Phelps Centre for the Study of Government and Business. Working Paper

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1 Pelps Centre for te Study of Government and Business Working Paper Strategic Use of Recycled Content Standards under International Duopoly Keikasaku Higasida Faculty of Economics, Fukusima University and Naoto Jinji Faculty of Economics, Hitotsubasi University Pelps Centre for te Study of Government and Business Sauder Scool of Business University of Britis Columbia 2053 Main Mall Vancouver, BC V6T 1Z2 Tel : or pelps_centre@sauder.ubc.ca Web: ttp://csgb.ubc.ca/

2 Strategic Use of Recycled Content Standards under International Duopoly Keisaku Higasida Faculty of Economics, Fukusima University, 1 Kanayagawa, Fukusima, , Japan; Naoto Jinji Faculty of Economics, Hitotsubasi University, 2-1 Naka, Kunitaci, Tokyo, , Japan. We would like to tank Smeet Glati, Miciiro Oyama, Kimiaki Sinozaki, Yoici Sugita, Makoto Tawada, and seminar participants at Hitotsubasi University, te University of Britis Columbia, and te 2003 Fall meeting of te Japanese Economic Association for elpful comments and discussions. Comments and suggestions from two anonymous referees elped to improve te paper significantly. Keisaku Higasida also tanks te HSBC Cair in International Business for financial support, and Strategy and Business Economics Division, te Sauder Scool of Business, at te University of Britis Columbia for teir ospitality wile writing tis paper. Naoto Jinji gratefully acknowledges financial support from te Japan Society for te Promotion of Science under a Grant-in-Aid for Young Scientists (B). Any remaining errors are our own. Corresponding autor. 1 Kanayagawa, Fukusima, , Japan. Tel & Fax: e038@ipc.fukusima-u.ac.jp. 1

3 Title: Strategic Use of Recycled Content Standards under International Duopoly Abstract: We examine te strategic use of recycled content standards (RCSs) under international duopoly. RCSs require firms supplying te domestic market to use a certain proportion of recycled materials as inputs. We demonstrate tat, wen tere is no trade in recycled materials, two identical countries bot set strategically stricter or more lax RCSs. However, wen tere is trade in recycled materials, it may be te case tat one country sets a stricter RCS wile te oter sets a more lax RCS. Wen a world supply constraint on recycled materials is not binding, te main source of te asymmetric distortion in RCSs is a demand effect for recycled materials. Keywords: recycling; recycled content standard; international trade; strategic trade policy. JEL classification: F12; F13; F18. 2

4 1 Introduction In recent years, many countries ave experienced substantial increases in recycling, partly because governments ave implemented policies to encourage recycling. However, since firms tend to be reluctant to use recycled materials, governments ave recognized te need for policy measures tat stimulate demand for recycled materials. Te imposition of recycled content standards (RCSs) is suc a policy. RCSs require tat a particular consumption good sold in te domestic market contains a certain percentage of recycled material. For example, in te United States (US), 12 states and Wasington DC enforce mandatory RCSs on newsprint as of Te strictest standards are adopted by California, Connecticut, and Missouri, wic require newsprint to contain at least 50% of recycled paper. Green procurement requirements are also a similar policy tool. For example, in te US, more tan 40 states ave State Paper Procurement Laws, wic require a certain percentage of paper purcased by state agencies to be recycled. In many cases, qualification standards for recycled paper, suc as te requirement for at least 50% recycled content, are also specified in tese laws. Anoter example is te Law on Promoting Green Purcasing, wic became effective in Japan in April Tis law requires te public sector to buy products tat contain a certain percentage of recycled materials or recyclable products. A wide variety of products are covered by te Law, including stationery, office furniture, office automation macines, ome electronic appliances, and 1 See te web site of American Forest & Paper Association (AF&PA) at ttp:// Tirteen oter states ave also implemented voluntary RCSs on newsprint. See also Laplante and Luckert [16]. 2 Te formal name is te Law Concerning te Promotion of Procurement of Eco-Friendly Goods and Services by te State and Oter Entities. For details, see ttp:// (Ministry of te Environment). 3

5 veicles. 3 Since public consumption expenditure accounts for at least 17% of GDP in Japan, te effect of te Law could be substantial. 4 Wile RCSs and green procurements are primarily aimed at reducing domestic waste by stimulating domestic demand for recycled materials, tey may ave some additional effects if consumption goods and/or recycled materials are internationally traded. Indeed, te volume of recycled materials, including paper, aluminum, copper, and zinc, wic are internationally traded, is growing (van Beukering [21]). For example, Canada produced 8.5 million tons of newsprint in 2002, 62% of wic was exported to te US. Te sare of Canadian producers in te US newsprint market was 49% in At te same time, Canada used 5.1 million tons of recyclable paper in 2002, 33% of wic was imported, mainly from te US. Te US recovered 47.6 million tons of paper and board from domestic sources in 2002, 24% of wic was exported. 5 Tus, RCSs on newsprint and State Paper Procurement Laws in te US affect Canadian firms as well as US firms. Canadian newsprint producers import recyclable paper from te US in order to comply wit RCSs in te US (Laplante and Luckert [16]). 6 Tis paper investigates te coice of RCSs were tere is trade in goods and recycled 3 Example of te standards set by te Law are: (i) at least 10% recycled content from used polyetylene tereptalate (PET) bottles must be used for carpets and curtains; and (ii) 100% recycled content must be used for printing paper. 4 Te sare was calculated from 2003 data, using OECD national account statistics. 5 Te Canadian data on newsprint were obtained from te Forest Products Association of Canada and te data on recyclable paper were taken from te Paper Recycling Association of Canada. Te US data on te newsprint market were obtained from FAOSTAT, te database provided by te Food and Agriculture Organization of te United Nations (FAO), and te data on recyclable paper were from AF&PA. 6 Japanese exports of recyclable paper and board are also increasing significantly. In 2003, Japan exported 1.97 million tons of used paper and board, 52% of wic was exported to Cina. Tese data are taken from trade statistics provided by te Customs and Tariff Bureau, Ministry of Finance, Japan (ttp:// e.tm). As far as old newspaper is concerned, 0.36 million tons were exported, wic is almost 10 % of total newspaper consumption. 4

6 materials. In particular, we are interested in te strategic aspects of RCSs. As already mentioned, wen goods and/or recycled materials are traded, governments may ave an incentive to use RCSs for reasons oter tan encouraging te domestic use of recycled materials. 7 We analyze te conditions under wic RCSs are distorted, relative to te RCSs tat maximize global welfare. Te strategic use of environmental policy as been examined by, e.g., Barrett [1], Kennedy [13], and Ulp [20]. Existing studies ave examined ow environmental policies, suc as emission taxes and standards, are distorted for strategic purpose wen tere is trade. Te strategic effects identified in previous studies include a rent capture effect and a pollution sifting effect. Tese effects are typically observed wen market structures are imperfectly competitive. Tese strategic effects motivate governments to distort environmental policy, in relation to policies tat fully internalize te externality. Our study relates to te literature on strategic environmental policy. Unlike existing studies, we examine te strategic aspects of policies tat are designed to affect consumption stages; existing studies ave mainly focused on policies aimed at affecting production stages. Unlike existing studies, a demand effect for recycled materials and a terms-of-trade effect are important in our analysis. Te former effect arises if, wen trade in recycled materials takes place, a country tat exports recycled materials may be able to increase not only te domestic firm s demand but also te foreign firm s demand for recycled materials generated in its own country by canging its RCS. An importing country of recycled materials, by contrast, may only increase its import demand for recycled mate- 7 Tis analysis can also be applied to interstate (interprovincial, interprefectural) trade in recycled materials. 5

7 rials by raising its RCS. Terefore, countries exporting and importing recycled materials may experience asymmetric effects on waste reduction, and accordingly, environmental damage. Te latter effect, wic is similar to te usual one under international trade, stems from trade in recycled materials. Tat is, an increase in te international price of recycled materials benefits te county tat exports recycled materials. In tis paper, we focus on te former effect and briefly discuss te latter effect. We do so for tree main reasons. First, te purpose of setting RCSs is to encourage te use of recycled materials. In oter words, tis type of policy is used to eliminate an excess supply (surplus) of recycled materials. Te demand effect for recycled materials is important in tis case. In practice, some countries ave often ad surpluses of recycled materials. 8 Second, in te absence of artificial trade barriers, no trade in recycled materials takes place only if supply constraints are not binding in eiter country. Tus, a clear-cut comparison can be made between trade and absence of trade in recycled materials wen at least one country as an excess supply of recycled materials. Tird, oter studies ave analyzed te terms-of-trade effect in a similar framework (e.g., Cassing and Kun [2]). Moreover, wile te terms-of-trade effect is important in te context of trade and te environment, it is not an effect tat is specific to environmental issues. To analyze te effect tat is specific to tis issue, we assume tat te two countries are identical except wit respect to te supply of recycled materials. A number of factors, suc as market scale and capacity constraints, potentially make te supply of recycled 8 For example, tere was an excess supply of used paper trougout te 1990s in Japan and in te early 1990s in te US. In te US, te success of recycling collection programs produced and excess supply, wic led to RCSs on newsprint (See Jacques et al. [12]). Moreover, te number of recovered PET bottles as always exceeded tat of recycled PET bottles (See te web site of te Japan Containers and Packaging Recycling Association at ttp:// 6

8 materials differ between countries. One is differences in recovery rates. Table 1 sows recovery rates for aluminum beverage cans and paper in selected countries in Te table sows wide diversities in recovery rates for bot materials. Similar differences are observed for oter materials. Since differences in recovery rates can generate trade in recycled materials in a straigtforward way, we incorporate tese differences to our analysis. We first consider te case in wic tere is no trade in recycled materials and ten consider te one in wic tere is trade in recycled materials. Te main results are as follows. First, if governments set teir RCSs noncooperatively, te RCSs may be stricter or more lax tan is required to maximize global welfare. Tis depends on te structure of demand, price differences between virgin and recycled materials, and te sape of te environmental damage function. Second, wile te RCSs in te two countries are distorted in te same direction wen tere is no trade in recycled materials, tey may be distorted in opposite directions wen tere is trade in recycled materials. Tat is, it may be te case tat te country exporting recycled materials imposes a stricter RCS and te importing country imposes a more lax RCS tan tose tat would be imposed under cooperation, or vice versa. A demand effect for recycled materials is a major source of asymmetric distortion in RCSs wen te world supply constraint for recycled materials is not binding. Tere are few teoretical studies of recycling and trade. Examples include Di Vita [3], van Beukering [21], and Hutala and Samakovlis [9], none of wic as examined te strategic use of RCSs. Our study is also related to te literature on local content requirements (LCRs) (e.g., Grossman [8], Krisna and Ito [14], and Ricardson [18]). LCRs require firms to use a certain proportion of locally made intermediate inputs. 7

9 RCSs differ from LCRs because RCSs do not specify from were te required types of intermediate inputs sould be procured. Tus, findings relating to LCRs do not necessarily apply to RCSs. Te rest of te paper is organized as follows. Section 2 describes te model. Section 3 examines te conditions under wic governments ave incentives to use RCSs strategically wen tere is no trade in recycled materials. Section 4 investigates te case in wic trade in recycled materials takes place. Section 5 provides concluding remarks. 2 Te Model Tere are two countries tat are identical in all respects except te supply of recycled materials. Te ome country is denoted by and te foreign country is denoted by f. One firm is located in eac country and produces a omogeneous good X. Te inverse demand function in eac country is given by p i = P [X i ], P < 0, for i =, f, (1) were p i and X i denote te consumer price and te total consumption of good X in country i, respectively. 9 Trougout tis paper, square brackets apply to functions. Eac firm uses one unit of material to produce one unit of good X. Material can be virgin, recycled, or a mixture of te two. Eac country imports te virgin material from te rest of te world. Te world price of te virgin material is fixed at w V We assume tat te price of good X is independent of ow muc recycled material is included in good X. Allowing price to depend on te proportion of recycled material included in te good is straigtforward, and altoug tis extension increases te number of conditions required to derive our main results, tose results are not greatly affected. 10 In reality, most virgin materials are exaustible. However, since we are focusing on waste rater tan on exaustible resources, for simplicity, we assume a constant price of virgin materials. 8

10 Te recycled material is only supplied witin te two countries. One unit of recycled material is produced from one unit of wasted good X. 11 It is assumed tat recycled materials are supplied under perfect competition. Te price of recycled material in eac country is denoted by w i R, i =, f. It is costly to recycle materials from waste goods. We assume tat a constant marginal cost of recycling, wic is denoted by c R (= c i R, i =, f). We also assume tat transportation costs are zero. Wen a supply constraint for recycled materials is not binding in country i, w i R = c i R olds. Moreover, no trade in recycled materials takes place only if supply constraints are not binding in eiter country. 12 Tus, w R = w f R w R olds weter or not tere is trade in recycled materials. We also assume tat w V < c R w R olds. Tus, unless it is compulsory to use recycled materials, firms ave no incentives to use tem. Let MC j i be firm j s marginal cost for supplying to country i s market. We ave MC i i = MC j i = µ i w R + (1 µ i )w V, i, j =, f, (2) were µ i [0, 1] denotes te RCS set by country i. Since te general aim of RCSs is to ensure tat goods consumed in te domestic market contain a certain percentage of recycled materials, te marginal costs differ not in production country but in consumption country. Te profit function of firm j is π j = P [X j ]x j j + P [X i ]x j i µ j w R + (1 µ j )w V } x j j, µ i w R + (1 µ i )w V } x j i, i, j =, f, (3) were x j i is te output of firm j for te market in country i and X i = x j i + x i i. 11 In practice, it is impossible to produce one unit of recycled material from one unit of a wasted good X in terms of material balance. For example, producers must remove te ink from used paper to produce re-usable paper. However, our results do not depend on tis assumption, wic is made only for simplicity. 12 Tis is sown in Appendix B. 9

11 Once consumed, units of good X are wasted. If tey are not recycled, tey are disposed of in landfills. Due to te depletion of landfill capacity or to externalities generated by landfills, wasted goods tat are not recycled cause environmental damage. Good X, wic is wasted at time t 1, is recycled to be used as recycled material at time t. Tus, te supply of recycled material at time t cannot exceed λ i X i,t 1, were λ i [0, 1] denotes te recovery rate in country i. We focus on te steady-state equilibrium, in wic X i,t 1 = X i,t = X i. 13 Te supply of recycled materials is λ i X i in eac period. Te demand for te recycled material in country i is given by µ i x i i + µ j x i j. Even if demand exceeds supply, (1 λ i )X i cannot be recovered and tis quantity is disposed of in landfills. Since we assume tat recovered material is not preserved for future periods, some proportion of λ i X i is also disposed of if supply exceeds demand. 14 Environmental damage experienced by citizens in country i is a function of te actually wasted goods in country i. Wen te supply constraint is not binding in country i, environmental damage is given by te following: 15 E i = E i [X i D i i[µ, µ f ] D j i [µ, µ f ]], i, j =, f, i j, (4) 13 Given te RCSs of bot countries, differences between demand and supply are quickly eliminated because prices for recycled materials cange daily. However, it usually takes time for recovery rates to cange because tis typically requires te beavior of consumers and production and consumption systems to cange. Te time lag between primary production and recycling may also affect firms outputs and profits (Gaudt and Long [7]). However, since our purpose is to examine te strategic use of RCSs given te time lag in recycling, we focus on te steady state and ignore dynamic processes. In fact, articles tat examine policies related to recycling often focus on te steady state (e.g., Eicner and Petig [5]). 14 We do not consider transportation costs. In practice, it is costly to preserve recycled materials. Tus, from bot teoretical and practical points of view, firms ave no incentives to preserve materials for future periods if world supply exceeds world demand. Even if te price of recycled materials canges due to excess demand or supply, firms do not stock recycled materials if it is costly to do so. 15 We implicitly make te following two assumptions. First, recycling causes no environmental damage. Second, for simplicity, environmental damage is measured in money terms. 10

12 were D j i denotes te demand by firm j for te recycled materials generated in country i. We assume tat E i > 0 and E i > However, if te demand for recycled materials generated in country i exceeds te supply of recycled materials in country i, environmental damage is given by E i = E i [(1 λ i )X i ], i =, f. (5) Te government of country i sets its RCS to maximize social welfare, wic is defined as te sum of consumers surplus (CS), te profit of firm i, and te producers surplus (P S) for te suppliers of recycled materials, minus te environmental damage suffered by country i, as follows: W i = Xi 0 P [y]dy P [X i ]X i + π i + (w R c R )λ i X i E i, for i =, f. (6) Note tat te P S for te suppliers of recycled materials is zero wen w R = c R. Moreover, world welfare, W, is given by W = W + W f. (7) Te structure of te two-stage game is as follows. In te first stage, bot governments simultaneously set teir own RCSs. In te second stage, bot firms simultaneously determine teir outputs. Tey compete in quantities in Cournot fasion. Te solution is te subgame perfect Nas equilibrium (SPNE). 16 We exclude te possibility tat E i = 0. Its inclusion would only add te case of RCSs being strategic neutral in Lemma 1. Tis case is of no interest in te context of te strategic effects of RCSs. 11

13 3 RCSs in te Absence of Trade in Recycled Materials In tis section, we examine te case were tere is an excess supply of recycled materials in eac country. In tis case, it is reasonable to assume tat eac firm procures recycled materials from its own country, since it would pay additional costs to procure tem from abroad. 17 Tus, tere is no trade in recycled materials, and w R = c R in eac country. 18 Altoug we focus on te ome RCS, te same results apply for te foreign RCS. 3.1 Effects of RCSs We first examine te effects of RCSs on CS, firms profits, and environmental damage. From (3), te first-order condition (FOC) for maximizing profits is given by π j x j = P + P x j µ w R (1 µ )w V = 0, j =, f (8) were P i = P [X i ] and P i = P [X i ]. We obtain te equilibrium outputs for eac specified level of µ, wic are denoted by ˆx [µ ] and ˆx f [µ ]. Totally differentiating (8) yields dˆx / dˆx f /dµ = 1 Ω 2P + P ˆx f (P + P ˆx ) (P + P ˆx f ) 2P + P ˆx w R w V w R w V were Ω = P 2 ( ), in wic ɛ X P [X ]/P [X ] denotes te elasticity of te slope of te inverse demand function. We assume tat te second-order conditions (SOCs) for stability old: i.e., 2P + P x < 0, 2P + P x f < 0, and P 2 ( ) > For example, a firm must pay an additional fixed cost to collect information. 18 See Appendix A for possible combinations of te two RCSs under wic tere is no trade in recycled materials. 19 It is well known tat ɛ often plays a crucial role in te analysis of monopoly and oligopoly (Seade [19], Isikawa and Spencer [10], and Furusawa et al. [6]). Wen ɛ is constant, te inverse demand function is P = a 1 X 1 ɛ /(ɛ 1) + a 2 for ɛ 1, and is P = b 1 ln X + b 2 for ɛ = 1, were a i, b i > 0, i = 1, 2. If te price elasticity is constant, ɛ is also constant. Wen ɛ < 0 (resp. ɛ = 0, ɛ > 0), te inverse demand curve is concave (resp. linear, convex). In general, te demand 12

14 Te effects of a cange in µ on firm outputs are given by dˆx j = w R w V P ( ) < 0, j =, f. (9) Since te outputs of bot firms fall, te price of good X rises and ome CS decreases. Furtermore, using te envelope teorem, from (3), (8), and (9), we obtain dπ j = P ˆx j dˆx i (w R w V )ˆx j = 2 ɛ (w R w V )ˆx j (10) for i, j =, f, i j. It is clear tat weter a cange in µ increases or decreases profits depends on te demand structure. Since w R w V > 0, if ɛ < 2 (resp. ɛ > 2), profits fall (resp. rise) wen µ increases. In oter words, if te demand curve is igly convex, firms profits increase as te RCS becomes stricter. Next, consider environmental damage in te ome country. Since D j i = 0 and D i i = µ i x i i + µ j x i j, from (4), we obtain de d = E ˆX ˆx dˆx } } µ = E (1 µ ) dˆx + dˆxf ˆx < 0. (11) Tis follows because µ [0, 1], E > 0, and dˆx / = dˆx f / < 0. Tus, environmental damage in te ome country decreases as µ becomes stricter. Te effect of an increase in µ on E can be decomposed into two effects. First, since an increase in µ reduces te output of bot firms in te ome country, te supply of wasted goods in te ome country also falls. Tis effect is represented by d ˆX / = dˆx / +dˆx f / < 0 in (11). Second, an increase in µ canges firm s demand for recycled materials, wic is represented by ˆx + µ dˆx / in (11). Altoug te sign of te second effect is ambiguous, te first effect dominates te second one, and ence E falls. curve is igly convex wen ɛ > 2. Moreover, te SOCs imply ɛ < 3 and ɛ x j /X < 2. In our model, x = xf, wic implies tat x j /X = 1/2. Tus, if te former condition is satisfied, te latter condition is also satisfied. Consequently, we can discuss te case in wic ɛ < 3. 13

15 Now we consider environmental damage in te foreign country. Differentiating (4) wit respect to µ yields de f = E f ˆx f dµ µ dˆx f }. (12) Since dˆx f / < 0 olds from (9), te sign of (12) is ambiguous. In tis case, only te effect of an increase in µ tat works troug te demand for recycled materials arises. As already discussed, tis effect may arm te foreign environment, and ence, E f may increase as µ becomes stricter. Weter a iger µ increases or decreases E f depends on te demand structure and te difference between w R and w V. 3.2 Te Optimal Degree of RCSs In tis subsection, we investigate te optimal non-cooperative degree of RCSs and compare tem wit te cooperative RCSs. Non-cooperative means tat eac government cooses its RCS to maximize welfare in its own country, wile cooperative means tat eac government cooses its RCS to maximize world welfare. We compare te non-cooperative RCSs wit te cooperative RCSs for te following reasons. In practice, given te increasing trend of trade in goods and recycled materials, countries must cooperate to deal wit te problem of waste, because it is an international problem rater tan a local problem. Teoretically, cooperative RCSs are efficient but do not represent te first-best solution. However, if countries also agree on side payments, te efficient solution is an important factor of te first-best solution. Moreover, by decomposing te inefficiency into several effects, we can investigate te strategic beavior of te government. In fact, te cooperative solution is used as a common bencmark for 14

16 evaluating environmental policies in open economies. 20 From (6), te FOC for te non-cooperative µ is given by W µ = P ˆX d ˆX + dπ de = 0. (13) We assume tat te SOCs are satisfied. 21 Since te outputs supplied to te foreign market (ˆx f and ˆx f f ) are affected by a cange in µ f, from (13), we obtain 2 W } = E (1 µ ) dˆx + dˆxf ˆx ˆx dˆx } f f µ f. (14) µ µ f From (11), (12), (14), and te symmetry of te two countries, we establis Lemma 1 Te RCSs are strategic complements (resp. substitutes) if and only if an increase in µ i raises (resp. reduces) te amount of waste generated in country j (i j). Te intuition is straigtforward. Wen an increase in µ f increases waste in te ome country, te ome country responds by raising µ to reduce te negative effect of an increase in µ f on its environment. Tus, RCSs are strategic complements in tis case. Wen an increase in µ f reduces waste in te ome country, te ome country responds by reducing µ. Tis is because a reduction in domestic waste due to an increase in µ f enables te ome country to make its RCS less strict witout damaging its environment. Tus, RCSs are strategic substitutes in tis case See, for example, Kennedy [13] and Duval and Hamilton [4]. 21 Te SOCs in tis case are given by 2 W / µ 2 < 0, 2 W f / µ 2 f < 0, 2 W / µ 2 2 W f / µ 2 f 2 W /( µ f µ ) 2 W f /( µ µ f ) > 0, 2 W/ µ 2 < 0, 2 W/ µ 2 f < 0, and 2 W/ µ 2 2 W/ µ 2 f ( 2 W/( µ f µ )) 2 > 0. If ɛ is constant, some conditions are obtained for te SOCs to be satisfied, and it is sown tat te sign of ˆx i j +µ jdˆx i j /dµ j is not important for te satisfaction of te SOCs. A proof is available from te corresponding autor upon request. 22 Note tat since ˆx i j + µ jdˆx i j /dµ j < 0 does not old globally (for example, ˆx i j + µ jdˆx i j /dµ j 0 at µ j = 0), strategic complementarity does not old globally. 15

17 Next, we compare te non-cooperative RCSs wit tose determined cooperatively. Differentiating (7) wit respect to µ and evaluating it at te non-cooperative µ yields W µ W µ =0 = dπf E f ˆx f µ dˆx f }. (15) From (10), (12), (15), Lemma 1, and given te symmetry of countries, we obtain Proposition 1 Suppose tat bot governments set teir own RCSs simultaneously. If te RCSs are strategic complements (resp. substitutes) and ɛ i 2 (resp. ɛ i 2) olds in te neigborood of te non-cooperative equilibrium, bot RCSs are stricter (resp. more lax) tan te cooperative RCSs. Te intuition is as follows. Wen te ome government maximizes its own country s welfare, it does not take into account te profits of te foreign firm and te damage to te environment of te foreign country. Tus, if an increase in te strictness of te ome RCS reduces te profits of te foreign firm and increases environmental damage in te foreign country, te ome country s non-cooperative RCS is stricter tan te cooperative RCS. Te reverse may also apply, and ence, te ome RCS may be more lax tan te cooperative RCS. In eiter case, te foreign country suffers from te distortion in te optimal non-cooperative RCS in te ome country. Note tat Proposition 1 sows te sufficient conditions required for tis result. Hence, even if one of te two conditions is not satisfied, te sign of (15) can be positive or negative. In tis case, since tere is no trade in recycled materials, tere is no demand for recycled materials generated in country i by firm j. Tus, by te symmetry of te countries, te effect of a cange in te RCS of country i on environmental damage in country j is not asymmetric. Terefore, it is clear tat in te SPNE, te ome non- 16

18 cooperative RCS is stricter (resp. more lax) tan te cooperative RCS if and only if te foreign non-cooperative RCS is stricter (resp. more lax) tan te cooperative RCS. Moreover, one point sould be noted about te decomposition of te inefficiency. Because of te symmetry of cost structure between te two firms, te ome RCS affects bot firms equally, wic implies tat teir profits cange in te same direction. Tus, unlike Kennedy [10], tere is no rent capture effect in our model, in wic firm s profit increases at te expense of firm f s. However, if te RCSs are strategic complements, an increase in µ i leads to a decrease (resp. an increase) in environmental damage in country i (resp. country j). Tis effect is considered a pollution sifting effect. 4 Trade in Recycled Materials In tis section, we determine te RCSs wen tere is trade in recycled materials between te two countries. Wen te world supply constraint for recycled materials is not binding, te main effect is a demand effect for recycled materials. By contrast, wen te world supply constraint for recycled materials is binding, te main effect is a terms-of-trade effect. We investigate tese two cases separately. 4.1 World Supply Constraint for Recycled Materials is not Binding We first examine te case were te difference in te recovery rate is large and, accordingly, tere is an excess demand for recycled materials in only one country. Witout loss of generality, we assume tat te recovery rate is iger in te ome country (i.e., λ > λ f ) and tat te supply constraint is binding in te foreign country Appendix A describes possible combinations of µ and µ f. Appendix B sows conditions required for trade to occur. 17

19 Since w R = c R in tis case, te effects of RCSs on firms outputs and profits are te same as tose wen tere is no trade in recycled materials. On te oter and, te effects of RCSs on environmental damage are different from te effects in te absence of trade and are asymmetric between te two countries. In tis case, since te foreign firm imports recycled materials from te ome country, D f = µ ˆx f + µ f ˆx f f λ f ˆX f 0, wile D f = 0. Tus, from (4) and (5), we obtain ( ) } de dˆx = E (1 µ ) + dˆxf ˆx ˆx f < 0, (16) de f = 0, de = E µ f de f = E f (1 λ f ) dˆx f + dˆxf f dˆx f + dˆxf f ˆx f ˆx f f + λ f dˆx f + dˆxf f (17), (18) < 0. (19) An increase in µ as no effect on environmental damage in te foreign country and an increase in µ f as an ambiguous effect on environmental damage in te ome country. Wen te foreign government cooses its RCS non-cooperatively, te FOC for te foreign government can be rewritten as W f µ f = P fx f d ˆX f 2 ɛ f f (w R w V )ˆx f f E f (1 λ f ) dˆx f + dˆxf f = 0. (20) We assume tat te SOCs old. 24 From (20), we obtain 2 W f / µ f µ = 0, wic implies tat RCSs are strategic neutral for te foreign country. Differentiating world welfare (7) wit respect to µ f and evaluating it at te non-cooperative µ f yields W µ f W f =0 µ f = dπ E ˆx f ˆx f f (µ f λ f ) dˆx f + dˆxf f. (21) 24 Te SOCs in tis case are analogous to tose in footnote 21, wic apply wen tere is no trade in recycled materials, wit sligt differences. Details are available from te corresponding autor upon request. 18

20 Since te sign of dπ / is ambiguous and E > 0 and dˆx f/ + dˆx f f / < 0 old, te sign of (21) is ambiguous. Tus, as in te case in wic tere is no trade in recycled materials, te foreign RCS may be stricter or more lax tan te cooperative RCS. On te oter and, te RCSs are not strategic neutral for te ome country. Since 2 W ( ) } dˆx = E µ µ (1 µ ) + dˆxf ˆx ˆx f f ˆx f ˆx f f µ f we obtain te following lemma. dˆx f + dˆxf f, (22) Lemma 2 Suppose tat te ome country exports recycled materials. Te RCSs are strategic complements (resp. substitutes) for te ome government if and only if an increase in µ f raises (resp. reduces) te amount of waste generated in te ome country. Te lemma implies tat te condition relating to te strategic relationsip for te ome country is similar to tat in te case in wic tere is no trade in recycled materials (Lemma 1). Tus, wen tere is trade in recycled materials, te strategic relationsip for te ome country and tat for te foreign country could be asymmetric. Differentiate (7) wit respect to µ and evaluate it at te non-cooperative µ to yield W µ W µ =0 = dπf. (23) In tis context, we use te fact tat waste in te foreign country is given by (1 λ f )X f. Since te sign of dπ f / is ambiguous, te ome RCS may be stricter or more lax tan te cooperative RCS. However, unlike in te case of te ome RCS wen tere is no trade in recycled materials, only a cange in te foreign firm s profits determines te difference between te cooperative and te non-cooperative RCSs. Tis contrasts wit te determination of te foreign RCS in te context of (21). 19

21 Te Nas equilibrium in te first stage is obtained by solving te FOCs simultaneously for bot countries. From (21), (23), and Lemma 2, we obtain Proposition 2 Suppose tat te ome country exports recycled materials. If ɛ i < 2 (resp. ɛ i > 2) and RCSs are strategic substitutes (resp. complements) for te ome country in te neigborood of te non-cooperative equilibrium, in te SPNE, te noncooperative RCS of te ome country is stricter (resp. more lax) tan te cooperative RCS. Te non-cooperative RCS of te foreign country may be more lax (resp. stricter) tan te cooperative RCS. Tus, it may be te case tat one country sets a stricter RCS and te oter country sets a more lax RCS tan te cooperative RCSs. First, if ɛ i < 2, ten from (10) dπ f / < 0 olds, and ence, (23) implies tat te ome RCS in te SPNE is stricter tan te cooperative RCS. Wit regard to te foreign RCS, from (10) te first term in (21) is negative. However, if ˆx i j +µ j dˆx i j/dµ j > 0, te second term is positive. Tus, if te second effect dominates te first one, te RHS of (21) is positive, wic implies tat te foreign RCS in te SPNE is more lax tan te cooperative RCS. From (18), in tis case, de / < 0, and ence, from Lemma 2, te RCSs are strategic substitutes for te ome government. Tis case is illustrated in Figure 1. Te tick curve (ωn, i i =, f) represents te locus of te RCSs of country i wen te government sets tem non-cooperatively. Te dotted curve (ωc, i i =, f) represents te locus of te RCSs of country i wen te government sets tem cooperatively. Moreover, EN and EC denote te non-cooperative and cooperative equilibria, respectively. Second, if ɛ i > 2, ten from (10), dπ f / > 0 follows, and ence, (23) implies tat te ome RCS in te SPNE is more lax tan te cooperative RCS. In tis case, from (10), te first term in (21) is positive. However, if 20

22 ˆx i j +µ j dˆx i j/dµ j < 0, te second term is negative. Tus, if te second effect dominates te first effect, te RHS of (21) is negative, wic implies tat te foreign RCS in te SPNE is stricter tan te cooperative RCS. From (18), in tis case, de / > 0 olds, and ence, from Lemma 2, te RCSs are strategic complements for te ome government. Te asymmetry between te two countries is due to trade in recycled materials. In particular, te demand effect for recycled materials plays an important role. Te ome government can reduce environmental damage in its own country in tree ways: by reducing te consumption of good X, by increasing in firm s demand for recycled materials generated in te ome country, and by increasing firm f s demand for recycled materials generated in te ome country. However, since te supply constraint is binding in te foreign country, te foreign government can only reduce environmental damage in its own country by reducing te consumption of good X. Tis asymmetry in te effect of RCSs on te demand for recycled materials is important to te opposing distortions. 4.2 World Supply Constraint for Recycled Materials is Binding In tis subsection, we analyze te case in wic total demand for recycled materials exceeds te total supply of recycled materials at w R. In tis case, from (5), it is clear tat environmental damage in bot countries depends on te consumption of X. Tus, governments can reduce environmental damage by reducing teir own consumption. However, it is still possible for bot ome and foreign non-cooperative RCSs to diverge from cooperative RCSs in opposite directions. In tis context, te terms-of-trade effect is an important factor. For simplicity, we assume tat bot ome and foreign firms, 21

23 wic produce good X, beave as price takers in te market for recycled materials. 25 In tis case, since te price of recycled materials canges due to a cange in eac RCS, a cange in te ome (resp. foreign) RCS affects te supply of good X to te foreign (resp. ome) market of good X. Let x j i [µ, µ f ] denote te equilibrium outputs in te second stage given te ome and foreign RCSs. Ten, te effect of a cange in µ on outputs, profits, and environmental damage is given by d x j = w R w V + µ dw R / P (, ) d x j f = µ fdw R / P f ( f), dπ j = 2 ɛ (w R w V + µ dw R ) x j 2 ɛ f f µ f dw R x j f, de i = E i(1 λ i ) d X i, were X i = x i i + x j i. Since te demand for recycled material may decrease at a certain price of recycled materials due to an increase in te strictness of te RCS, te price of recycled materials may fall wen an RCS becomes stricter. Tis implies tat, wen µ i becomes stricter, te supply of good X to country j s market may increase. 26 If eac government acts non-cooperatively, te FOC is given by W i = P µ X } i i E i(1 d λ i ) + (w R c R )λ X ( i µi x i i i + + µ j x i ) j dw R i dµ i i j dµ i 2 ɛ i i (w R w V ) x i i (µ i x i i + µ j x i j λ i Xi ) dw R dµ i = 0. (24) 25 For example, in Japan, te Japan Containers and Packaging Recycling Association administers te recycling system of PET bottles, and olds auctions of used PET bottles. Buyers (recycling firms) make bids for tose used bottles. In tis case, it is likely tat buyers, and ence final goods producers, beave as if tey are price takers in te market for recycled materials. See te association s web site (ttp:// for more details. 26 We are grateful to an anonymous referee for is or er elpful comment on tis point. Even if bot firms and f ave bargaining power in te market for recycled materials and te price of recycled materials remains at w R, bot ome and foreign firms may increase te supply of good X to te foreign market strategically wen te ome RCS becomes stricter. Tis is because marginal revenue from supplying good X to te ome market may fall substantially. 22

24 W µ i Differentiate (7) wit respect to µ i and evaluate it at te non-cooperative µ i to yield Wi =0 µ i = P j X j E j(1 λ j ) + (w R c R )λ j } d X j dµ i + µ j x j j + µ i x j i j i dw R dµ i 2 ɛ i i (w R w V ) x j i (µ j x j j + µ i x j i λ j Xj ) dw R dµ i. (25) In (25), te tird term is te direct effect of µ i on firm j s profit, wic appeared in te analysis of te previous section. Te first term represents te effects on CS, environmental damage, and P S for producers of recycled materials in country j troug a cange in te supply of good X to te market in country j. Note tat µ i affects X j only troug a cange in w R. Te second and last terms represent effects tat operate troug a cange in w R. Te second term represents te indirect effect on firm j s profit. Te last term is a terms-of-trade effect. Te signs of te second and tird terms in (25) are te same for bot countries weter tey export or import recycled materials. Altoug te sign of te first term is ambiguous, te sign of te last term in (25) clearly differs between te exporting and importing countries. Wen te price of recycled materials increases because RCSs become stricter, te latter term is negative (resp. positive) for te exporting (resp. importing) country. Tus, a terms-of-trade effect provides te country tat exports (resp. imports) recycled materials wit an incentive to set its RCS tat is stricter (resp. more lax) tan te cooperative RCS. Tis is because te exporting (resp. importing) country ignores te negative (resp. positive) effect of its own RCS on te welfare of te oter country. 27 Consequently, it is possible tat ome and foreign non-cooperative RCSs are distorted in opposite directions Wen te price of recycled materials falls because RCSs become stricter, bot countries ave te opposite incentives. 28 Since (24) for country i and (25) for country j sare common terms, te comparison of tem is useful. See Appendix 23

25 5 Conclusions In tis paper, we ave investigated te strategic use of recycled content standards (RCSs) in a model of two-country reciprocal trade under international duopoly. In a simple framework, we ave demonstrated tat governments ave an incentive to distort RCSs for reasons oter tan stimulating te domestic use of recycled materials, and tat te non-cooperative RCSs may be stricter or more lax tan te globally optimal RCSs, depending on various factors, suc as te demand structure and te price difference between virgin and recycled materials. An interesting result in tis paper is tat wen two countries are identical in all respects except te recovery rates of recycled materials, te RCSs adopted noncooperatively by te governments of tese countries may be distorted in opposite directions if tese countries trade not only in consumption goods but also in recycled materials. In oter words, it may be tat, relative to te cooperative RCS, te exporting country of te recycled material cooses a stricter RCS and te importing country cooses a more lax RCS, or vice versa. We ave empasized te importance of te demand effect for recycled materials. However, if tey trade in consumption goods but not in recycled materials, te non-cooperative RCSs are distorted in te same direction. Te results in tis paper imply tat te RCSs tat are currently effective in a number of countries may not be globally optimal levels. In particular, our study indicates tat wen te demand curve is not igly convex, countries tat export recycled materials may impose excessively strict RCSs and importing countries may impose excessively lax RCSs. It seems tat tis result fits te current situation. Tat is, as argued in C for more details about te comparison wen te inverse demand function is linear. 24

26 te introduction, te US and Japan impose strict RCSs, including RCSs for newsprint and green procurement requirements for various products. At te same time, te US and Japan are large exporters of recycled materials. 29 However, importers of recycled materials, including Canada and Cina, impose only lax RCSs or none at all. We suggest tat te current RCSs in exporting and importing countries are distorted in opposite directions and not globally optimal. Under te current world system, waste management and recycling are treated as domestic issues. Consequently, RCSs, wic are intended to facilitate te utilization of recycled materials, are not internationally coordinated. Our analysis suggests tat problems may arise under te current system. Te international coordination of RCSs will improve social welfare in countries tat export or import recycled materials. However, suc coordination requires tat waste management and recycling are recognized as international issues. We ave demonstrated tat trade in recycled materials can alter non-cooperative RCSs. Similar results may apply to oter environmental policies. Consider, for example, te case of regulating production-generated emissions by tradable emission permits. 30 Witout trade in permits, eac country faces te same strategic incentive to distort emission standards (Barrett [1]; Kennedy [13]). Tus, non-cooperative emission standards are necessarily distorted in te same direction. Wit trade in permits, it may be 29 One may argue tat te US case is inconsistent wit our model, because US recovery rates are relatively low for some materials (Table 1). Despite tese low recovery rates, te US exports a large amount of recycled materials mainly because supplies of recycled materials are ig. In tis sense, our results apply to te US. For example, in 2002, te US recovered more paper and board tan any oter country: 47.6 million tons. Corresponding figures for oter countries (millions of tons) are: Canada, 3.4; Cina, 10.1; Germany, 13.7; Japan, 20.0; UK, 5.9. See te caption below Table 1 for data sources. 30 We are grateful to an anonymous referee for pointing out tis application. 25

27 te case tat exporting (resp. importing) countries of permits issue fewer (resp. more) permits tan te cooperative number. Te main driving force is a terms-of-trade effect in permits. However, similar to te demand effect for recycled materials, a demand effect for permits may also contribute to asymmetric distortion in te unusual case in wic te importing country issues less tan te tecnologically feasible number of permits. In tat case, a cange in permits in te exporting country affects te terms of trade but does not affect te partner country s import demand for permits, wereas a cange in permits in te importing country affects bot te terms of trade and its import demand for permits but does not affect its domestic emission level. As already mentioned, tere is no rent capture effect in our model. Our model can be extended to include suc an effect. Te rent capture effect strengtens te strategic motive to distort RCSs and ence may exacerbate te problem caused by non-cooperative decision-making. 31 For example, if sipments of recycled materials are subject to transportation costs, te marginal cost of te firm producing a consumption good in te country tat imports recycled materials is iger tan tat in te exporting country. In fact, since te recycled materials are relatively eavy and bulky, teir transportation is often costly. In tat case, RCSs may affect firms profits differently, and tereby generate a rent capture effect. Consequently, te exporting country of te recycled materials may ave an additional incentive to make its RCS iger. Our future task is to examine tis effect in detail and to investigate wic effects are more important in practice. 31 Using data on RCSs and garbage collection programs, Jacque [11] suggested tat US recycled content newsprint regulations are a trade barrier. 26

28 Appendix A Possible Combinations of Home and Foreign RCSs In tis Appendix, we examine possible combinations of µ and µ f. Te relationsip between te demand for and supply of recycled materials at time t is: λ X,t 1 [w R,t 1 ; µ, µ f ]+λ f Xf,t 1 [w R,t 1 ; µ, µ f ] µ X,t [w R,t ; µ, µ f ]+µ f Xf,t [w R,t ; µ, µ f ], (A.1) were X i,t [w R,t ; µ i, µ j ] denotes ˆXi,t [w R,t ; µ i ] or Xi,t [w R,t ; µ i, µ j ]. In te steady state, w R,t 1 = w R,t = w R and, accordingly, Xi,t 1 = X i,t = X i. In wat follows, we divide te possible combinations of ome and foreign RCSs into tree cases. First, any combination of µ and µ f is possible wen total world supply exceeds total world demand if w R = c R. Since te price of te recycled materials depends on neiter µ nor µ f, wen (λ µ ) ˆX [µ ] = (λ f µ f ) ˆX f [µ f ], (A.2) total world demand is exactly equal to total world supply at w R. It is clear tat tis equality olds if µ = λ and µ f = λ f. From (A.2), we obtain = ˆX f (λ f µ f ) d ˆX f ˆX (λ µ ) d ˆX. (A.3) Two results relating to te sign of (A.3) can be obtained. First, if bot λ = µ and λ f = µ f, te slope is negative. Second, if te demand for recycled materials increases as an RCS becomes stricter (tat is, if ˆXi + µ i d ˆX i /dµ i > 0 olds for all µ i ), te slope is also negative. In Figure A.1, te orizontal (resp. vertical) axis represents te ome (resp. foreign) RCS, and te tick curve, CGHK, represents equality (A.2) wen ˆX i + 27

29 µ i d ˆX i /dµ i > 0. If λ µ = (λ f µ f ) and µ = µ f, te equality (A.2) olds, since µ = µ f implies ˆX = ˆX f. Tus, te curve goes troug bot H and G, were µ = µ f on te line labeled α and λ µ = (λ f µ f ) on te line labeled β. Moreover, from (A.3), since µ = λ and µ f = λ f implies µ > µ f, / < 1 at H. Moreover, / > 1 at G, since λ f µ f < 0 and λ µ > 0 at G. Consequently, in te area ACKMO, te total supply of recycled materials exceeds total demand for recycled materials at w R. Terefore, any combinations of RCSs are possible, and te supply constraint is not binding. Second, we focus on te area DEIH in Figure A.1. Since tis area is located in te upper-rigt of te curve CGHK, if w R,t 1 = w R,t = w R, demand for recycled materials exceeds supply of recycled materials. Tus, te price of te recycled materials is likely to increase. However, since µ > λ and µ f > λ f, if w R,t 1 = w R,t, demand exceeds supply watever te price of te recycled materials. Tis implies tat tere is no steady-state equilibrium, wic implies tat tere are no feasible combinations of RCSs. Tird, combinations of ome and foreign RCSs may be possible in te areas CDH and HIK, since te gap between demand and supply may be adjusted by a cange in te price of te recycled materials. However, witin tose areas, some combinations must be eliminated because tey are not feasible. First, in te area FGH, since µ > µ f, te marginal cost of supplying good X to te ome market is greater tan tat of supplying to te foreign market. Terefore, X f > X. Moreover, since (λ f µ f ) > λ µ, it follows tat (λ f µ f ) X f > (λ µ ) X. (A.4) 28