 0and K 1 1/ Moreover, K follos by arallel reasoning Note that 1/ K 1/ diversification Hence Proof of 0, the value of and 1/ K under Eq 19 also has to roots 3 r L L, rk 1 4 r L L rk 1, here r 4r L L 4 L L We no rove 0 for any 0 L L Think of the exression of as a function of L, and rerite it after some maniulations as follos f ( L ) L BL Z, here 4 0, B 4 r 8 L, Z r r L L 4 4 The quadratic function ( ) f L has a minimum at L B/ L r/ minimal value is f( L ) r 1 any 0 L L, here the Note that 0 1, thus 0 for Then e rove that 3, not 4, is the autarkic rice under enforcement regime, since 3 0hile 4 0 To see this, define V r L L, thus e have V r 4r L L 4 L L The unique difference beteen V and is the first term of their exressions Since0 1, it follos thatv Furthermore, V holds no matter hat V is ositive or negative Thus the nominator of 3 and 4 is negative and ositive, searately, hile their same denominators are negative due to 0 1 Therefore, 3 0 hereas 4 0, 19

20 imlying must be 3 Finally, e rove 3, ie exceed 1/ K Differentiating ith resect to L yields V 1 L rk 1 ecalling that V and 0 1, thus / L 0, imlying is strictly decreasing in L Setting L L obtains 1/ Therefore, L must exceed 1/ K L K feasible L 0, L since is monotonically decreasing in L Proof for the value of L and 0 L L Setting L in Eq 18 equal to L in Eq 19 yields to roots 4 /, L r r 4 L / L r r L 1 1 It can be readily seen that L 0 hile L 0 We no rove L L / for any Thus the critical value L must be L 1 L L M N, here M r L, N r 4L M N r L rl r L L L r ecalling that M 0 and N 0, thus M N and L L endix B: Proofs of Proositions Proof of Proosition 1 of It can be directly seen from Eq 18 that L is a strictly increasing function L, hile L is a strictly decreasing function of holds for any L above Given L L L, hile L L, thus for L L L, it follos that L Hence L L holds for any L above L, hich imlies the autarkic economy must adot oen access regime Similarly, for 0 L L, it follos that imlying enforcement regime is referred Proof of Corollary 1 0

21 It can be directly obtained thatl is a monotonically increasing function in and L The comarative steady-state effects of changes in r, and r/ Lare slightly more subtle Note that r r 4L, thus e have L / r 1 r/ r 4 L / 0 L / r r/ r 4 L 1 / 0 Caseiii follos by Proosition 1 Proof of Lemma 1 The roof is simle and illustrated in Figure, here is denoted as 3 In the o case of 3 under mild overuse, the relative suly at orld rice, S ( 3 ), exceeds the relative demand, D( 3 ) Therefore, the economy exorts resource good and imorts manufactures in free trade Proof of Proosition 3 i By Eq 11 and 15, under enforcement, elfare function for an oen economy is /, here / 1 / 4 U C L T In section 3, e have calculated r K K L / 1 1/ K rk /4 With this derivative in hand, differentiating UT ith resect to, and doing some maniulations yields 1 1 4K K r K r L L r U / (B1) T Setting the nominator of Eq B1 equal to zero yields to roots: r L L r L L 1, rk 1 rk 1, here r 4r L L 4 L L eferring back to endix, it can be found that 1 3, 4, and 0 Hence, Eq B1 can be reritten as: 1

22 1 4 4K K r U / (B) T ecalling that 4 0 and 0 1, for any feasible rice, if, UT / 0holds Conversely, if, UT / 0holds ThusUT must be decreasing for any feasible rice belo imlying minimizesu T ii This case is similar to the case of r/ L, and increasing for any rices above, described in Brander and Taylor (1997a) See age 548 and Figure 5 in their aer for more detailed exlanation iii The only ossible discontinuous oint is at since elfare function changes at / this oint Welfare function under to regimes is U C L and / searately t, 0, thus U U U CL Proof of Lemma The roof is simle and illustrated in Figure 1, here is denoted as 6 In the o case of 6 under severe overuse, the relative suly at orld rice, S ( 6 ), exceeds the relative demand, D( 6 ) Therefore, the economy exorts resource good and imorts manufactures in free trade desite aearing to have comarative disadvantage in resource good To summarize the analysis in the other cases under high cost of enforcement (see aragrah above Lemma ), it can be found that as long as regime sitched after trade under high enforcing cost, this country must be an exorter of resource good and imorter of manufacturing Proof of Proosition 5 Consider the case of lo cost of enforcement and assume the roerty rights are enforced in the initially trading steady state Let ' be the orld rice for resource good after the rice falls caused by trade sanctions If ', then the economy shifts to the oen-access regime Caseii and iii can be simly roved as described in section 4 For the roof of caseiv, Proosition 1 in Jinji (007b) is valid

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