Foreign Direct Investment and Technology Licensing in a Polluting Industry

Cao, Jiyun; Mukherjee, Arijit Article — Published Version Foreign Direct Investment and Technology Licensing in a Polluting Industry Environmental and Resource Economics Provided in Cooperation with: Springer Nature Suggested Citation: Cao, Jiyun; Mukherjee, Arijit (2024) : Foreign Direct Investment and Technology Licensing in a Polluting Industry, Environmental and Resource Economics, ISSN 1573-1502, Springer Netherlands, Dordrecht, Vol. 87, Iss. 9, pp. 2361-2399, https://doi.org/10.1007/s10640-024-00886-7 This Version is available at: https://hdl.handle.net/10419/315260 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) https://doi.org/10.1007/s10640-024-00886-7 Foreign Direct Investment andTechnology Licensing inaPolluting Industry JiyunCao1,6· ArijitMukherjee2,3,4,5 Accepted: 22 May 2024 © The Author(s) 2024 Abstract We consider a firm’s incentive for foreign direct investment (FDI) and international technology licensing in a polluting industry. We explain the rationale and the welfare implications of complementarity between FDI and licensing, i.e., the firm’s strategy of “FDI and licensing” (FL), which is empirically relevant but ignored in the literature. When the environmental tax cannot be committed, the firm adopts the licensing strategy if the pollution intensity is not high, and the licensing strategy may create lower consumer surplus and welfare compared to both FDI and FL. However, if the pollution intensity is high, the firm undertakes FL, which provide higher consumer surplus and welfare compared to both licensing and FDI. When the government can commit to the environmental tax, the firm always prefers FL. The host-country welfare is higher but the consumer surplus and world welfare may be lower under the committed tax policy compared to the non-committed tax policy. These results hold under Cournot competition and Stackelberg competition. We further show that FL can be the equilibrium strategy of the foreign firm if there is fixed-fee licensing instead of a two-part tariff licensing, which is considered in the main analysis. Keywords Emission fee· Foreign direct investment· Technology licensing· Welfare JEL Classification F18· F23· L13· L24· Q56· Q58 * Arijit Mukherjee [email protected] 1 The School ofEconomics, Nankai University, Tianjin, China 2 Nottingham University Business School, Jubilee Campus, Wollaton Road, NottinghamNG81BB, UK 3 INFER, Cologne, Germany 4 CESifo, Munich, Germany 5 GRU, City University ofHong Kong, Kowloon, HongKong 6 Collaborative Innovation Center forChina Economy, Tianjin, China Environmental and Resource Economics (2024) 87:2361–2399 / Published online: 6 August 2024 J.Cao, A.Mukherjee 1 Introduction Many developing countries and transitional economies liberalized their economies in last few decades, and foreign direct investment (FDI) and international technology licensing constitute two important ways to serve the host-country markets by the foreign firms.1 There is a vast literature examining the profitability and the implications of FDI and licensing strategies, which we review in the next section. However, this literature is restrictive for two reasons. First, they mostly ignored polluting industries. However, given the climate change problem at hand, it is important to investigate how environmental policies affect these strategies and the corresponding welfare. Secondly, the extant literature mostly considered FDI and licensing as substitutes, while evidence shows that foreign firms often undertake FDI and also license their technologies to the host-country firms in the same market. In other words, there is a complementarity between FDI and licensing. We explain this phenomenon and its welfare implications. The evidence of “FDI and licensing” (FL for brevity) in polluting industries, such as petrochemical and pharmaceutical industries, is abound. For example, BP (UK) has a plant in China, and licensed its latest generation technology to China’s Dongying Weilian Chemical Co., Ltd.2 LyondellBasell is operating three polypropylene compounding plants in China,3 and also licensed its polypropylene technology to Chinese companies, such as Qingdao Jinneng New Material Co., Ltd,4 Shandong Chambroad Sinopoly New Materials Co., Ltd.,5 and Wanhua Chemical Group Co., Ltd.6 Belderbos (1998) illustrates that Shell has by far grown into the third largest fully integrated oil company in Japan, and licensed its technology to Japanese companies, such as Sumitomo Chemical, Seibu Oil, and Chiyoda Kako Kentetsu from 1981 to 1986. There are also evidences where the foreign firms only license to the host-country firms.7 As Sikimic etal. (2013) documented, several leading Italian pharmaceutical and biotech companies adopted technology licensing as the foreign market-entry mode. Given this background, we examine a foreign monopolist’s decision on FDI, licensing, and FL, in a polluting industry and show the corresponding welfare implications. Since the foreign monopolist needs to internalize the effects of its strategies on the emission fee (or the environmental tax) imposed by the host-country government, whether the host-country government can commit to its policies may play important roles. 1 FDI stock in developing economies is over US$12 trillion in 2020 (UNCTAD Handbook of Statistics, 2021). 2 https:// gulfo iland gas. com/ webpr o1/ main/ mainn ews. asp? id= 901043. 3 https:// cen. acs. org/ busin ess/ petro chemi cals/ Lyond ellBa sellinvestChine seproje ct/ 97/ web/ 2019/ 09. 4 https:// gulfo iland gas. com/ webpr o1/ main/ mainn ews. asp? id= 66206. 5 https:// gulfo iland gas. com/ webpr o1/ main/ mainn ews. asp? id= 70993. 6 https:// gulfo iland gas. com/ webpr o1/ main/ mainn ews. asp? id= 67044. 7 For example, North Carolina-based vTv Therapeutics signed an exclusive licensing agreement with Hangzhou Zhongmei Huadong Pharmaceutical Co., Ltd., in China, for the rights to develop and commercialize vTv Therapeutics’ GLP-1r agonist program in China and other Pacific Rim countries (See https:// www. busin esswi re. com/ news/ home/ 20171 22100 5238/ en/ vTvThera peuti csAnnou ncesLicen singAgree mentwithHangz houZhong meiHuado ngPhar m aceut icalCo.- toRightsforvTv% E2% 80% 99sGLP1rAgoni st% C2% A0Dia betesProgr aminChinaandOtherPacifi cRimTerri tories). Huadong Medicine Co., Ltd., in China won the exclusive rights for two autoimmune products, Arcalyst (rilonacept) and mavrilimumab, of Kiniksa Pharmaceuticals (UK) Ltd. in the Asia Pacific region (including China, South Korea, Australia and 18 other countries, excluding Japan) (see http:// www. pharm adj. com/ en/ cms/ detail. htm? item. id= ecb84 5cca8 cb11e cbee6 fa163 e4204 9a). 2362 Foreign Direct Investment andTechnology Licensing inaPolluting… In Section 4, we follow the literature on non-committed government policies where the governments cannot commit to their policies (often because of the time inconsistency problem) and adjust their policies after firms’ decisions. Since licensing or FL by the foreign monopolist transfers (part of) its production to the host-country firm, it encourages the host-country government to reduce the emission fee. A higher marginal cost of the hostcountry licensee because of a positive royalty rate charged by the foreign monopolist also helps to reduce the emission fee by reducing pollution. Thus, a less stringent emission fee resulted from licensing or FL makes the foreign monopolist better off compared to FDI.8 When comparing between licensing and FL, lower competition and less stringent emission fee under licensing make the foreign monopolist better off compared to FL if the pollution intensity is not high. Hence, depending on the pollution intensity, the foreign monopolist prefers licensing only (FL) when the pollution intensities are mild (high).9 When looking at the welfare implications, we find that licensing as a substitute of FDI reduces the host-country welfare, and may reduce consumer surplus and world welfare (which is the host-country welfare plus the profit of the foreign monopolist) compared to FDI, although the market structure is the same under licensing and FDI. However, if the foreign monopolist does FL where licensing complements FDI, it increases consumer surplus and welfare in the host country compared to FDI. FL also increases the host-country welfare and world welfare compared to licensing, but it reduces consumer surplus compared to licensing when the pollution intensity is low. Hence, licensing reduces (increases) the host-country welfare compared to FDI if it substitutes (complements) FDI. Therefore, internalizing the foreign monopolist’s entry decision, we find that if the pollution intensity is not high, the foreign monopolist adopts the licensing strategy, which may create lower consumer surplus and welfare compared to both FDI and FL. However, if the pollution intensity is high, the foreign monopolist does FL, which creates higher consumer surplus and welfare compared to both licensing and FDI. Section5 considers the case of a committed government policy where the host-country government can commit to an emission fee before the foreign monopolist’s decision. This may be due to the administrative or political difficulties in policy adjustment that may affect the reputation of the government. We find that the foreign monopolist is better off under FL compared to licensing and FDI since FL helps to reduce the total tax payment compared to licensing and FDI. We also show that the committed policy reduces pollutant emission, increases domestic welfare, and may increase or decrease consumer surplus compared to the non-committed policy. We assume in Sectsion 4 and 5 that firms play Cournot competition under FL. Section6 considers Stackelberg competition under FL. The above-mentioned results derived from Cournot competition still hold under Stackelberg competition. In Section7, we consider a licensing contract with fixed-fee only. In this situation, the foreign monopolist prefers FL under the non-committed policy when the pollution intensity is high and always prefers it under the committed policy. 8 There is a recent literature showing the effects of licensing of cleaner technologies (see, e.g., Sibailly 2013, Hattori 2017, Kim etal. 2018 and Xia etal. 2019). In contrast, we consider licensing the technology of a new product. 9 The literature on pollution haven hypothesis shows the effects of environmental regulation in the host countries on inward FDIs (see, e.g., Dijkstra etal. 2011, Chung 2014 and Cai etal. 2016, for some recent contributions, and the references therein). Zhao etal. (2019) compare the welfare effects of FDI in polluting industries to that under closed polluting sectors. In contrast, we consider the choice between FDI, licensing, and FL. 2363 J.Cao, A.Mukherjee Thus, we contribute to the literature by providing a new framework that considers FDI and licensing in a polluting industry, explains environmental tax as a rationale for FL, and shows the implications of committed and non-committed host-country policies, Cournot and Stackelberg competition under FL, and two-part tariff and fixed-fee licensing contracts. Hence, in contrast to the existing literature on FDI and licensing, we consider a polluting industry, and show the existence of FL (i.e., complementarity between FDI and licensing) even if there is a monopolist final good producer under FDI or licensing. Rather than the business stealing incentive in the product market, the foreign firm has the incentive to create competition in the product market through FL to manipulate the environmental tax. The remainder of the paper is organized as follows. Section2 reviews the relevant literature. Section3 describes the model. Section4 investigates the situation where the government cannot commit to an emission fee before the foreign monopolist’s market-entry decision. Section5 examines the situation where the government can commit to the emission fee before the foreign monopolist’s market-entry decision, and compares the results under the committed and non-committed policies. While Sections4and 5consider Cournot competition under FL, Sect. 6 extends the analysis by considering Stackelberg competition under FL. Section7 consider a licensing contract with fixed-fee only. Section8 concludes. 2 Literature Review While the proximity-concentration hypothesis explains the multinational firms’ incentive for FDI compared to export (see, e.g., Krugman 1983, Horstman and Markusen, 1992, Brainard 1993 and 1997), there is another literature examining the multinational firms’ benefits from the internalisation strategies, such as FDI, compared to their arm’s length transactions, such as technology licensing, which is the focus of this paper. Started with Dunning (1958), the literature examining the multinational firms’ benefits from FDI compared to technology licensing focused on different types of transaction costs arising from technology licensing. Rugman (1986) provides a survey of the earlier literature on the internationalisation theory focusing ondifferent types of transaction costs. Horstman and Markusen (1987) show that the foreign firm’s risk of losing reputation under licensing due to a lower quality product provided by the licensee may create the incentive for FDI. Saggi (1996) shows that a foreign firm’s incentive for FDI and licensing may depend on the trade-off created by the foreign firm’s loss of profit under FDI due to a higher product-market competition and its loss of profit in other markets due to the licensee’s opportunistic behaviour under licensing. Saggi (1999) considers a two period model where a foreign firm chooses licensing or FDI (but not licensing and FDI) in each period. In this set up, it explores how the trade-off between a lower knowledge spillover under FDI and higher rent dissipation under FDI due to an increased product-market competition affects the foreign firm’s decision on FDI and licensing. Wright (1993) shows how the information asymmetry about the technology type and the cost of FDI interact to determine a foreign firm’s decision on export, FDI, or licensing. It shows that the market share restrictions and per-unit royalties can signal the technology type and make licensing the most attractive option for the foreign firm. Vishwasrao (1994) considers the foreign firm’s decision on export, FDI, or licensing when the licensee has private information about its ability to imitate the technology of the foreign firm under licensing. It considers a screening framework where the foreign firm 2364 Foreign Direct Investment andTechnology Licensing inaPolluting… uses the licensing contract to gain information about the licensee’s ability to imitate the technology. It shows that FDI dominates licensing if the probability of imitation is high. Considering a quality ladder model of innovation, Glass and Saggi (2002) show the effects of the foreign firm’s mode of operation (licensing or FDI) on innovation by the foreign firm. If the foreign firm needs to sacrifice more rent to the licensee or the cost disadvantage of FDI reduces, the foreign firm’s incentive for FDI increases compared to licensing. Further, the firm doing FDI chooses larger innovation compared to the firm undertaking licensing. Yang and Maskus (2009) show the implications of the host-country patent protection on a foreign firm’s decision on export, FDI, or licensing. It shows that a foreign firm prefers FDI in countries with weak patents and lower costs of setting subsidiaries; strengthening the patent protection in this situation creates the incentive for licensing by the foreign firm. While the above mentioned papers provide several important insights, unlike this paper, they consider FDI and licensing as substitutes. Sinha (2010) considers a framework where a foreign firm, competing with a host-country firm, decides on FDI or export after taking a decision on licensing its technology to the host-country competitor. It shows that licensing reduces the possibility of FDI. However, if the fixed cost of FDI is not high, the foreign firm undertakes FDI after licensing. Wang etal. (2016a) extend Sinha (2010) to show the implications of better information acquisition under FDI about the market condition. In contrast to Sinha (2010), it shows that, due to the benefit of better information acquisition under FDI, licensing may increase the incentive for FDI.10 Although these papers consider the possibility of FDI after offering the licensing contract, we differ from them in some important ways. First, unlike our paper, those papers did not consider a polluting industry. Second, the incentive for FDI after licensing occurs in those papers due to the foreign firm’s incentive for stealing market share from the host-country licensee, since, unlike our paper, licensing does not create a monopoly market structure in those papers. Mukherjee (2000) and Mukherjee and Pennings (2006) show that strategic host-country tax policy and strategic tariff imposed by the importing countries may encourage foreign innovators to license their technologies to host-country firms. However, these papers neither looked at the environmental problems nor considered the strategy of FL. While Mukherjee (2000) and Mukherjee and Pennings (2006) showed the implications of strategic government policies, Arya and Mittendorf (2006) and Mukherjee etal. (2008) showed a monopolist final goods producer’s incentive for creating competition through licensing when there is strategic input price determination. Shepard (1987) and Farrell and Gallini (1988) showed a monopolist input supplier’s incentive for technology licensing to another input supplier to reduce the hold-up problem faced by the final goods producers. Unlike these papers, we consider an open economy with market entry where the host-country environmental policy is the reason for encouraging the foreign monopolist to license its technology.11 10 Wang etal. (2016b) extend Wang etal. (2016a) to show the implications of patent protection in the hostcountry. 11 There is a related literature where exogenous entry of a new final goods producer may increase the profits of the incumbent firms or the industry profit in the absence of strategic government policies. See, e.g., Tyagi (1999), Naylor (2002a, b), Mukherjee etal. (2009), Matsushima (2006) and Mukherjee (2019) for strategic input price determination, Pal and Sarkar (2001) and Mukherjee and Zhao (2017) for Stackelberg competition, Ishibashi and Matsushima (2009) for vertical product differentiation and heterogeneous consumer groups, Ishida etal. (2011) for innovation by asymmetric cost firms, and Fanti and Buccella (2017) for network externality with corporate social responsibility. 2365 J.Cao, A.Mukherjee In contrast to the vast literature considering exogenously given outside innovators, which do not compete with the licensees, or inside innovators, which compete with the licensees (see, e.g., Rostoker 1984, Kamien 1992, Saggi 2002 and Mukherjee 2009, for surveys of this literature), the endogenous decision on licensing and FL in our analysis makes the foreign monopolist an outside innovator (in the case of licensing only) or inside innovator (in the case of FL) endogenously. Our paper also contributes to the growing literature on welfare reducing technology licensing. Licensing may reduce welfare by creating collusive outcome (Faulí-Oller and Sandonis 2002; Erkal 2005), affecting the R&D organization (Mukherjee 2005), creating excessive entry (Mukherjee and Mukherjee 2008), affecting the mode of entry of the foreign firm (Sinha 2010), reducing R&D incentive (Chang etal. 2013), and increasing (decreasing) the government’s subsidy bill (tax revenues) (Ghosh and Saha 2015). In contrast, we show the welfare reducing licensing in a polluting industry. Further, when the government cannot commit to an emission fee, licensing reduces welfare in our analysis if it acts as a substitute of FDI but increases welfare if it complements FDI. In our analysis, licensing only gives the host-country licensee the exclusive right to use the technology, since only the licensee uses the technology in this situation. On the other hand, FL gives the host-country licensee the non-exclusive right to use the technology, since both firms use the technology in this situation. Hence, our paper can also be related to the literature on exclusive contracts.12 In that literature, the buyers and sellers, which decide on exclusive contrasts, are not competitors in the product market. In contrast, we consider whether a foreign monopolist prefers to give a host-country firm the exclusive right to use its technology or prefers to offer a non-exclusive right where it competes with the licensee. Further, unlike that literature, we consider a polluting industry with emission fee.13 3 The Model Consider a foreign innovator, called firm 1, which holds patent for a new product that has no substitutes. Firm 1 wants to sell the product in a host-country, called domestic country. Firm 1 can serve the domestic country through FDI or licensing or “FDI and licensing” (FL). FDI Under FDI, only firm 1 produces and sells the product in the domestic country. Firm 1 can produce the good at a constant marginal cost, c . Licensing Under licensing, firm 1 licenses its technology to a domestic firm exclusively, called firm 2. Hence, only firm 2 produces and sells the product in the domestic country. Firm 2 can also produce the good at the constant marginal cost, c. 12 See, e.g., Calzolari and Denicolò (2013, 2015), Gratz and Reisinger (2013), Kitamura et al. (2018, 2022), Calzolari etal. (2020), Chen and Shaffer (2019), Ulsaker (2020) and the references therein. 13 Banerjee and Poddar (2019) and Niu (2019) considered exclusive versus non-exclusive licensing in a closed economy and in a non-polluting industry. Hence, unlike our paper, those papers neither considered FDI and licensing, nor considered a polluting industry. Saggi (1996) compared the incentive for FDI and licensing with the possibility of exclusive and non-exclusive licensing. However, unlike our paper, he neither considered a polluting industry nor considered the possibility of FDI and licensing as complement. 2366 Foreign Direct Investment andTechnology Licensing inaPolluting… FL Under FL, firm 1 licenses its technology to firm 2, and both firms 1 and 2 produce and sell the product in the domestic country like Cournot duopolists.14 Both firms produce the products at the constant marginal cost, c. As mentioned in the introduction, our paper follows the literature examining the preference for and consequences of FDI and licensing. Hence, we assume away firm 1’s choice for exporting to the host-country. High international transportation cost, lower cost of production in the domestic country, tariff imposed by the domestic country and environmental tax imposed by the home country of firm 1 provide some reasons to exclude exporting as an option for firm 1. The absence of exporting also helps us to focus on the effects of the domestic environmental policy by ignoring the effects of the trade policies, which are discussed in Kabiraj and Marjit (2003) and Mukherjee and Pennings (2006). We assume that pollution is a by-product of the production process. Without loss of generality, we normalize the emission-to-output ratio to one. The producers can abate pollution by investing in pollution abatement technologies. If firm i ( i=1, 2 ) produces qi units of output and chooses the amount of pollution abatement as ai ( 0≤ai≤qi ),15 the pollutant emission level is qi −ai . However, pollution abatement is costly and the cost of pollution abatement ai is CA = 1 2 a 2 i , for the ith firm where i=1, 2 . In line with the existing literature (see, e.g., Ulph 1996, Barcena-Ruiz and Garzon 2002, Long and Soubeyran 2005, Antelo and Loureiro 2009 and Pal 2012), we consider that the environmental damage from pollution is ED = 1 2 d(q−a) 2 , where q=q1+q2 is the total output, a=a1+a2 is the total pollution abatement, and d>0 shows the pollution intensity in the domestic country. We assume that the domestic government imposes an emission fee, t ( t≥0 ), per-unit of pollutant emitted. In other words, we assume away the possibility of output subsidy, which, e.g., may occur to reduce the distortion created by the imperfect product market competition. However, given the climate change problem at hand, it may be difficult to get a public support for output subsidy in a polluting industry. Hence, we confine our analysis to d > 1 3 so that the emission fee under licensing is positive. Assume that the inverse market demand function is p=A−q , which comes from the utility function U =Aq − 1 2 q2+𝜁 of a representative consumer, where p is the price, 𝜁 is the numeraire good, and A>c . Given this utility function, the consumer surplus is CS =Aq − 1 2 q2−pq =Aq − 1 2 q2−(A−q)q= 1 2 q 2 .16 The domestic government sets an emission fee to maximize welfare of the domestic economy, which is the sum of the consumer surplus, the profit of the domestic firm after deducting the cost of pollution abatement 𝜋2 , and the tax revenue T=t(q−a) , minus the environmental damage ED , i.e.: As mentioned in the introduction, we will consider the following two situations in the next two sections respectively. Section4 will consider that the government cannot commit (1) W =CS +𝜋2+T−ED = 1 2 q2+𝜋2+t(q−a)− 1 2 d(q−a) 2 14 We will consider Stackelberg competition under FL in Section6. 15 The pollution abatement technology can reduce pollutant emission to zero at most. Hence, a producer has no incentive to choose an abatement that is greater than its output. 16 See Varian (1992, p. 164–166) for a discussion on consumer surplus for a quasilinear utility function, which is widely used in the partial equilibrium analysis like ours. 2367 J.Cao, A.Mukherjee to an emission fee before firm 1’s market-entry decision. This can be motivated by the observation that the government policies are often “time inconsistent”, implying that the government has an incentive to reverse the preannounced policies. According to Staiger and Tabellini (1987), governments may find it difficult to commit when it has some degree of discretionary power to decide its policy. In the case of energy policy, Helm etal. (2003) noticed that no commitment by the government might occur since the energy policy is used to achieve multiple objectives, such as international competitiveness, political interests, and lower energy prices.17 Thus, this situation is in line with the papers considering the effects of the non-committed government policies.18 Section5 will consider that the government can commit to its policy before firm 1’s decision due to the administrative or political difficulties in policy adjustment that may affect the reputation of the government. 4 Non‑Committed Policy In this section, we consider the following three-stage game. In stage 1, firm 1 decides whether to do FDI, licensing or FL. In case of licensing, firm 1 makes a take-it-or-leave-it offer to firm 2. Following the literature on technology licensing, we assume that the licensing contract (under licensing only or under FL) consists of a two-part tariff with a nonnegative up-front fixed-fee ( L ) and a non-negative per-unit output royalty ( r ), and firm 2 accepts the offer if its payoff under licensing is not less than that of under no licensing, which is normalized to zero. In stage 2, the government sets the emission fee ( t ) to maximize the domestic welfare given by (1). In stage 3, the producers determine the amount of pollution abatements a1 , a2 , and outputs q1 , q2 , and the profits are realized. We solve the game through backward induction. 4.1 FDI First, consider the case where firm 1 undertakes FDI. Firm 2 is inactive in this situation, and the maximization problem for firm 1 in stage 3 is: The equilibrium output and the pollution abatement by firm 1 are (2) max a1 , q1 𝜋1= ( A−q1−c ) q1−t ( q1−a1 ) − 1 2 a 2 1 17 As mentioned in Iida and Mukherjee (2020), “the Australian government repealed the Clean Energy act 2011 and abolished the carbon price mechanism to lower the cost of domestic production and consumption (see the website of the Australian Department of the Environment http:// www. envir onment. gov. au/).” Helm etal. (2003) also provide examples of time inconsistency problems for the energy policies. 18 For the effects of non-committed environmental policies, one may look at Poyago-Theotoky (2007), Golombek etal. (2010) and Hattori (2013) for environmental investments, Eerola (2006), Dijkstra etal. (2011) and De Santis and Stähler (2009) for firms’ location decisions, and Iida and Mukherjee (2020) for bi-sourcing. For the effects of non-committed non-environmental policies, one may look at Staiger and Tabellini (1987), Al-Saadon and Das (1996), Mukherjee (2000), Neary and Leahy (2000), Mukherjee and Pennings (2006), Mukherjee and Tsai (2013), Lee etal. (2018) and Basak and Mukherjee (2022). 2368 Foreign Direct Investment andTechnology Licensing inaPolluting… On the one hand, FL increases the output, but on the other hand, it increases the pollution abatement. We find that the former effect overweighs the latter, making the pollutant emission under FL higher compared to FDI, i.e. qFL −aFL >qF−aF . FL (compared to FDI) increases the total output and consumer surplus by increasing competition and reducing the emission fee. Although the profit of firm 2 does not help to increase the domestic welfare,28 higher consumer surplus under FL compared to FDI dominates the negative effect due to a higher environmental damage and lower tax revenue. As a result, compared to FDI, FL increases domestic welfare, and the world welfare, since it also makes the foreign firm better off. 4.4 Equilibrium Choice: Licensing orFL We have shown that firm 1 prefers both licensing and FL compared to FDI. Now we determine firm 1’s optimal mode of entry by comparing licensing with FL and see the corresponding welfare implications. We attain 𝜋L 1⋛ 𝜋 FL 1 for d⋚d , where d≈0.88753 .29 Hence, we have the following proposition immediately. Proposition 1 Firm 1 prefers licensing compared to FL if and only if d ≤ d(≈ 0.88753 ) . Licensing (compared to FL) not only creates lower product-market competition but also creates lower emission fee for a low pollution intensity.30 However, the effective marginal cost of production under licensing is higher than that of firm 1 under FL since firm 2 has to pay a royalty rate, which is low if the pollution intensity is not high. Hence, lower competition and lower emission fee under licensing make firm 1 better off compared to FL if the pollution intensity is not high. 4.5 Welfare Implications Now look at the welfare implications. While FL increases consumer surplus, domestic welfare and world welfare compare to FDI, the licensing strategy reduces domestic welfare and may reduce consumer surplus and world welfare compared to FDI. By comparing the consumer surplus and welfare under licensing with those under FL, we get the following Lemma. Lemma 5 Compared to licensing, FL. 28 The reason is that firm 1 uses the fixed-fee to extract the profit of firm 2. 29 d is a solution of the equation 108d4+ 396 d3+ 389 d2− 202 d− 471 =0 , and is the cutoff value of the pollution intensity for which the profit of firm 1 under FL is the same to that of under licensing. It increases with Stackelberg competition under FL, as shown in subSection6.1.2. 30 We have tL<tFL for d<d0 , where d0 ( d0≈1.57688 ) is a solution of the equation 108d4+225d3−97d2−563d−421 =0 , and is the cutoff value of the pollution intensity for which the emission fee under FL is the same to that of under licensing. 2375 J.Cao, A.Mukherjee (i) increases (reduces) the consumer surplus if , where 31 (ii) increases the domestic welfare and world welfare. Proof Appendix 7. We know from Lemmas 2 and 4 that the consumer surplus under FL is always higher than that of under FDI which is higher than that of under licensing for d >2 √ 3− 1 3 . However, the consumer surplus under licensing is higher than that of under FDI for d <2 √ 3− 1 3 . On the one hand, higher competition under FL compared to licensing tends to create higher consumer surplus under the former than the latter. On the other hand, if the pollution intensity is not high, higher royalty rate and emission fee under FL compared to licensing tend to reduce consumer surplus under the former than the latter. As a result, the consumer surplus under FL is lower than that of under licensing for low pollution intensity, i.e. d< . Compared to FDI, licensing reduces the domestic welfare while FL increases it. Hence, it is obvious that the domestic welfare under FL is higher than that of under licensing. Compared to FL, licensing tends to increase the world welfare by making the foreign firm better off for d≤d , but tends to decrease the world welfare by reducing the domestic welfare. The latter effect dominates the former effect, thus making the world welfare lower under licensing compared to FL. To sum up, since d �=2 √ 3−1 3 ≈0.82137 <0.88753 ≈d , We get the following two results from Lemmas 2, 4 and 5, and Proposition 1. Proposition 2 (i) For d ≤ d(≈ 0.88753 ) , firm 1 prefers licensing. In this situation, licensing (a) increases the consumer surplus compared to both FDI and FL if and only if d <  d (≈ 0.354329) , (b) increases the consumer surplus compared to FDI but decreases it compared to FL if and only if <d<d�(≈0.82137) , (c) decreases the consumer surplus compared to both FDI and FL if and only if d ′ <d≤d . (ii) For d>d , firm 1 prefers FL, which benefits the consumers compared to both licensing and FDI. Proposition 3 (i) For d ≤ d(≈ 0.88753) , firm 1 prefers licensing. In this situation, licensing (a) reduces the domestic welfare compared to both FDI and FL, (b) increases (decreases) the world welfare compared to FDI for d<� d(≈ 0.64101) ( � d<d≤d ), but always decreases it compared to FL. 31 is the cutoff value of the pollution intensity for which the consumer surplus is the same under FL and under licensing. As shown in subSection6.1.2, it increases with Stackelberg competition under FL. 2376 Foreign Direct Investment andTechnology Licensing inaPolluting… (ii)For d>d , firm 1 prefers FL, which creates higher domestic welfare and world welfare compared to both licensing and FDI. Figure1 shows firm 1’s choice and the implications on the consumers, domestic welfare and world welfare. 5 Committed Policy Now we consider a situation where the domestic government can commit to its policy before firm 1’s market-entry decision. Hence, in terms of the game structure, the order of stages 1 and 2 in the previous section is switched. To be specific, the government sets an emission fee ( t ) to maximize the domestic welfare in stage 1, and firm 1 decides whether to do FDI, licensing or FL in stage 2. 5.1 Market‑Entry Decision ofFirm 1 The problem and solutions in stage 3 here are totally the same as those under the non-committed policy. Hence, given the emission fee set by the domestic government in stage 1, we examine the market-entry decision of firm 1 by comparing its profits under FDI, licensing and FL in stage 2. 5.1.1 FDI If firm 1 undertakes FDI in stage 2, the profit of firm 1 under FDI is 𝜋 1=(A−c−t) 2 +2t 2 4 5.1.2 Licensing If firm 1 licenses the technology to firm 2 but does not produce through FDI in stage 2, firm 1 maximizes the expression (13) to determine the licensing fee. Since the equilibrium L equals ( A−q2−c−r ) q2−t ( q2−a2 ) − 1 2 a 2 2 , the profit of firm 1 reduces to 𝜋 1=(A−c−t) 2 +2t2−r 2 4 . It is obvious that the optimal royalty rate is 0 and the profit of firm 1 under licensing in stage 2 is 𝜋 1=(A−c−t) 2 +2t 2 4 , the same as that of under FDI. This result is very different from the situation of the non-committed policy. The reason is that, under the Fig. 1 Firm 1’s choice and the welfare implications 2377 J.Cao, A.Mukherjee committed policy, firm 1 has no ability to induce the host-country government to reduce the emission fee by licensing. 5.1.3 FL If firm 1 undertakes FL in stage 2, the maximization problem for firm 1 is similar to the situation in subSection 4.3 with the exception that the emission fee is given in stage 1 here. Because q2⋛t for r ⋚ A−c−4t 2 , a2=t if the royalty rate determined by firm 1 is not greater than A−c−4t 2 ; otherwise a2=q2 . We get the equilibrium royalty rate under FL as r = A−c−3t 2 ,32 making a2=q2 and the profit of firm 1 under FL is 𝜋 1=3(A−c−t) 2 +10t 2 12 , which is greater than that of under FDI or licensing. Hence, firm 1 prefers FL to both FDI and licensing. The reason for this is as follows. Although licensing under FL creates competition and the emission fee is not affected by firm 1’s decision, FL saves the total tax payments by reducing firm 1’s output and pollutant emission.33 In addition, firm 1 can use a positive royalty rate to soften competition from firm 2. 5.2 Equilibrium In stage 1, the government determines the emission fee to maximize (1) with q1 and q2 given by (19), a1 given by (20), a2=q2 , r = A−c−3t 2 and 𝜋2=0 . We find the equilibrium emission fee under the committed policy is t C= 3(11d+5)(A−c) 121d+131 . The corresponding equilibrium pollution abatements, outputs, pollutant emission, royalty rate, fixed-fee, profits, domestic welfare and world welfare are as follows: Thus, the following proposition is immediate from the above analysis. a C 1 = 3(11d+5)(A−c) 121d+131 aC 2 = 2(11d+5)(A−c) 121d+131 aC= 5(11d+5)(A−c) 121d+131 q C 1 = (33d+53)(A−c) 121d+131 qC 2 = 2(11d+5)(A−c) 121d+131 qC= (55d+63)(A−c) 121d+131 q C−aC=38(A−c) 121d+131 rC=(11d+43)(A−c) 121d+131 LC=8(11d+5) 2 (A−c) 2 (121d+131) 2 𝜋 C 1=(5687d2+11858d+7103)(A−c) 2 2 ( 121 d+ 131 ) 2𝜋C 2=0WC=(25d+39)(A−c) 2 2 ( 121 d+ 131 ) GW C=2(2178d2+4963d+3053)(A−c) 2 ( 121 d+ 131 ) 2 32 If firm 1 chooses r ≤ A−c−4t 2 , it attains the maximum profit ( A−c−t) 2 +3t2 4 ( < 3(A−c−t) 2 +10t2 12 ) at r = A−c−4t 2 . 33 The tax payment under FL (which is t[3(A−c)−11t] 6 ) is less than that of under FDI or licensing (which is t(A−c−3t) 2 ) by t2 3 . 2378 Foreign Direct Investment andTechnology Licensing inaPolluting… Proposition 4: Firm 1 always prefers FL compared to both FDI and licensing in a polluting industry when the host-country government commits to the emission fee before firm 1’s market-entry decision. The equilibrium licensing contract under FL consists of a positive fixed-fee and a royalty. We have 𝜕 tC 𝜕 d =2508(A−c) (121d+131) 2>0, 𝜕rC 𝜕 d =− 3762(A−c) (121d+131) 2<0, 𝜕aC 𝜕 d =4180(A−c) (121d+131) 2>0, 𝜕q C 𝜕 d =− 418(A−c) (121d+131) 2< 0, 𝜕( q C −a C) 𝜕 d =− 4598(A−c) (121d+131) 2<0, 𝜕𝜋 C 1 𝜕 d =27588(d−3)(A−c)2 (121d+131) 3⋚ 0 for d ⋚3, 𝜕W C 𝜕d=− 722(A−c) 2 (121 d +131) 2< 0 and 𝜕 GW C 𝜕d =− 494(121d+359)(A−c) 2 (121d+131) 3< 0 , indicating that similar to FL under the non-committed policy, the emission fee and pollution abatement increase with the pollution intensity, d , the royalty rate, outputs, pollutant emission, domestic welfare and world welfare decrease with d , while the profit of firm 1 decreases first and then increases with d . 5.3 Comparison withtheNon‑Committed Policy Now compare the equilibrium values under the committed host-country policy with those of under the non-committed host-country policy. We denote the equilibrium values under the non-committed host-country policy by superscript N. Hence, they are equal to those under licensing for d≤d and those under FL for d>d as shown in Section4. For example, the equilibrium emission fee under the non-committed host-country policy is tN=tL for d≤d and tN=tFL for d>d . As Fig.2(a) shows, the emission fee under the committed policy is higher than that of under the non-committed policy, i.e. tC>tN , if and only if d<d1(≈ 24.032) .34 Compared to the non-committed policy, the pollution abatement is higher while pollutant emission is lower under the committed policy, as shown in Fig. 2(b) and 2(c) respectively. Figure2(d) shows that although firm 1 makes the market-entry decision after the committed emission fee, its profit is higher under the committed policy compared to the noncommitted policy if and only if d2(≈ 4.00676)<d<d3(≈ 42.8541) .35 Figure2(e) shows that the total output under the committed policy is lower than that of under the non-committed policy if d<d4(≈ 0.41446) or d<d<d5(≈ 6.68214 ) ,36 indicating that the committed policy makes the consumers worse off compared to the non-committed policy if d<d4 or d<d<d5 . The domestic welfare under the committed policy is higher than that of under the non-committed policy, as shown in Fig. 2(f). However, as the committed policy lowers the profit of firm 1 for d<d2 , it makes the world welfare worse off if and only if d<d<d6(≈ 2.47245 ) , as shown in Fig.2(g).37 34 d1 is the cutoff value of the pollution intensity for which the emission fee under the committed policy is the same to that of under the non-committed policy. 35 d2 and d3 are two cutoff values of the pollution intensity for which the profit of foreign firm under the committed policy is the same to that of under the non-committed policy. 36 d4 and d5 are two cutoff values of the pollution intensity for which the total output under the committed policy is the same to that of under the non-committed policy. 37 d6 is the cutoff value of the pollution intensity for which the world welfare under the committed policy is the same to that of under the non-committed policy. 2379 J.Cao, A.Mukherjee Fig. 2 Comparison between two policies with A – c = 1 2380 Foreign Direct Investment andTechnology Licensing inaPolluting… Based on the aforementioned comparisons, we have the following two results immediately. Proposition 5 Compared to the non-committed host-country policy, the committed hostcountry policy increases the pollution abatement and decreases the pollutant emission. However, the profit of firm 1 is higher under the committed policy than the non-committed policy if and only if ( d<)d 2 (≈ 4.00676)<d<d 3 (≈ 42.8541 ) . Proposition 6 Compared to the non-committed host-country policy, although the committed host-country policy increases the domestic welfare, it reduces the consumer surplus if d <d 4 (≈ 0.41446)or d <d<d 5 (≈ 6.68214),and reduces world welfare if d <d<d 6 (≈ 2.47245 ) . The intuitions for Propositions 5 and 6 are as follows. Firm 1 prefers licensing for d<d and FL for d>d under the non-committed host-country policy, while it prefers FL under the committed host-country policy. First, consider d<d . Here, both firms produce under the committed policy while only firm 2 produces under the non-committed policy. Compared to the non-committed policy, this tends to increase the output and pollutant emission for a given pollution abatement and emission fee, which induces the government to set a higher emission fee under the committed policy. As a result, firms choose a higher pollution abatement and a lower pollutant emission occurs under the committed policy compared to the non-committed policy. At the same time, higher product-market competition gives firm 1 the incentive to set a higher royalty rate under the committed policy.38 Although the product-market competition under the committed policy is higher, higher marginal cost due to a higher emission fee and a higher royalty rate makes the output under the committed policy lower compared to the non-committed policy for d<d4 . Although the consumer surplus under the committed policy may be lower, the lower environmental damage from the reduced pollutant emission makes the domestic welfare higher under the committed policy compared to the non-committed policy. Higher product-market competition under the committed policy helps to decrease the profit of firm 1 under the committed policy compared to the non-committed policy. However, this effect is dominated by the higher domestic welfare under the committed policy to make the world welfare under the committed policy higher compared to the non-committed policy. Now consider d>d , where both firms compete in the product-market under the noncommitted and committed policies. On the one hand, for a given royalty rate, the non-committed policy allows the host-country government to charge a higher emission fee compared to the committed policy by allowing to the government to move after firm 1.39 On the other hand, firm 1 tries to induce the host-country government to lower the emission 38 We find r C−rL= ( 297d 3 +303d 2 +1355d+997 ) (A−c) (121d+131) ( 27d2+54d+11 ) > 0 . 39 When both firms compete in the product market, the host-country government sets a high emission fee, making a2=q2 in equilibrium under the non-committed and committed policies. Thus, with q1 and q2 given by (19), a1=t and a2=q2 , for a given royalty rate that is less than (4d+15)(A−c) 7 ( 4 d+ 5 ) , the optimal emission fee under the non-committed policy, i.e., (4d+1)(A−c+r) 16d+25 , is higher than that of under the committed policy, i.e. (4d−1)(A−c)+(4d+5)r 4 ( 4 d+ 5 ) . At the same time, we get (4d+15)(A−c) 7 ( 4 d+ 5 ) >rFL >rC from (4d+15)(A−c) 7 ( 4 d+ 5 ) −rFL = (2d+11)(4d+1)(16d+25)(A−c) 7 ( 4 d+ 5 )( 144 d 2 + 380 d+ 233 ) > 0 and r FL −rC=(352d 3 +1162d 2 +2447d+2033)(A−c) ( 121 d+ 131 )( 144 d 2 + 380 d+ 233 ) > 0 . 2381 J.Cao, A.Mukherjee fee by charging a higher royalty rate under the non-committed policy compared to the committed policy. Since a higher pollution intensity tends to increase the emission fee, the royalty rate is more effective to reduce the emission fee if the pollution intensity is not very high. Hence, if the pollution intensity is not very high (i.e. d<d1 ), the emission fee is higher under the committed policy than the non-committed policy. The emission fee under the committed policy may be lower or higher than that of under the non-committed policy. However, if the pollution intensity is not very high (i.e. d<d<d5(<d1) ), although the royalty rate under the non-committed policy is higher than that of under the committed policy, the emission fee under the non-committed policy becomes much lower than that of under the committed policy to make the marginal cost lower under the former than the latter. As a result, the output and consumer surplus under the committed policy is lower compared to the non-committed policy for d<d<d5 . A higher royalty rate under the non-committed policy compared to the committed policy not only helps to reduce pollution abatement by firm 1 by lowering the emission fee, it also helps to reduce the pollution abatement by firm 2 by reducing its output. Thus, the pollution abatement under the committed policy is higher compared to the non-committed policy. This makes the pollutant emission lower under the committed policy than the noncommitted policy, even though the output under the former may be higher than that of under the latter. For a given royalty rate, the host-country government tends to set a lower emission fee under the committed policy compared to the non-committed policy, thus making the profit of firm 1 higher under the former than the latter. However, the higher royalty rate under the non-committed policy compared to the committed policy may increase the profit of firm 1 by lowering the emission fee and reducing the intensity of product-market competition. If the pollution intensity is low, the higher royalty rate is effective to reduce the emission fee significantly under the non-committed policy, thus making the profit of firm 1 higher under the noncommitted policy compared to the committed policy. If the pollution intensity is high, the higher royalty rate makes the profit of firm 1 higher under the non-committed policy compared to the committed policy by reducing the product-market competition under the former than the latter. Therefore, the profit of firm 1 is higher under the committed policy compared to the non-committed policy for moderate pollution intensity (i.e. d2<d<d3 ). The domestic welfare is higher under the committed policy compared to the non-committed policy since the committed policy helps to curb firm 1’s power to manipulate the emission fee through the royalty rate. Although the committed policy helps to increase the domestic welfare compared to the non-committed policy, the committed policy reduces the profit of firm 1 compared to the non-committed policy for low and high pollution intensity. This lower profit of firm 1 under the committed policy makes the world welfare lower under the committed policy compared to the non-committed policy if the pollution intensity is not high, i.e., d<d6 . 6 Stackelberg Competition Under FL We have considered so far that the firms behave like Cournot duopolists under all arrangements. In this section we want to show the implications of Stackelberg competition under FL where, in stage 3, firm 1 chooses output q1 and pollution abatement a1 like the Stackelberg leader and firm 2 chooses output q2 and pollution abatement a2 like the Stackelberg follower. We find that all our main results hold under Stackelberg competition. 2382 Foreign Direct Investment andTechnology Licensing inaPolluting… 6.1 Non‑Committed Policy 6.1.1 FL Under FL, the maximization problems for the firms under Stackelberg competition in stage 3 give the equilibrium outputs and the pollution abatements as: In stage 2, the government determines the emission fee to maximize (1) subject to (18), (19’) and (20’). As shown in Appendix 8, the equilibrium emission fee set by the government in stage 2 is as follows. As shown in Appendix 9, in stage 1, we can have the equilibrium royalty rate under FL as r FL = (6d+31)(A−c) 3 ( 18 d+ 23 ) . Accordingly, under FL, we get the equilibrium emission fee, pollution abatement, outputs, pollutant emission, fixed-fee, profits, domestic welfare and world welfare, as follows: By comparing the above-mentioned values with those under FDI as shown in Appendix 10, we find that Lemmas 3 and 4 hold with the exception that the pollution abatement under FL is higher compared to FDI only for d > √ 769− 13 36 . This happens since, compared to Cournot competition, the output and pollution abatement of firm 2 is lower. (19’) q 1= A−c−t 2 q2= A−c−2r−t 4 (20’) a 1=ta 2= { t, if q2≥t q2, if q2≤t (21’) t = ⎧ ⎪ ⎨ ⎪ ⎩ (33d+1)(A−c)−2(11d−1)r 121d+61 , if 0 ≤r≤(14−11d)(A−c ) 33(d+1) A−c−2r 5, if (14−11d)(A−c) 33(d+1)<r≤3(3−2d)(A−c) 18d+23 (6d+1)(A−c) 18d+23 , if 3(3−2d)(A−c) 18d+23 <r≤(6d+11)(A−c) 18d+23 t FL = (6d+1)(A−c) 18 d+ 23 aFL 1= (6d+1)(A−c) 18 d+ 23 aFL 2= (6d+1)(A−c) 3 ( 18 d+ 23 ) a FL = 4(6d+1)(A−c) 3 ( 18 d+ 23 ) qFL 1= (6d+11)(A−c) 18 d+ 23 qFL 2= (6d+1)(A−c) 3 ( 18 d+ 23 ) q FL = 2(12d+17)(A−c) 3(18d+23) qFL −aFL = 10(A−c) 18d+23 L FL =7(6d+1)2(A−c) 2 18(18d+23) 2𝜋FL 1=5(36d2+84d+73)(A−c)2 3(18d+23) 2𝜋FL 2= 0 W FL =2(144d2+453d+334)(A−c) 2 9 ( 18 d+ 23 ) 2GWFL =(828d2+1083d+1763)(A−c) 2 9 ( 18 d+ 23 ) 2 2383 J.Cao, A.Mukherjee 6.1.2 Equilibrium Choice andWelfare Implications Even if the firms compete like Stackelberg duopolists, firm 1 still prefers FL compared to FDI (see Appendix 10). We also get 𝜋L 1⋛𝜋FL 1 for d⋚ d S , where d S ≈1.26372 , indicating that the result shown in Proposition 1 also holds.40 As shown in Appendix 11, by comparing the consumer surplus and welfare under licensing with those under FL, we get that a result similar to Lemma 5 holds in this section with a different cutoff value ≈0.387691 . Hence, the results like Propositions 2 and 3 also hold even if the firms behave like Stackelberg duopolists under FL. 6.2 Committed Policy 6.2.1 FL The equilibrium outputs and the pollution abatements under FL in stage 3 are given by (19’) and (20’). Because q2⋛ t for r ⋚ A−c−5t 2 , we get a2=t , if the royalty rate determined by firm 1 is not greater than A−c−5t 2 ; otherwise a2=q2 . The equilibrium royalty rate under FL is r = 3(A−c)−7t 6 ,41 making a2=q2 and the profit of firm 1 under FL as 𝜋 1=3(A−c−t) 2 +8t2 12 , which is greater than that of under FDI or licensing. Hence, firm 1 prefers FL to both FDI and licensing. 6.2.2 Equilibrium In stage 1, the government determines the emission fee to maximize (1) with q1 and q2 given by (19’), a1 given by (20’), a2=q2 , r = 3(A−c)−7t 6 and 𝜋2=0 . We get the equilibrium emission fee under the committed policy as t C= 3(9d+5)(A−c) 81d+107 . The corresponding equilibrium pollution abatements, outputs, pollutant emission, royalty rate, fixed-fee, profits, domestic welfare and world welfare are as follows: a C 1 = 3(9d+5)(A−c) 81d+107 aC 2 = (9d+5)(A−c) 81d+107 aC= 4(9d+5)(A−c) 81d+107 q C 1 = (27d+46)(A−c) 81d+107 qC 2 = (9d+5)(A−c) 81d+107 qC= 3(12d+17)(A−c) 81d+107 q C−aC=31(A−c) 81d+107 rC=9(d+4)(A−c) 81d+107 LC=7(9d+5) 2 (A−c) 2 2(81d+107) 2 𝜋 C 1=(1215d2+3024d+2266)(A−c) 2 ( 81 d+ 107 ) 2𝜋C 2=0WC=(16d+33)(A−c) 2 2 ( 81 d+ 107 ) 41 If firm 1 chooses r ≤ A−c−5t 2 , it attains the maximum profit ( A−c−t) 2 4 ( < 3(A−c−t) 2 +8t 2 12 ) at r = A−c−5t 2 . 40 d S is a solution of the equation 972d4+2268d3+1287d2−2262d−6253 =0 , and is the cutoff value of the pollution intensity for which the profit of firm 1 under licensing is the same to that of under FL. 2384 Foreign Direct Investment andTechnology Licensing inaPolluting… where t 1= 16d(A−c)−(8d−3)r 64d+33 and r 0= 11(A−c) 32d+26 . The corresponding domestic welfare is: If the emission fee is set at t≥t0 , the domestic welfare is: In this situation, since 𝜕W 𝜕t = (4d+1)(A−c+r)−(16d+25)t 9 and 𝜕2 W 𝜕t 2=− 16d+25 9 < 0 , the equilibrium emission fee is: where t 2= (4d+1)(A−c+r) 16d+25 , r 1= 7(A−c) 16d+18 and r 2= 4(d+2)(A−c) 12d+17 . The condition r≤r2 is to guarantee q2≥0 if the royalty rate set in stage 1 is greater than r1 . The corresponding domestic welfare is: Comparing W1 with W2 , we have: Hence, the equilibrium emission fee set by the government in stage 2 will be: Appendix4: Proof oftheEquilibrium Royalty Rate insubSection4.3 We get t = { t1, if t1≤t0i.e. r≤r 0 t 0 , if t 1 >t 0 i.e. r>r 0 W 1= { 2(14d+11)(A−c) 2 −4(15d+11)(A−c)r+(55d+34)r 2 128d+66 −L, if r≤r 0 7(A−c)2−4(A−c)r−4(4d+1)r2 32 −L, if r>r0 W =(5−d)(A−c) 2 −2(d+4)(A−c)r−(d−5)r2+2(4d+1)(A−c+r)t−(16d+25)t2 18 − L t = { t0, if t2≤t0i.e. r≤r1 t 2 , if t 2 >t 0 i.e. r 1 <r≤r 2 W 2= { 7(A−c) 2 −4(A−c)r−4(4d+1)r2 32 −L, if r≤r1 7(d+2)(A−c)2−2(9d+11)(A−c)r+7(d+2)r2 32d+50 −L, if r>r 1 W 1−W2= ⎧ ⎪ ⎨ ⎪ ⎩ [(32d+26)r−11(A−c)]2 32(64d+33)>0, if r≤r0 0, if r0<r≤r1 −[2(8d+9)r−7(A−c)]2 512d+800 <0, if r>r1 . t = ⎧ ⎪ ⎨ ⎪ ⎩ t1, if 0 ≤r≤r0 t0, if r0<r≤r1 t2, if r1<r≤r2 . 2391 J.Cao, A.Mukherjee Since 𝜕𝜋 1 𝜕r > 0 for r≤r0 52 and for r0<r≤r1 , the equilibrium royalty rate must be greater than r1 . Thus, the first order condition gives the equilibrium royalty rate under FL as r FL = 2(d+2)(8d+23)(A−c) 144d 2 +380d+233 Appendix5: Proof ofLemma 3 It is obvious from the expressions of rFL and LFL that the equilibrium royalty rate and fixedfee under FDI and licensing are positive. We get: Appendix6: Proof ofLemma 4 We have: W FL −WF=(16128d5+93980d4+203740d3+199487d2+84594d+11175)(A−c) 2 2(9d+11)(144d 2 +380d+233) 2> 0 , and 𝜕𝜋 1 𝜕r= ⎧ ⎪ ⎨ ⎪ ⎩ (256d 2 +560d+77)(A−c)−2(320d 2 +520d+121)r (64d+33)2, if 0 ≤r≤r 0 r 2, if r0<r≤r1 4(d+2)(8d+23)(A−c)−2(144d2+380d+233)r (16 d +25)2, if r1<r≤r2. t FL −tF=− 2 ( 36d 3 +143d 2 +140d+45 ) (A−c) (9d+11) ( 144d2+380d+233 ) < 0 a FL −aF=2(72d 3 +232d 2 +211d+21)(A−c) ( 9 d+ 11 )( 144 d 2 + 380 d+ 233 ) > 0 ( qFL −aFL ) − ( qF−aF ) =3(18d 2 +23d+23)(A−c) (9d+11) ( 144d2+380d+233 ) > 0 𝜋 FL 1−𝜋F 1=(324d 4 +1332d 3 +2143d 2 +1486d+411)(A−c) 2 ( 9 d+ 11 ) 2 ( 144 d 2 + 380 d+ 233 ) > 0 q FL −qF= ( 144d 3 +518d 2 +491d+111 ) (A−c) (9d+11) ( 144d2+380d+233 ) > 0 GW FL −GWF=(d+1) ( 238464d 5 +1414620d4+3233308d3+3480575d2+1721494d+314451 ) (A−c) 2 2 ( 9d + 11 ) 2 ( 144d2 + 380d + 233 ) 2> 0 52 𝜕𝜋1 𝜕r reduces with r for r≤r0 but 𝜕𝜋 1 𝜕 r (r=r0)=2(32d 2 +52d−5)(A−c) ( 16 d+ 13 )( 64 d+ 33 ) > 0 2392 Foreign Direct Investment andTechnology Licensing inaPolluting… Appendix7: Proof ofLemma 5 (i) Since consumer surplus is 1 2 q 2 , the comparison of total outputs will help to compare the consumer surplus. We get q FL −qL= ( 432d4+2466d3+3647d2+696d−821 ) (A−c) ( 27d2+54d+11 )( 144d2+380d+233 ) ⋛ 0 for d⋛ , where is the solution of the equation 432d4+2466d3+3647d2+696d−821 =0 . (ii) W e h a v e W FL −WL=Φ(A−c) 2 2(27d 2 +54d+11) 2 (144d 2 +380d+233) 2> 0 , and GW FL −GWF=Ψ(A−c) 2 2(27d 2 +54d+11) 2 (144d 2 +380d+233) 2> 0 , where and Ψ=( 2146176d 8+ 19709244d 7+ 75636288d 6+ 153609759d 5+ 170556655d 4 + 92075690d 3+ 10554982d 2− 7498293d − 988485 ) > 0 for d > 1 3 Appendix8: Proof oftheEquilibrium Emission Fee insubSection6.1.1 Because q2⋛t for t ⋚t0= A−c−2r 5 , the government has two choices. One is to set t≤t0 making a2=t in stage 3, and the other is to set t≥t0 making a2=q2 in stage 3. Suppose the government sets t≤t0 . In this situation, the domestic welfare is. We get from 𝜕 W 𝜕t = ( 33d + 1 ) (A − c) − 2(11d − 1)r − (121d + 61) t 16 and 𝜕2 W 𝜕t 2=− 121d + 61 16 < 0 that the equilibrium emission fee is: where t 1= (33d+1)(A−c)−2(11d−1)r 121d+61 and r 0= (14−11d)(A−c) 33(d+1) in Section 6. The corresponding domestic welfare is: If the emission fee is set at t≥t0 , the domestic welfare is: In this situation, since 𝜕W 𝜕t = (6d+1)(A−c)−(18d+23)t 8 and 𝜕2 W 𝜕t 2=− 18d+23 8 < 0 , the equilibrium emission fee is: Φ =( 1306368d 8 +12734172d 7 +52193592d 6 +115039071d 5 + 145585273d4 + 105466450d3 + 42080906d2 + 9326963d + 1425861 ) > 0 W =(11 −9d)(A−c) 2 +4(3d−5)(A−c)r−4(d−3)r2+2(33d+1)(A−c)t−4(11d−1)rt −(121d+61)t2 32 − L t = { t1, if t1≤t0i.e. r≤r 0 t 0 , if t 1 >t 0 i.e. r>r 0 W 1= { (53d+42)(A−c) 2 −4(25d+19)(A−c)r+2(35d+23)r 2 2(121d+61)−L, if r≤r 0 (14−d)(A−c)2−2(3d+8)(A−c)r−(9d−1)r2 50 −L, if r>r0. W =(5−2d)(A−c) 2 −8(A−c)r+4r2+2(6d+1)(A−c)t−(18d+23)t2 16 − L 2393 J.Cao, A.Mukherjee where t 2= (6d+1)(A−c) 18d+23 , r 1= 3(3−2d)(A−c) 18d+23 and r 2= (6d+11)(A−c) 18d+23 in Section 6. The condition r≤r2 is to guarantee q2 ≥ 0 if the royalty rate set in stage 1 is greater than r1 . The corresponding domestic welfare is: Comparing W1 with W2 , we have: Hence, the equilibrium emission fee set by the government in stage 2 will be: Appendix9: Proof oftheEquilibrium Royalty Rate insubSection6.1.1 In stage 1, the maximization problem for firm 1 is the same as that in subSection4.3 with q1 and q2 given by (19’), a1 and a2 given by (20’), and t given by (21’). We get Since 𝜕𝜋 1 𝜕r > 0 for r≤r0 53 and for r0<r≤r1 , the equilibrium royalty rate must be greater than r 1= 3(3−2d)(A−c) 18d+23 . Thus, the first order condition gives the equilibrium royalty rate under FL as r FL = (6d+31)(A−c) 3 ( 18 d+ 23 ) , which is greater than r1 . Appendix10: Comparison Between FL andFDI insubSection6.1.1 It is obvious from the expressions of rFL and LFL that the equilibrium royalty rate and fixedfee under FL are positive. We also have: t = { t0, if t2≤t0i.e. r≤r1 t 2 , if t 2 >t 0 i.e. r 1 <r≤r 2 W 2={(14−d)(A−c) 2 −2(3d+8)(A−c)r−(9d−1)r 2 50 −L, if r≤r1 (14d+29)(A−c)2−2(18d+23)(A−c)r+(18d+23)r2 4 ( 18d + 23 ) −L, if r>r1 . W 1−W2= ⎧ ⎪ ⎨ ⎪ ⎩ [33(d+1)r+(11d−14)(A−c)] 2 50(121d+61)>0, if r≤r0 0, if r0<r≤r1 −[(18d+23)r+3(2d+3)(A−c)]2 100(18d+23)<0, if r>r1 . t = ⎧ ⎪ ⎨ ⎪ ⎩ t1, if 0 ≤r≤r0 t0, if r0<r≤r1 t2, if r1<r≤r2 . 𝜕𝜋 1 𝜕r= ⎧ ⎪ ⎨ ⎪ ⎩ 2(968d 2 +1837d+437)(A−c)−8(605d 2 +880d+239)r (121d+61)2, if 0 ≤r≤r 0 4(A−c)+2r 25 , if r0<r≤r1 (6d+31)(A−c)−3(18d+23)r 4(18 d +23), if r1<r≤r2. 53 𝜕𝜋1 𝜕r reduces with r for r≤r0 but 𝜕𝜋 1 𝜕 r (r=r0)=2(484d 2 +561d+17)(A−c) 33 (d+ 1 )( 121 d+ 61 ) > 0 2394 Foreign Direct Investment andTechnology Licensing inaPolluting… a FL −aF= ( 54d 2 +39d−25 ) (A−c) 3 ( 9 d+ 11 )( 18 d+ 23 ) ⋛ 0 for d ⋛ √ 769− 13 36 W FL −WF=(2268d 3 +6444d 2 +4839d+413)(A−c) 2 18(9d+11)(18d+23) 2> 0 , and Appendix11: Comparison Between Licensing andFL insubSection6.1.2 (i) We get q FL −qL= ( 162d 3 +621d 2 +372d−247 ) (A−c) 3(18d+23) ( 27d2+54d+11 ) ⋛ 0 for d⋛ , where is the solution of the equation 162d3+621d2+372d−247 =0 . (ii) W e h a v e W FL −WL=ΦS(A−c) 2 18(18d+23) 2 (27d 2 +54d+11) 2> 0 , and GW FL −GWF=Ψ S (A−c) 2 9(18 d +23)2(27 d 2+54 d +11)2> 0 , where and ΨS=( 131220d 6+ 791694d 5+ 1909737d 4+ 2130948d 3+ 760230d 2− 274026d − 43771 ) > 0 for d > 1 3 . Appendix12: The Market‑Entry Decision ofFirm 1 inEquilibrium insubSection7.2 Suppose the host-country government sets a high emission fee in stage 1 to make firm 1 undertaking FL in stage 2. In this case, with q 1=q2= A−c−t 3 , a1=a2=t and 𝜋2=0 , we get 𝜕W 𝜕t = 2[(8d+1)(A−c)−2(16d+11)t] 9 . Thus, under the constraint of t ≥(3 √ 2−1)(A−c ) 17 , the equilibrium emission fee is: t FL −tF=− 12(d+1)(A−c) ( 9 d+ 11 )( 18 d+ 23 ) < 0 ( qFL −aFL ) − ( qF−aF ) = 18(d+1)(A−c) ( 9 d+ 11 )( 18 d+ 23 ) > 0 𝜋 FL 1−𝜋F 1=(2916d4+8100d3+12645d2+14754d+7393)(A−c) 2 6 ( 9 d+ 11 ) 2 ( 18 d+ 23 ) 2> 0 q FL −qF= ( 54d2+93d+29 ) (A−c) 3 ( 9 d+ 11 )( 18 d+ 23 ) > 0 GW FL −GWF= ( 14580d 4 +53622d 3 +76185d 2 +50604d+13361 ) (A−c) 2 9(9d+11) 2 (18d+23) 2> 0 ΦS=(183708d6+1242216d5+3315735d4+4161780d3+2350926d2+539580d+118807)>0 2395 J.Cao, A.Mukherjee - The corresponding domestic welfare is: If a low emission fee is set in stage 1 so that firm 1 undertakes FDI or licensing, then with 𝜋2=0 , we have 𝜕W 𝜕t = (3d+1)(A−c)−(9d+11)t 4 . Hence, under the constraint of t ≤(3 √ 2−1)(A−c ) 17 , the equilibrium emission fee is: The corresponding domestic welfare is: Comparing WH with WL , we have This indicates that the host-country government prefers a high emission fee in stage 1 to make firm 1 undertaking FL in stage 2. Acknowledgements We thank two anonymous referees of this journal for comments and suggestions. Jiyun Cao acknowledges the financial support from the Humanities and Social Sciences Planning Fund from Chinese Ministry of Education (Grant No. 21YJA790001) and the Fundamental Research Funds for the Central Universities from Nankai University, Tianjin, China (Project Code: 63212010). The usual disclaimer applies. Data Availability Data sharing not applicable to this article as no datasets were generated or analysed during the current study. 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The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the t = ⎧ ⎪ ⎨ ⎪ ⎩ (3 √ 2−1)(A−c) 17 , if d<6 √ 2+ 5 8 (8d+1)(A−c) 2(16d+11), if d≥6√2+5 8 W H= ⎧ ⎪ ⎨ ⎪ ⎩ 2 �� 56 √ 2−81 � d+13 √ 2+7 � (A−c)2 289 , if d<6√2+ 5 8 (4d+5)(A−c)2 32d+22 , if d≥6 √ 2+5 8 t = ⎧ ⎪ ⎨ ⎪ ⎩ (3d+1)(A−c) 9d+11 , if d<12 √ 2+1 21 (3√2−1)(A−c) 17 , if d≥12√2+ 1 21 W L= ⎧ ⎪ ⎨ ⎪ ⎩ (d+3)(A−c)2 18d+22 , if d<12 √ 2+1 21 ��720√2−1124�d+336√2+92�(A−c)2 4624 , if d≥12 √ 2+ 1 21 W H−WL= ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ �� 2016 √ 2−2916 � d2+(2932 √ 2−3601)d+572 √ 2−559 � (A−c)2 578(9d+11)>0, for d<12 √ 2+1 21 ��268√2−367�d+20√2+33�(A−c)2 1156 >0, for 12√2+1 21 ≤d<6√2+5 8 ��4496−2880 √ 2�d2+�5035−3324 √ 2�d+2637−924 √ 2�(A−c)2 1156 ( 16 d+ 11 ) >0, for d≥6 √ 2+5 8 . 2396 Foreign Direct Investment andTechnology Licensing inaPolluting… material. 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