Location, taxation and governments: An exchange theory of intellectual property

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Location, taxation and governments: An exchange theory of intellectual property ✩ Sinclair Davidson a, Vijay Mohan a,b,∗, Jason Potts a a b

RMIT Blockchain Innovation Hub, RMIT University, Melbourne, Australia Lattice Analytics Pty Ltd, Melbourne, Australia

a r t i c l e

i n f o

Article history: Received 15 February 2018 Revised 12 November 2019 Accepted 13 November 2019 Available online xxx JEL classification: D4 F1 H2 H7 L1 K3

a b s t r a c t The standard economic model of intellectual property is an efficient property rights solution to a market failure problem of investment in a non-rival and non-excludable good. We propose an exchange theory of intellectual property based on a contracting approach in the context of market-making and enforcement of economic rights in exchange for monopoly taxation rights. We use a Hotelling (1929) type spatial model to show the relationship between location and pricing decisions of innovating firms under differing intellectual property, institutional quality, and taxation regimes. © 2019 Elsevier B.V. All rights reserved.

Keywords: Intellectual property Hotelling model Tax competition Tax harmonization Strategic trade policy

1. Introduction Intellectual property—including patents, copyright and trademarks—is a major component of modern economies.1 It is also an ancient institution: in the United Kingdom patent law dates from the Statute of Monopolies (1623) and copyright law from the Statute of Anne (1710). The practice of granting monopoly privileges to inventors was well established in Europe by the 15th Century. In 1450 Venetian glassmakers, for instance, could petition for 10 years of legal protection from potential infringers (May and Sell, 2006). Feudal institutions for intellectual property protection were consolidating by the late 18th century: France enacted patent law in 1791, the United States in 1793, and Austria, Russia, Netherlands, Prussia, Spain, Bavaria, Sweden and Saxonia between 1810 and 1843. The need for international conventions was already apparent by ✩ We thank an anonymous referee and the participants of the following conferences for valuable comments and suggestions: ITIF and US Chamber of Commerce, Washington DC, (May 2016); Western Economic Association, Washington DC (Nov 2016); Stern School of Business, New York University (Nov 2016); School of Economics, Macquarie University, Sydney (Aug 2017). ∗ Corresponding author. E-mail addresses: [email protected] (S. Davidson), [email protected] (V. Mohan), [email protected] (J. Potts). 1 Athreye and Yang (2011) and Antonipillai and Lee (2016) estimate that intellectual property-intensive industries contribute over one-third of US GDP.

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the time of the Great Exhibition in London in 1851, ideas that were subsequently realized in the Vienna Congress (1873),2 the Paris Convention (1883),3 and the Berne Convention (1886), which became the antecedents of the World Intellectual Property Organization (1967) and Trade-Related Aspects of Intellectual Property Rights (1995). As an institutional incentive to private investment in innovation, the economic significance of intellectual property has never really been in doubt.4 However, the exact institutional mechanism by which it works, and the sign of its effect, is less clear. Specifically, there is a perennial debate among economists caught between analytic representations of intellectual property as a natural law property right (and therefore an inducement mechanism) versus that of a monopoly privilege (and therefore a re-allocation mechanism). There are highly divergent perspectives on the economic nature of intellectual property even within the mainstream of modern economics. Some view intellectual property as an efficient property right in consequence of the economics of information (Arrow 1962; Nordhaus 1969; Posner 2005), while others have mounted vigorous theoretical and empirical critiques of this position, emphasizing the role of competitive markets (Boldrin and Levine, 2013). A similarly polarized debate has unfolded among legal scholars.5 As digital technologies and the internet saturate through economic life, along with the surprising success of open source production, these concerns with the economic status of intellectual property seem urgently modern. But as Machlup and Penrose (1950) make clear, these same debates raged along almost identical lines in the mid-19th century between the patent abolitionists (mostly economists)6 who were concerned about monopoly, and supporters of the patent system (mostly lawyers and industrialists) who emphasized the necessity of the institution to promote industry. The main arguments, then as now, followed four distinct but convergent lines: (1) natural property rights in ideas; (2) just reward for socially beneficial contributions; (3) an efficient mechanism to incentivize investment in industrial progress; (4) an effective mechanism to incentivize public disclosure of discoveries. The first two—natural property rights and social justice—argue for the moral rights of inventors, while the second two—incentives to invest and to reveal—argue that intellectual property is a politically expedient and economically efficient mechanism. The abolitionists, then as now, took the other side of these arguments: that there is no natural property in ideas; that other institutional mechanisms allow sufficient reward, or are more efficient and effective. Economists who otherwise agree on many things can nevertheless find themselves on entirely different sides of this ongoing controversy, brandishing different theoretical models and assumptions and appealing to different data sets and evidence.7 Irrespective of whether one thinks intellectual property too weak or too strong, the basic economics of this debate been largely conducted within a single framing of the problem: namely as a social contract theory approach to the institutions of intellectual property. The idea that intellectual property is an institutional mechanism chosen in order to benefit society (i.e. a social choice)—whether as individual or social justice, or as a welfare maximizing economic outcome—is a social contract way of thinking about the problem. In this paper, we examine an alternative perspective: an exchange view of intellectual property and intellectual property rights. We relax the standard assumption of a benevolent government simply maximizing social welfare. We build on insights into the emergence of the state first articulated by North (1981, 1990, 20 05), Barzel (20 02), Olson (1993, 20 0 0), and Sened (1997). North argues that the state exchanges services and protection for revenue—as do we. All of these authors to some extent or another explain how the state comes into existence, and how institutions evolve to constrain behavior. The state constrains private (mis)behavior through the deployment of violence, development of ideology, or paying off elites but, over time, itself becomes constrained in its own use of violence through the establishment of institutions such as the rule of law, constitutions, and democratic elections. As North (2005) recognizes, the state evolves from being extortionary to exchanging legal rights for revenue. Of course, it is not just states that provide order in exchange for revenue—Barzel (2002), for example, discusses ‘criminal states’ where organized crime provides order in exchange for revenue. Leeson (2014) provides multiple examples of private self-governance. We build upon all these insights to examine issues relating to intellectual property and intellectual property rights. Our contribution lies in the recognition of the existence of other states in the world. In the literature, other states are seen as being potential rivals to the existing state—competition to provide public goods and collect tax exists between states. The literature, however, is somewhat silent on the prospects of international trade—implicitly the literature assumes a world of autarky. When trade is discussed, in Barzel (2002) for example, it relates to the setting of standards, the building of roads, and the like. This ignores the scope for international trade, or international location decisions. It may well be that case that a firm operates under the protection of a state that is constrained by the rule of law, democratic elections, and other institutions that promote prosperity and economic growth exactly as North de-

2 The first international conference, which addressed the possibility of an international industrial property regime, was a conference on patent law, convened on the occasion of the 1873 Vienna International Exposition. The conference was motivated by exhibitors’ fears at the Festival of Inventions that non-signatories would steal their ideas. 3 The Paris Convention for the Protection of Industrial Property (1883) established a Union for the protection of industrial property among signatories. A key aspect was Priority Right, establishing that a claim filed in one member state of the union will conditionally be recognized in others. 4 Romer (1990), Besen and Raskind (1991), Helpman (1993), Gould and Gruben (1996) and Menell and Scotchmer (2007). 5 For example, Benkler (2008), Bessen and Meurer (2008) and Lemley (2004). 6 This group was championed by the staunchly free-trade supporting newspaper, The Economist. 7 Compare, for instance, Gallini and Scotchmer (2002), Romer (2002), Grossman et al. (2004), Hall (2005), Boldrin and Levine (2008) and Dourado and Tabarrok (2015).

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scribes. Yet what is to stop a foreign state from expropriating its property? Our argument is that the state must offer both domestic protection and international protection to its subjects. It is here that terminology proposed by Olson (1993, 20 0 0) becomes useful. He provocatively describes governments (or the state) as being ‘stationary bandits’. A ‘stationary bandit’ is a former ‘roving bandit’ that has settled down to establish a monopoly on theft in return for protecting their tributes, now called ‘tax-paying citizens’. Both Sened (1997) and Barzel (2002) explain how institutions, such as the rule of law, emerge to constrain the monopoly on theft (and violence) in this situation. A stationary bandit can be thought of as a state that has evolved from being extortionary to exchanging legal rights for revenue, whereas a roving bandit can be thought of as one that still engages in extortion or uncompensated expropriation. In this paper, we use the terminology of the stationary and roving bandit to establish the impact that this exchange of revenue for rights has on the location of innovative activity when there are multiple states involved. Specifically, once an innovative firm has chosen its location, it is affected not only by the taxation regime imposed by its domestic government, but also the tax regimes imposed by foreign governments. The relationship that the firm has with its own government, however, is different than that it has with other governments. With its own government, there is an explicit exchange of rights for revenue; in other words, to use Olson’s terminology, the domestic government is a stationary bandit. Other governments, with whom no such exchange relationship exists, are in essence roving bandits capable of appropriating the returns of the firm’s innovative activities through their tax policies that alter the incentives of their own firms. While the term ‘bandit’ can often carry negative connotations in terms of entities that appropriate wealth using violence or that engage in behavior outside the law, our own usage of the term is not intended to imply any such connotation (though it can do so if the context requires it). Rather, it simply recognizes that Olson’s terminology is useful in characterizing the different types of relationships that a firm can have with different governments.8 The possible application of a ‘stationary bandit model’ to intellectual property is presented in Davidson and Potts (2017), who argue that new ideas—of the sort that become patents, copyrights, and trademarks—emerge as economic rights; born global into a world of roving bandits. Barzel (2002) defines economic rights as being the ability to consume the services of an asset or to exchange it. Economic rights are distinct from legal rights. But intellectual property has public good characteristics (Arrow, 1962) in that it is (often) non-rival and (largely) non-excludable (but see Kealey, 1996). In order to profit from intellectual property entrepreneurs or firms need to hold legal rights to that intellectual property. The state needs to establish and enforce intellectual property rights – this differentiates a stationary bandit from a roving bandit. Barzel (2002) defines legal rights are existing where the state delineates property as belonging to particular individuals or institutions. As Sened (1997) explains, the creation and enforcement of legal rights is expensive and the state will only do if it gains some benefit from doing so. Sened suggests that states exchange legal rights for political support and taxation revenue. Our paper investigates the implications of this exchange view of intellectual property and intellectual property rights. To do so, we construct a simple model comprising two countries, two governments, and two firms in a linear-city (Hotelling, 1929) framework. The firms sell a horizontally differentiated product and are positioned at the two end-points of a unit interval, with consumers distributed uniformly along the unit line. In the long run, firms can choose the country where they locate; this is an important aspect of our model because it endogenizes the identity of the stationary bandit and the roving bandit for a firm. A firm that locates in one country forms an allegiance with the government there, which becomes its stationary bandit and the other government becomes (potentially) a roving bandit. The benefit of aligning with a particular government is the protection for new intellectual property that the government provides, while the cost is the tax that must be paid to the government. In keeping with the spirit of the stationary bandit model, we assume that governments are tax-revenue maximizing Leviathans. Once firms have chosen location, the possibility exists that a firm innovates. An innovating firm produces a product that is valued more by consumers. Consequently, there exists vertical differentiation as well as horizontal differentiation in our model.9 The probability that a firm innovates is exogenous, and allows us to distinguish between a strong and weak innovator. There are two possible avenues for dissipation of the fruits of an innovation: first, the other (non-innovating) firm may steal the intellectual property, which represents ‘private theft’; second, a roving bandit may attempt to appropriate some of the returns through its tax policy, which in the context of our model is a form of ‘public theft’.10 The extent to which private theft can occur is conditioned by a stationary bandit’s strength, which is equivalent in our model to the government’s power to enforce intellectual property rights domestically and abroad. This strength is treated as an exogenous

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In what follows, consequently, we use the terms ‘government’, ‘state’, and ‘bandit’ interchangeably. See Belleflamme and Peitz (2010; pp. 52 – 54) for the simple textbook approach for introducing quality differentials in a Hotelling model that we essentially follow in this paper. Kabiraj and Lee (2011) use this framework to examine licensing agreements for technology transfer in a duopoly, while Garella (2003) employs it to analyze the impact of minimum quality standards. In terms of context and structure, our paper perhaps has the closest resemblance to Adnan (2013), who outlines a model of innovation and intellectual property rights where a firm exerts effort to imitate an innovation while, at the same time, the innovator attempts to mitigate this by expending effort to mask the innovation. For an alternative approach to incorporating vertical differentiation in a Hotelling model, see Ferreira and Thisse (1996), who motivate vertical differentiation through access to different transportation costs. 10 If both firms locate in a single country, the role of a roving bandit disappears in our model. So does tax competition, and the single stationary bandit becomes a monopoly taxer of both firms. 9

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variable and permits us to differentiate between a strong bandit and a weak one. A stronger bandit is a government that is able to enforce a greater degree of intellectual property rights both domestically and abroad. Based on this simple model, we derive a number of interesting results that highlight the interplay between the strength of intellectual property rights, international tax competition, and firm location. These results are summarized below. First, we examine the case when firms locate in different countries, and show that a government’s ability to impose a higher tax is a function not only of the relative strength of the two governments, but also of the relative innovativeness of the two firms. So, it is quite possible that a stronger government sets lower taxes if it is the stationary bandit for a weak innovator. The same factors also determine an innovator’s ability to set prices. Thus, counterintuitively, an innovator may ex post end up charging a lower price than the other firm, even though it sells a product that consumers value more, if it is aligned with a weak stationary bandit. Our paper also shows that greater intellectual property protection by a government (or equivalently, an increase in the strength of a bandit) always benefits the innovator. While this is not surprising for an increase in intellectual property rights by an innovator’s own government (the stationary bandit), it is also true for an increase in the intellectual property right protection by the other government (the roving bandit). Second, we present the outcomes when both firms choose to locate in the same country. That country’s government is then a monopoly taxer of both firms, and there is no roving bandit for either firm. Intellectual property rights afforded by the government against private theft by a potential imitator now occurs domestically. The absence of the roving bandit ensures that, unlike the counterintuitive possibility with separate firm location, the innovator always sets a higher price. However, we show that in this case greater intellectual property right protection by a government can reduce the price paid by consumers as well as the tax rate paid by the firms, which presents a strong argument for greater intellectual property right protection domestically. Third, we examine the optimal location choices of firms. We show that if firms are relatively homogenous in terms of their likelihood of innovating, then aligning with the government that provides greater intellectual property rights is a dominant strategy for each firm, and the unique Nash equilibrium involves both firms locating in the same country. On the other hand, if the firms are sufficiently heterogeneous, then the weak innovator has the incentive to align with the weaker government, while the strong innovator aligns with the strong government. Finally, we analyze two forms of harmonization in government policy: harmonization of intellectual property rights and tax harmonization. When there is a harmonized intellectual property policy, we show that firms engage in an asymmetric matching pennies game when choosing location; consequently, there is no equilibrium in pure strategies. With tax harmonization, aligning with the government that provides greater intellectual property rights is a dominant strategy for each firm; unlike the outcome with competitive taxes, however, this occurs even when firms are heterogeneous. Tax harmonization, therefore, eliminates the incentives of the weak innovator to align with the weaker government and we expect greater agglomeration in a harmonized tax regime than a competitive one. The framework adopted in our paper is closely related to the literature on strategic trade policy (specifically, the thirdmarket export model in Brander and Spencer, 1985; Grossman and Eaton, 1986), and the idea of ‘public theft’ through tax policy in our model is similar to the profit-shifting role that subsidies and taxes play in the strategic trade literature. From that perspective, our paper can be viewed as extending the third-market export literature to incorporate innovation and intellectual property rights. There are two key insights that distinguish our model from the debates that have come before. The first is to emphasize the significance of taxation rights to a single government as the other side of the exchange to the award of intellectual property rights. This aspect is obscured in the social contract model, in which it appears that it is ‘as if’ other citizens are mutually agreeing not to copy (i.e. to limit their own freedoms) in return for the social benefit of the innovation. In this model, the government is just the agent of the mutual intentions of the citizens, and taxation is not a key part of the story: i.e. just an expedient in the transfer that could potentially be substituted by an alternative mechanism, such as prizes, were that to be more efficient.11 But in our model, monopoly taxation is the rationale for extending intellectual property rights. This is a market making model of intellectual property, rather than a market-failure model (Arrow, 1962). This market making model approach to intellectual property should also be differentiated from a crony capitalism or rentseeking model of intellectual property. George Stigler’s story of regulatory capture, for example, could be extended to explain intellectual property rights – here these rights would simply exist to generate monopoly returns. A better version of that argument follows North et al. (2009). In their argument, the state is a coalition of interests and not a single agent or stationary bandit. In a ‘natural state’ rents are generated and distributed to keep the peace amongst elites that comprise a ruling coalition. It is easy to imagine intellectual property rights – especially say, patents – performing this role.12 Monopoly rights are created and transferred to favored elites in return for political support and/or revenue. The North, Wallis and Weingast story is somewhat different in what they describe as being an open access order. In an open access order, the state is institutionally constrained from blatant manipulation of economic opportunity and the distribution of rents. Allocating rents to elites is undermined by ‘impersonality’. In such an environment the pursuit of rents is competitive, and Schumpeterian creative destruction ensures that rents are quickly eroded. North, Wallis and Weingast specifically argue that while the state

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Polanyi (1944), Kremer (1998) and Shavell and Van Ypersele (2001). Boldrin and Levine (2013), for example, make a strong argument that patent rights are over-protected. We baulk, however, at their description that ‘intellectual property’ is a ‘propaganda term’. 12

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in an open access economy may attempt to create rents (monopoly rights) their ability to do so in a manner that harms society is limited. Similarly, we do not argue that there is no cronyism or rent-seeking in intellectual property right allocations, but rather that they are just as likely, if not more so, to be market making. As alluded to previously, there is a vast discussion on the optimal level of intellectual property right rights. Specifically, we argue intellectual property rights as a market failure story is seriously incomplete and provides misleading policy recommendations (see Davidson and Potts, 2016a, 2016b, 2017). In the standard model of intellectual property, benevolent national governments grant a temporary monopoly privilege to protect the creative inventor citizen from the unscrupulous depredations of private competitors, who will steal their designs, or even consumers, such as teenagers pirating music. The social contract model once again obscures what is going on here, as it sets the problem up as if the main economic actors are the citizens, and governments are simply third-party enforcers of agreements between citizens. But in our model, governments can be roving bandits, and while private theft is a hazard of trade, so too is public theft (Ezell et al., 2016). A common example is the treatment of biopharma, routinely subject to outright theft, compulsory licensing, and other practices that diminish its value by those who seek to engage in trade (Wu and Ezell, 2016). Those engaged in economic production and trade need their own government (the stationary bandit) to protect them from other governments (roving bandits), and the stronger that roving bandits are, the stronger you need your stationary bandit to be. This model of intellectual property suggests that we should, therefore, observe a distinct link between the growth of ideas, the ability to protect them (i.e. to project force, to create and enforce rights), the location of innovative activity and expectation of tribute (tax). It also presents a new theory of imperial expansion in which the growth of ideas by domestic entrepreneurs provides the entrepreneurial bandit (the state) with the case for rational investment in military or naval capabilities for force projection in order to expand an institutionally inclusive empire in pursuit of a growing tax share of those opportunities for trade. The standard social contract-based theory of intellectual property, on the other hand, makes no such prediction about an interrelation between imperial venturing, intellectual property rights and global tax policy. The paper is organized as follows. In Section 2, we set up the basic Hotelling model that links intellectual property rights, tax competition and firm location. Section 3 then characterizes the outcome of market and tax competition for given location choices by the firms. Section 4 derives the equilibrium location choices by firms. Section 5 extends the model to examine the impact of intellectual property and tax harmonization. Section 6 concludes. 2. An exchange model of intellectual property in a Hotelling framework Consider a Hotelling type model with: (a) Two countries, A and B. In what follows, we refer to an arbitrary country as country m, where m ∈ {A, B}, and the other country as n. (b) Two governments, GA and GB , who are located at A and B, respectively. From country m’s perspective Gm is a stationary bandit and Gn is a roving bandit. (c) Two firms, F1 and F2 . We refer to an arbitrary firm as Fi , where i ∈ {1, 2}, and the other firm as Fj . Firms produce differentiated output that is sold to consumers who are dispersed globally. In other words, we consider the consumers as third markets, distinct from A and B. Following Mohan and Hazari (2012), we examine a simple Hotelling model, where third market consumers have tastes for the two types of output that are distributed uniformly along a unit interval [0, 1]. For concreteness, we suppose that along this consumer taste space, F1 is located at point 0 and F2 is located at point 1.13 Each consumer purchases one unit of output. If a consumer purchases from Fi , the consumer gets benefit vi and pays a price pi . Given that consumers vary in tastes for the two products, a consumer located at distance di from Fi ’s product location gets a utility:

u = vi − θ di − pi

(1)

Essentially, vi is sensitive to the quality of the output produced by Fi , while 1/θ captures the degree of substitutability between the two differentiated products. Consequently, even if the two firms produce output of the same quality (vi = v j ) and charge the same price ( pi = p j ), consumers will still prefer the output closest to their taste. This implies that there exists horizontal differentiation in the model that is based on the tastes of consumers for a particular product. On the other hand, if vi = vj there also exists vertical differentiation arising from quality differences. Firms can choose to locate in either country A or country B. We have in mind a situation in which capital is mobile in the long run, and firms can choose jurisdiction to maximize profits. As such, the possible outcomes are: • Fi locates in country m and Fj locates in country n, m = n • Both Fi and Fj locate in the same country m 13 In contrast to Mohan and Hazari (2012), which allows for only horizontal differentiation, in this paper we incorporate the possibility of vertical differentiation as well.

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It is evident that this results in four possible outcomes in terms of the ‘location game’ that firms play. A firm that chooses to locate in country m has to pay taxes, tm , to Gm . In return for the tax paid, the firm gets protection, domestically and internationally, over the preservation of any intellectual property it creates. Specifically, how much protection it gets depends on the government’s strength. Consider a situation where Fi locates in country m and Fj locates in country n; that is, the firms are located in different jurisdictions and are governed by different stationary bandits. Now suppose Fi comes up with an innovation that results in greater value generated for customers, and vi increases; innovation here, therefore, refers to improvements in product quality, and consequently affects consumer valuations of the firms’ products. Potentially, Fj can mimic this innovation and generate a similar increase in the value it offers for its customers. This mimicry can be prevented if Gm can exert influence over Gn to preserve property rights. We parameterize the strength of this (international) influence by a variable sm ∈ [0, 1]; greater the value that sm takes, less the extent to which Fj is able to mimic the value generated by other firm’s invention. So, intuitively, sm captures the extent to which a stationary bandit (Gm ) can protect its subject (Fi ) from intellectual property theft by Fj aligned with a roving bandit (Gn ). In contrast to the above situation, suppose both firms locate in country m. In this situation, when Fi innovates, the extent to which Fj can mimic the innovation in terms of adding value to its customers depends on the domestic strength, sdm ∈ [0, 1], that Gm has in enforcing protection for its innovator. Intuitively, sdm captures the strength a government has in protecting one of its subjects (Fi ) from theft by another of its subjects (Fj ). While it is quite possible that sdm = sm , to simplify matters, we assume in the subsequent analysis that a government’s international strength equals its domestic strength; that is, we assume that sdm = sm , ∀m ∈ {A, B}. It is worth emphasizing that in this model, strength (sm ) translates exclusively to the strength of intellectual property rights enforcement by the government. This strength is assumed to be exogenous, so one may question why the government does not endogenously choose the strength of intellectual property rights. Our answer to that is that, in reality, the intellectual property rights regime adopted by a government at any point in time is a complex function of historical economic and socio-political processes. Given the multitude of idiosyncratic factors and chance events that can drive these processes, altering an intellectual property rights regime is costly. For example, ensuring greater patent protection for pharmaceutical products in developing countries has considerable implications for the health of the population, and a government cannot enforce greater intellectual property rights without considerable political and monetary costs. Given this, and the essentially static nature of this study, we leave strength as being an exogenous phenomenon. The innovating firm (Fi ) located in country m provides value vi = v¯ to its customers. If Fj is not able to mimic the value generated by the innovation at all, it provides a baseline value v to its customers. Thus, v = v¯ − v is the maximum benefit to customers from the innovation. The actual value provided by the non-innovator (Fj ) to its customers depends on how much it is able to imitate the innovation, which in turn depends on sm .14 Specifically, it provides value v j = v + (1 − sm )(v¯ − v ) = v + (1 − sm ) v. So, to consider the two extreme cases, when Gm is the strongest possible bandit and sm = 1, it is evident that v j = v, which implies that Fj is prevented from mimicking the innovation to improve the value of the product it offers its customers; on the other hand, when Gm is the weakest possible bandit and sm = 0, it follows that v j = v¯ , and Gm is unable to exert influence internationally to prevent theft by Fj . Implicit in the above formulation is the assumption that the identity of the innovator does not matter in terms of the value of the innovation; that is to say, after the innovation the innovator always provides value v¯ to its customers, irrespective of whether the innovator is F1 or F2 . While this is not necessary for the analysis that follows, it does simplify the exposition. We do, however, allow for differences between the two firms in terms of their ability to innovate by assuming that the probability that F1 is the first to innovate is φ 1 , while the probability that F2 is the first to innovate is φ 2 . Assuming that innovation does occur with probability 1, we let φ1 = φ and φ2 = 1 − φ . States affect the innovation process in general, and the location of innovative activity in particular, in two ways: first, through the strength parameter, sm , they control theft of innovative ideas and, consequently, the competition between firms; secondly, they tax their subjects, which theoretically links tax policy to innovation policy. In keeping with the idea that bandits tax their subjects optimally, we assume that states are Leviathans and follow the objective of tax revenue maximization.15 The timeline is as follows: • At T = 1, F1 and F2 choose their country of location. • At T = 2, GA and GB announce (irrevocable) tax rates tA and tB , respectively. We assume that states can commit to these tax rates, and that the tax rates cannot be contractually dependent on innovation occurring. • At T = 3, one firm innovates, whose identity is revealed publicly.

14 Note that, given our assumption that sdm = sm , the value provided by Fj is not affected by Fj ’s location. If this assumption is dropped, the potential for imitation depends on sdm when the two firms are located in the same country. 15 While we simply assume that governments are revenue-maximizing Leviathans, we note there exists a strand of the strategic trade policy literature that shows that welfare-maximizing governments may find it strategically optimal under certain conditions to mimic Leviathan behaviour and set taxes rates consistent with revenue-maximization. The literature also explores actions such as delegation of tax setting authority to a policymaker (like a bureaucrat) to ensure that the strategy is credible. See, for example: Clarke and Collie (2008) and Mohan and Hazari (2012).

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• At T = 4, firms set prices, p1 and p2 , for their output conditional on their location, the identity of the innovator and tax rates. • At T = 5, consumers purchase the output. At T = 1 the two firms play a ‘location game’, where the pure strategy space for Fi , i ∈ {1, 2}, is the set Si = {LA , LB }, where LA refers to locate at country A and LB to locate at country B. So, the location game at T = 1 has four possible outcomes (in pure strategies): Case I: The outcome is {LA , LB } Case II: The outcome is {LB , LA } Case III: The outcome is {LA , LA } Case IV: The outcome is {LB , LB } The innovation at T = 3 bifurcates the sequence of events into the ex ante period (dates prior to innovation at T = 3) and the ex post period (dates following the innovation at T = 3). To ensure that both firms face a positive demand for all possible parametric ranges in all the equilibria that follow, we assume that 53 (v¯ − v ) < 3θ < (v¯ + v ); this parametric range is feasible as long as v < v¯ < 4v. When this assumption holds, all prices and tax rates are also positive at equilibrium. To maintain the focus on taxes and innovativeness of firms, we assume that firms have constant marginal cost of production, which we normalize to zero. Finally, we suppose that in all cases that the entire market is served; this allows for comparability between the various cases. The model is solved through backward induction. 3. Taxes and firm competition with fixed location We begin by examining the tax and competitive outcomes when location of firms is fixed; in other words, we examine Case I – Case IV individually. Intuitively, each case corresponds to a short run situation where firms have chosen their location, but are free to set prices. In a subsequent section, we will look at the overall long-run equilibrium when firms can choose location as well. 3.1. Firms locate in different countries Case I: In this case, F1 has located in country A and F2 has located in country B. At T = 3 one of two mutually exclusive events occur: (i) F1 (located in A) innovates first and F2 (located in B) imitates; ex ante, this occurs with probability φ . (ii) F2 (located in B) innovates first and F1 (located in A) imitates; ex ante, this occurs with probability 1 − φ . Consider (i) to begin with, so that F1 innovates at T = 3. At T = 5, a consumer located at x gets utility:

u = v¯ − θ x − p1 , if x buys from F1

(2a)

u = v + (1 − sA )v − θ (1 − x ) − p2 , if x buys from F2

(2b)

The indifferent consumer is:

x˜ =

1 ( θ + sA v + p2 − p1 ) 2θ

(2c)

It follows that the demands for the two firms’ outputs are:

d1 =

1 ( θ + sA v + p2 − p1 ) 2θ

(3a)

d2 =

1 ( θ − sA v + p1 − p2 ) 2θ

(3b)

At T = 4, and firms set prices, p1 and p2 , to maximize profits:

πi = di ( pi − tm ), for i ∈ {1, 2}

(4)

where m = A when i = 1, and m = B when i = 2 Solving for the optimal prices charged by the two firms, we get:

p1 =

1 (3θ + sA v + 2tA + tB ) 3

(5a)

p2 =

1 (3θ − sA v + 2tB + tA ) 3

(5b)

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Substituting these prices in (3a) and (3b):

d1 =

1 ( 3 θ + sA v + tB − tA ) 6θ

(6a)

d2 =

1 ( 3 θ − sA v + tA − tB ) 6θ

(6b)

Profits are:

πi = 2θ (di )2 for i ∈ {1, 2}

(7)

Now consider the outcomes for possibility (ii) above, when F2 innovates at T = 3. To differentiate this situation from the one where F1 innovates, we use the notation ‘^’ to signify that variables are realized contingent on F2 being the innovator. So, repeating the procedure at T = 5 and T = 4, we get:

  ˆ 5 a  5ˆ b   6ˆ a  

pˆ 1 = 13 (3θ − sB v + 2tA + tB ) pˆ 2 = 13 (3θ + sB v + 2tB + tA ) dˆ1 = 61θ (3θ − sB v + tB − tA ) dˆ2 = 1 (3θ + sB v + tA − tB ) 6θ

 2

πˆ i = 2θ dˆi

6ˆ b

for i ∈ {1, 2}.

(7ˆ )

At T = 2, GA and GB , being Leviathans, set taxes to maximize expected tax revenue. Specifically, Gm maximizes:

E {T Rm } =



 φ di + (1 − φ )dˆi tm , m ∈ {A, B}

(8)

where i = 1 when m = A, and i = 2 when m = B and E{.} is the expectations operator. Solving the tax game summarized by (8), we get the optimal taxes, tAI and tBI , where the superscript ‘I’ indicates the equilibrium values of variables corresponding to Case I. Lemma 1. Consider Case I. Let σ = (φ sA v − (1 − φ )sB v ). Equilibrium tax rates, prices, demand, profits and tax revenues are: (a) Tax rates: tAI = 13 (9θ + σ ) and tBI = 13 (9θ − σ ) (b) Demand: d1I = 181θ (9θ + 3sA v − 2σ ) and d2I = 181θ (9θ − 3sA v + 2σ ) dˆI = 1 (9θ − 3sB v − 2σ ) and dˆI = 1 (9θ + 3sB v + 2σ ) 1

18θ

2

18θ

(c) Price: pI1 = 19 (36θ + 3sA v + σ ) and pI2 = 19 (36θ − 3sA v − σ ) pˆI1 = 19 (36θ − 3sB v + σ ) and pˆI2 = 19 (36θ + 3sB v − σ ) I I d I and T I dˆI , m ∈ {A, B}  (d) Tax revenues (ex post): T RIm = tm Rm = tm i i I I I Expected tax revenues (ex ante): E {T Rm } = tm (φ di + (1 − φ )dˆiI )where i = 1 when m = A, and i = 2 when m = B (e) Profits (ex post): π I = 2θ (dI )2 and πˆ I = 2θ (dˆI )2 for i ∈ {1, 2} i

i

i

i

Expected Profits (ex ante): E {πiI } = 2θ [φ (diI )2 + (1 − φ )(dˆiI )2 ] We note that given the parametric ranges where sA , sB and φ all lie in the interval [0, 1], (φ sA − (1 − φ )sB ) ∈ [−1, 1]. Case II: This is similar to Case I, with the two firms locating in different countries; specifically, F1 is located in country B and F2 located in country A. The solution for this is, therefore, analogous to that of Case I, and we simply summarize the equilibrium outcomes for this case in Lemma 2 below. Lemma 2. Consider Case II. Let σ  = (φ sB v − (1 − φ )sA v ). Equilibrium tax rates, prices, demand, profits and tax revenues are: (a) Tax rates: tAII = 13 (9θ + σ  ) and tBII = 13 (9θ − σ  ) (b) Demand: d1II = 181θ (9θ + 3sB v − 2σ  ) and d2II = 181θ (9θ − 3sB v + 2σ  ) dˆ1II = 181θ (9θ − 3sA v − 2σ  ) and dˆ2II = 181θ (9θ + 3sA v + 2σ  )

(c) Price: pII1 = 19 (36θ + 3sB v + σ  ) and pII2 = 19 (36θ − 3sB v − σ  ) pˆII1 = 19 (36θ − 3sA v + σ  ) and pˆII2 = 19 (36θ + 3sA v − σ  ) II II d II and T II dˆII , m ∈ {A, B}  (d) Tax revenues (ex post): T RIIm = tm Rm = tm i i II (φ d II + (1 − φ )dˆII )where i = 1 when m = B, and i = 2 when m = A Expected tax revenues (ex ante):E {T RIIm } = tm i i (e) Profits (ex post): π II = 2θ (dII )2 and πˆ II = 2θ (dˆII )2 for i ∈ {1, 2} i

i

i

i

Expected Profits (ex ante): E {πiII } = 2θ [φ (diII )2 + (1 − φ )(dˆiII )2 ] We are now in a position to state some basic insights of the model given that firms locate in different countries. As mentioned before, this is relevant for analyzing short-run situations where firm location is fixed. We state these results in the context of Lemma 1 (and Case I). It is evident from Lemma 2 that similar results follow for Case II as well. Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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Proposition 1. Consider Case I, and the equilibrium described by Lemma 1. (a) Which country imposes a higher tax rate depends on the relative innovativeness of the two firms and the relative strength of the two governments. Specifically:

tAI

> I φ > sB t when < B 1 − φ < sA

(b) The firm that innovates at T = 3 captures a greater share of the market. That is:

d1I > d2I and dˆ2I > dˆ1I (c) Suppose σ > 0 holds. Then pI1 > pI2 is true, and the innovator F1 sets a higher price than the imitator F2 . However, pˆI2 > pˆI1 holds only if the probability that F2 innovates is high enough. Similarly, suppose σ < 0 holds. Then pˆI2 > pˆI1 is true, but pI1 > pI2 holds only if the probability that F1 innovates is high enough. (d) Suppose σ > 0 holds. Then T RIA > T RIB , and the country that houses the innovator (F1 ) receives higher tax revenues. I I I I However, T R > T R holds only if the probability that F innovates is high enough. Similarly, when σ < 0, T R > T R is true B

A

2

B

A

and the country that houses the innovator (F2 ) receives higher tax revenues. On the other hand, T RIA > T RIB follows only if the probability that F1 innovates is high enough. (e) The firm that innovates always receives a higher ex post profit:

π1I > π2I and πˆ 2I > πˆ 1I Proof: See Appendix Part (a) of the proposition suggests that innovativeness of the firms and strength of governments are substitutes when it comes to setting higher taxes. In general, tAI is higher than tBI when φ sA > (1 − φ )sB , and a strong government can compensate for a weak domestic innovator (and vice versa) to set higher taxes than the weaker government . Parts (b) and (e) suggest that the innovator benefits from receiving a higher market share (part (b)) and a higher profit (part (e)) than the imitator. Part (d) presents the interesting proposition that the country housing the innovator may not always receive higher tax revenues ex post than its counterpart that hosts the imitator. Similarly, part (c) suggests that, counter-intuitively, the innovator may end up charging a lower price than the imitator, even though it sells a product that consumers value more. To see why these counterintuitive possibilities may occur, suppose that country A hosts a firm that has a low likelihood of innovation (low φ ), and is governed by a weak bandit (low sA ). In this case, part (a) of the proposition suggests that tAI < tBI will hold, and at T = 2, GA will set a lower tax than GB to ensure future competitiveness. However, since innovation is a chance event, it is quite possible that F1 ends up being the innovator at T = 3. Since GA is also a weak government, it is unable to prevent intellectual property mimicking by F2 . From (5a) and (5b) we see that if the impact of the ex ante higher tax set by GB offsets the influence of a low sA , it is quite possible that the innovator sets a lower price than the other firm, even though it sells a more valuable product. Indeed, this occurs when the ex ante assessment of F1 being the innovator (φ ) is low enough. A similar intuition holds for tax revenues as well in this circumstance. In spite of housing the innovator, GA may collect a lower ex post tax revenue than GB . This occurs when the lower tax rate set by GA offsets the higher market share cornered by F1 by virtue of being the innovator. We now consider some comparative results. Proposition 2. Consider Case I, and the equilibrium described by Lemma 1. (a) An increase in the strength of a government increases its own tax rate and lowers the tax rate of the other government. (b) The innovator’s market share rises both when its stationary bandit enforces stronger intellectual property rights (the strength of its stationary bandit rises), as well as when the roving bandit increases intellectual property rights enforcement (the strength of the roving bandit increases). The imitator’s market share decreases both when the strength of its stationary bandit rises and when the strength of its roving bandit rises. (c) The price charged by a firm increases when its stationary bandit improves intellectual property rights (the strength of the stationary bandit rises) and falls when the roving bandit improves intellectual property rights (the strength of the roving bandit rises). (d) An increase in a given government’s strength raises its ex post tax revenues, and reduces the tax revenues of the other government, when the firm in the given government’s jurisdiction is the innovator. However, if the firm in the other government’s jurisdiction is the one to innovate, then an increase in the given government’s strength decreases its ex post tax revenues and has an ambiguous impact on the tax revenues of the other government. (e) The innovator’s ex post profit rises both when its stationary bandit enforces stronger intellectual property rights (the strength of its stationary bandit rises), as well as when the roving bandit increases intellectual property rights (the strength of the roving bandit increases). The imitator’s ex post profits decrease both when the strength of its stationary bandit rises and when the strength of its roving bandit rises. Proof: See Appendix. The results in part (a) and (c) are expected: an increase in the strength of a government increases its tax rate, which results in a higher price being charged by the firm in its jurisdiction. Part (b) is more interesting: the innovator’s market Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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share increases not only when its stationary bandit enforces higher intellectual property rights, but also when the roving bandit does. The former occurs because a higher strength of its stationary bandit increases the extent of vertical differentiation for the innovator, which allows it to charge a higher price (part (c)) and still command a higher market share. In the latter case, increased strength of the roving bandit results in the other firm being less competitive (part (c)), which allows greater market share to be captured by the innovator. Similar arguments hold for the imitator. Part (e) follows directly from the changes in parts (a)–(c). In part (d), the first statement is a consequence of the fact that an increased strength of a government increases (decreases) both its (the other government’s) tax rate and its firm’s (the other firm’s) market share when its own firm is the innovator (parts (a) and (b)). When the firm in the other jurisdiction is the innovator, however, these effects move in opposite directions, and may give rise to ambiguities. 3.2. Firms locate in the same country Case III: This focuses on a situation where both firms have located in the same country, A. As such, they are governed by, and pay taxes to, the same government, GA . Consequently, this case involves some manner of harmonization, since both firms receive the same rights for their innovation that is conditioned by sA , and pay the same tax rate, tA . This form of harmonization stems from the locational choices of firms at T = 1, and is a useful benchmark to contrast with other forms of harmonization that are based on cooperation and treaties between countries, which we examine in Section 5. Specifically, in cases I and II above, GA and GB may explicitly agree to harmonize taxes tA and tB , or harmonize the strength of intellectual property rights by equalizing sA and sB .16 As before, we consider the two separate cases when F1 innovates at T = 3, as opposed to when F2 innovates (and, as before, use ‘^’ to distinguish the latter scenario from the former). Solving for demand at T = 5 and price at T = 4 (along the same lines as Case I), conditional on the tax rate, tA , set by GA at T = 2 we get:

d1 =

1 1 (3θ + sA v ) and d2 = ( 3θ − sA v ) 6θ 6θ

1 1 dˆ1 = (3θ − sA v ) and dˆ2 = ( 3θ + sA v ) 6θ 6θ p1 =

1 1 (3θ + sA v + 3tA ) and p2 = (3θ − sA v + 3tA ) 3 3

pˆ 1 =

1 1 (3θ − sA v + 3tA ) and pˆ 2 = (3θ + sA v + 3tA ) 3 3

(9)

  9ˆ

(10)

   10

πi = 2θ (di )2 , i ∈ {1, 2}

(11)

 2 πˆ i = 2θ dˆi , i ∈ {1, 2}

  11

It is evident from (9) and (9ˆ ) that demands for the two products are independent of the tax rate set by the government. ) indicate This is because consumers care only about relative prices when choosing between the two firms, and (10) and (10 that taxes enter the price levels symmetrically for the two firms; consequently, relative prices are independent of taxes. Intuitively, the prices set by the two firms move identically in response to any change in taxes, which ensures that relative prices remain constant. In essence, the firm passes on a dollar increase in taxes as a dollar increase in prices due to the ) are also inelastic demand here with each consumer consuming exactly one unit of the output. The profits in (11) and (11 independent of the tax rate set by GA . At T = 2, GA sets tA to maximize expected tax revenues:





E {T RA } = φ tA (d1 + d2 ) + (1 − φ )tA dˆ1 + dˆ2 = tA

(12)

Eq. (12) suggests that since demand, net prices and profits of firms are independent of taxes, GA maximizes tax revenues simply by setting the tax rate as high as possible. In doing so, however, GA is constrained by the willingness to pay by the consumer. To factor this in, we note that the entire market is served in this model (by assumption). Consequently, the furthest consumer from each firm must receive at least zero utility. Focusing, first, on the case when F1 innovates, the consumer furthest from F1 and F2 is the indifferent consumer:

x˜ =

1 ( θ + sA v + p2 − p1 ) 2θ

(13)

16 We note that another way to think about this situation is to recognize that GA is now a monopolist dealing with competing firms; this then serves to contrast with a situation where firms merge in cases I and II above to create a monopoly that deals with competing governments (and is another avenue for extending this model).

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If this consumer buys from F1 , she receives utility:

u = v¯ − θ x˜ − p1

(14)

Setting this utility to zero, we get that this occurs when:

p1 + p2 = 2v¯ − θ − sA v

(15)

Similarly, if the consumer buys from F2 , her utility is:

u = v + (1 − sA )v − θ (1 − x˜) − p2

(16)

Setting this equal to zero yields the same condition as Eq. (15). Consequently, Eq. (15) represents the price constraint that GA must consider when raising tA . Now, from Eq. (10), we get that the sum of prices must also satisfy:

p1 + p2 = 2θ + 2tA

(17)

It is readily verified that the same price constraints (15) and (17) hold when F2 innovates as well. Equating (15) and (17) yields:

tAIII =

1 (2v¯ − 3θ − sA v ) 2

(18)

Lemma 3. Consider Case III. Equilibrium tax rates, prices, demand, profits and tax revenues are: (a)Tax rates: tAIII = 12 (2v¯ − 3θ − sA v ) (b) Demand: d1III = 61θ (3θ + sA v ) and d2III = 61θ (3θ − sA v ) dˆIII = 1 (3θ − sA v ) and dˆIII = 1 (3θ + sA v ) 1

6θ

6θ

2

(c) Price: pI1II = 16 (6v¯ − 3θ − sA v ) and pI2II = 16 (6v¯ − 3θ − 5sA v) pˆI1II = 16 (6v¯ − 3θ − 5sA v) and pˆI2II = 16 (6v¯ − 3θ − sA v ) III (d) Tax revenues (ex post): T RIII = t III and T R = t III A

A

A

Expected tax revenues (ex ante): E {T RIAII } = tAIII

A

(e) Profits (ex post): πiIII = 2θ (diIII )2 and πˆ iIII = 2θ (dˆiIII )2 for i ∈ {1, 2} Expected Profits (ex ante): E {π III } = 2θ [φ (dIII )2 + (1 − φ )(dˆIII )2 ] i

i

i

Case IV: Finally, consider Case IV, where both firms locate in country B. It is evident that the solution mirrors Case III. For future reference, we outline the equilibrium for Case IV below. Lemma 4. Consider Case IV. Equilibrium tax rates, prices, demand, profits and tax revenues are: (a) Tax rates: tBIV = 12 (2v¯ − 3θ − sB v ) (b) Demand: d1IV = 61θ (3θ + sB v ) and d2IV = 61θ (3θ − sB v ) dˆIV = 1 (3θ − sB v ) and dˆIV = 1 (3θ + sB v ) 1

6θ

6θ

2

(c) Price: pIV = 16 (6v¯ − 3θ − sB v ) and pIV = 16 (6v¯ − 3θ − 5sB v ) 1 2 1 IV = 1 (6v ¯ ¯ ˆ pˆIV = ( 6 v − 3 θ − 5 s v ) and p − 3θ − sB v ) B 6 6 1 2 IV IV  (d)Tax revenues (ex post): T R = T R = t IV B

B

B

Expected tax revenues (ex ante): E {T RIV } = tBIV B

(e)Profits (ex post): πiIV = 2θ (diIV )2 and πˆ iIV = 2θ (dˆiIV )2 for i ∈ {1, 2} Expected Profits (ex ante): E {π IV } = 2θ [φ (dIV )2 + (1 − φ )(dˆIV )2 ] i

i

i

Below we summarize some results that are implied by Lemma 3. While we focus on the case when both firms locate in country A, parallel results for Case IV readily follow. Proposition 3. Consider Case III, where both firms are located in country A. (a) The firm that innovates at T = 3 captures a greater share of the market:

d1III > d2III and dˆ2III > dˆ1III (b) The firm that innovates sets a higher price: III ˆIII ˆIII pIII 1 > p2 and p 2 > p 1

(c) The firm that innovates receives a higher ex post profit:

π1III > π2III and πˆ 2III > πˆ 1III These results follow directly from Lemma 3. The absence of any influence of a roving bandit makes the outcomes simpler and eliminates the indeterminacy inherent in the situation when both firms locate in different countries (as highlighted in Proposition 1). Clearly, when both firms locate in the same country, the superior outcomes (greater market share and greater profits) accrue to the innovator. Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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Next, we examine the impact that a stronger enforcement of intellectual property rights has on equilibrium variables. Proposition 4. Suppose both firms locate in the same country. Greater intellectual property rights enforcement: (a) Reduces the tax rate and lowers the tax revenues collected by the government. (b) Reduces prices paid by consumers in the third market. (c) Increases the market share and profits of the innovator at the expense of the imitator. Proof: See Appendix Part (c) of Proposition 4 is intuitive and expected: greater intellectual property rights favors the innovator both in terms of cornering a higher market share and gathering greater profits. Parts (a) and (b) suggest that greater intellectual property rights leads to lower tax rates (and lower tax revenues collected by the government), as well as lower prices for consumers in the third market. This, possibly counterintuitive result, presents a compelling case for stronger domestic intellectual property rights. The intuition behind these results is as follows. To fix ideas, suppose F1 is the innovator. As sA increases, the extent to which F2 is able to imitate the innovation decreases, and consequently, the value offered by F2 to consumers, v + (1 − sA ) v, also falls. As a result, the indifferent consumer (x˜ in Eq. (13)) moves further away from F1 (who is located at point 0) and closer to F2 (located at point 1); indeed, this movement is captured by a higher demand for F1 ’s now more attractive product (part (c) of Lemma 3). Since GA now extracts the surplus from an indifferent consumer who is further away from F1 (and buying a less valued product from F2 ), the maximum tax that GA can charge (and continue to ensure that the entire market is served) falls. Strategic complementarity between the firms then ensures that prices of both firms fall, and reflects the lower cost they have due to lower taxes.

4. Location choice We now consider the location choice of firms under certain parametric restrictions. Proposition 1(a) emphasized that equilibrium taxes (and consequently other endogenous variables) are sensitive to both the relative innovativeness of the two firms and the relative strength of governments. Essentially, a firm’s innovativeness and the strength of the government it is allied with are substitutes in terms of their impact on taxes. While this presents a rich array of possibilities, it nevertheless complicates our attempt to emphasize the importance of government strength on locational choices; consequently, we assume that firms are equally innovative (that is, φ = 12 ). Subsequently, we allow for one firm to be a better innovator to check the robustness of the equilibrium to this change. Second, without loss of generality, we suppose that GA is the stronger government (sA > sB ). With these assumptions in place, we examine the optimal choice of location by firms at T = 1. Recall that each firm has a pure strategy space {LA , LB } in this location game. Proposition 5 below summarizes the outcomes. Proposition 5. Suppose φ = 12 and sA > sB . Then, LA is a dominant strategy for both F1 and F2 and {LA , LA } is the unique Nash equilibrium of the location game. Proof: See Appendix Proposition 5 suggests that when firms are similar in terms of innovativeness, they will gravitate towards the stronger government. This is intuitive. If both firms are equally likely to innovate, they both prefer the high intellectual property rights afforded by the stronger government. In this instance, forming an alliance with the weaker government is counterproductive for a firm in two ways: first, the weaker government affords less protection from private theft if the firm were to innovate (which occurs with a 50 percent chance in Proposition 5); second, if the other firms allies with the stronger government, the stronger government becomes a roving bandit engaging in ’public theft’. The above discussion indicates, intuitively, that the weaker government becomes more attractive for a firm when its innovativeness is relatively low. In this case, the probability that the firm will innovate is relatively low and, consequently, the chances that the firm will require the protection of a stronger government are lower. At the same time, by aligning with the weaker government, the firm now benefits from the public theft carried out by the government as a roving bandit. While we do not undertake a detailed examination of outcomes for every possible parametric combination, we do capture the intuition described here in the proposition below, since this enables some interesting comparison with outcomes established in subsequent sections. Proposition 6. Suppose, without loss of generality, that F1 is the more innovative firm (so that φ > 12 ) and that sA > sB . For high enough φ , the less innovative firm (F2 ) has the incentive to deviate away from the outcome {LA , LA } as long as GA is not too strong, while the more innovative firm (F1 ) does not. Proof: See Appendix Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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5. Harmonization through treaties, or how governments collude17 We now consider outcomes when governments collude through intellectual property and tax harmonization. As pointed out in Section 3, there are two ways in which firms can face a harmonized set of intellectual property rights and tax rules. The first is by locational choice of firms: if both firms choose the same location endogenously, they are governed by the same government and are, therefore, subject to the same intellectual property rights and tax rules. Indeed, in Section IV we showed that if the firms are similar in terms of innovativeness, they agglomerate in the country governed by the stronger (now monopoly) government. The second is through explicit cooperation by governments that results in harmonized intellectual property or tax rules; as such, firms are exogenously subject to these harmonized rules. In order to investigate the impact of such cooperation between governments on the locational choice of firms, we assume in this section that decision to harmonize has been (irrevocably) put in place (at say T = 0) before firms choose their location at T = 1.18 5.1. Intellectual property harmonization Suppose at T = 0 governments agree to harmonize intellectual property rights rules leading to similar strengths of intellectual property enforcement. The harmonization results in governments now sharing the same strength sA = sB = s. Given that we have assumed that the governments’ strengths are exogenous in the previous sections, it is worthwhile pausing to clarify how such harmonization is feasible. As outlined in Section 2, our motivation for modeling government strength as an exogenous phenomenon stems from the fact that this strength is a complex function of historical economic and sociopolitical processes. In keeping with this motivation, this section, essentially, examines a situation when these complex processes have resulted in a harmonized intellectual property regime at T = 0, where the now common strength is exogenously equal to s. We allow for the innovativeness between firms to differ; without loss of generality we suppose that F1 is the more innovative firm by assuming that φ > 12 .19 The solution to the model remains the same as Section 3, with the only change being that sA = sB = s holds in the lemmas in Section 3. This change yields σ = σ  = (2φ − 1 )sv > 0 in Lemmas 1 and 2. Proposition 7. Suppose φ > firms at t = 1.

1 2

and sA = sB = s. There exists no pure strategy Nash equilibrium in the location game between

Proof: See Appendix The proof of Proposition 7 highlights the stark contrast between the locational preferences of the more innovative firm (F1 ) and the less innovative one (F2 ) in response to a harmonized intellectual property regime. Specifically, the more innovative firm always prefers agglomeration, since this reduces profit dissipation through the presence of a roving bandit following the (more likely) innovation by the firm. On the other hand, the less innovative firm always prefers heterogeneous location choices by the two firms, since this allows the firm to increase its profits through the actions of a roving bandit following the (more likely) innovation by the other firm. Overall, Proposition 7 indicates that harmonization of intellectual property right rules will result in a location game that resembles an asymmetric matching pennies game, with no clear incentives for firm agglomeration or separation emerging in equilibrium. 5.2. Tax harmonization We now consider the impact of a tax harmonization agreement in place before firms choose location at T = 1. The agreement implies that GA and GB jointly set taxes tA = tB = τ at T = 2 when firms choose different locations at T = 1. Other than that, the model remains the same as the one described in Section 2. In general, at T = 2, governments GA and GB may cooperate over the tax setting process based on a variety of possible shared objectives. In keeping with the assumption that the governments are Leviathans, however, we assume that the taxes are set to maximize joint tax revenues, subject to the constraint that the entire market is served. Given that all cases now involve harmonized taxes, it is useful to summarize the difference between Cases I and II on the one hand, and Cases III and IV on the other. Cases III and IV remain identical to Section 3 (having equilibria summarized 17 Our paper thus far has focused to a large extent on the relationship between firms and governments. In this section, we extend the analysis to include cooperation between governments. Throughout this paper, we suppose that firms are competitive, and do not cooperate. This need not be so. Specifically, firms can also cooperate (even if governments do not) in different ways: through the formation of cartels, or with the innovator licensing the innovation to the other firm, either through a fixed fee, a royalty, or a two-part pricing scheme. Moreover, there exists different information, bargaining and contractual structures under which this cooperation may take place; for example, the innovator may possess more information on the value of the innovation than the other firm, or licensing arrangements may involve incomplete contracts. Given the rich set of theoretical possibilities, cooperation between firms is not examined in-depth in this paper. Nevertheless, cross-border acquisitions and the licensing of IP across countries are commonplace in the real world. These deserve closer examination in our framework and represent an interesting area for future research. We thank an anonymous referee for directing our attention to this. 18 We do not examine the incentives for governments to cooperate in this paper; rather, our focus is on establishing the impact on firm choices when such cooperation is undertaken. 19 It is evident from Section 3 that sA = sB = s and φ = 12 would make the firms indifferent between governments and location.

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by Lemmas 3 and 4), with both firms being governed by the same government, and therefore being subject to harmonized tax rates as well as harmonized intellectual property right strengths. Cases I and II now share this feature of harmonized tax rates; however, firms are aligned with different governments, which affects the equilibria relative to Lemmas 3 and 4. We proceed in a manner similar to Section 3, by considering each location outcome in succession. Case IH: F1 has located in country A and F2 has located in country B. The demand for the output at T = 5 is given by (3a) and (3b) when F1 innovates, and by parallel expressions when F2 innovates. At T = 4, firms set prices to maximize profits:

πi = d i ( p i − τ )

(19)

When F1 innovates, the outcomes are:

d1 =

1 1 (3θ + sA v) and d2 = ( 3θ − sA v ) 6θ 6θ

(20)

p1 =

1 1 (3θ + sA v + 3τ ) and p2 = (3θ − sA v + 3τ ) 3 3

(21)

πi = 2θ (di )2 for i ∈ {1, 2}

(22)

We note that demand is independent of taxes in this case. This occurs because taxes enters prices symmetrically (Eq. (21)), and is eliminated from consumer consideration when they compare relative prices. Similarly, when F2 innovates at T = 3, we have:

   20 

dˆ2 = 61θ (3θ − sB v ) and dˆ2 = 61θ (3θ + sB v ) pˆ 1 = 13 (3θ − sB v + 3τ ) and pˆ 2 = 13 (3θ + sB v + 3τ )

 2

πˆ i = 2θ dˆi

 21

   22

for i ∈ {1, 2}

Now consider the expected joint tax revenue for the governments at T = 2:





E {T R} = φτ [d1 + d2 ] + (1 − φ )τ dˆ1 + dˆ2 = τ

(23)

In a manner similar to Cases III and IV in Section 3 (see Eq. (12)), the two governments set taxes as high as possible, constrained only by the desire to serve the entire market. Unlike Cases III and IV, however, the maximum tax they can charge while meeting this constraint when F1 innovates is not the same as the maximum tax that they can charge when F2 innovates due to the differing bandit strengths associated with these two innovation possibilities. To see the impact of this, suppose F1 innovates. Following the procedure similar to Case III in Section 3, we find that the maximum harmonized tax the governments can charge (and still serve the entire market) when F1 innovates is τ = 12 (2v¯ − 3θ − sA v ). Similarly, the maximum harmonized tax rate they can set when F2 innovates is τˆ = 12 (2v¯ − 3θ − sB v ). Now, since this harmonized tax must be set before the outcome of the innovation process is known, given the constraint that the entire market is served in all contingencies, the binding harmonized tax satisfies:

τ IH = min {τ , τˆ }.

(24)

As before, without loss of generality, if we suppose that sA > sB , then τ IH =

1 ¯ 2 ( 2v − 3θ

− sA v ), and Lemma 5 follows.

Lemma 5. Consider Case IH, and suppose that sA > sB . Equilibrium tax rates, prices, demand, profits and tax revenues are: (a) Tax rates: τ IH = 12 (2v¯ − 3θ − sA v ) (b) Demand: d1IH = 61θ (3θ + sA v ) and d2IH = 61θ (3θ − sA v ) dˆIH = 1 (3θ − sB v ) and dˆIH = 1 (3θ + sB v ) 1

6θ

6θ

2

(c) Price: pIH = 16 (6v¯ − 3θ − sA v ) and pIH = 16 (6v¯ − 3θ − 5sA v) 1 2 1 IH IH pˆ 1 = 6 [6v − 3θ − (3sA + 2sB )v] and pˆ 2 = 16 [6v¯ − 3θ − (3sA − 2sB )v] IH (d) Joint tax revenues (ex post): T RIH = T R = τ IH

Expected tax revenues (ex ante): E {T RIH } = τ IH (e) Profits (ex post): πiIH = 2θ (diIH )2 and πˆ iIH = 2θ (dˆiIH )2 for i ∈ {1, 2} Expected Profits (ex ante): E {π IH } = 2θ [φ (dIH )2 + (1 − φ )(dˆIH )2 ] i

i

i

Comparing this to Case III, we can see the similarities and differences between the two. It is evident that the harmonized tax rate (Lemma 5(a)) is the same as the tax rate that the monopoly government GA would have charged had both firms located in country A (Lemma 3(a)). Similarly, the joint tax revenue collected by the government through harmonization (Lemma 5(d)) is identical to the tax revenue collected by the monopolist government (Lemma 3(d)). The ex post demands and prices in the two cases (parts (b) and (c) in Lemmas 5 and 3) differ, however, which is the main consequence of the firms being located in different countries in Lemma 5 as opposed to being located in the same country in Lemma 3. Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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Case IIH: F2 has located in country A and F1 has located in country B. This yields parallel results to Case IH, with the locations of F1 and F2 reversed. The outcome for this case is summarized in Lemma 6 below: Lemma 6. Consider Case IIH, and suppose that sA > sB . Equilibrium tax rates, prices, demand, profits and tax revenues are: (a) Tax rates: τ IIH = 12 (2v¯ − 3θ − sA v ) (b) Demand: d1IIH = 61θ (3θ + sB v ) and d2IIH = 61θ (3θ − sB v ) dˆIIH = 1 (3θ − sA v ) and dˆIIH = 1 (3θ + sA v ) 1

6θ

6θ

2

(c) Price: pI1IH = 16 [6v¯ − 3θ − (3sA − 2sB )v] and pIIH = 16 [6v − 3θ − (3sA + 2sB )v] 2 pˆI1IH = 16 (6v¯ − 3θ − 5sA v) and pˆI2IH = 16 (6v¯ − 3θ − sA v ) IIH (d) Joint tax revenues (ex post): T RIIH = T R = τ IIH

Expected tax revenues (ex ante): E {T RIH } = τ IIH (e) Profits (ex post): πiIIH = 2θ (diIIH )2 and πˆ iIIH = 2θ (dˆiIIH )2 for i ∈ {1, 2} Expected Profits (ex ante): E {π IIH } = 2θ [φ (dIIH )2 + (1 − φ )(dˆIIH )2 ] i

i

i

It is evident from Lemmas 5 and 6 that the optimal harmonized tax rate depends only on the strength of the two governments, and not on the location choices or innovativeness of firms. Consequently, when sA > sB , τ IH = τ IIH = 1 ¯ 2 (2v − 3θ − sA v ), and the harmonized tax rate always equals the one the stronger government would set if both firms were to locate in the stronger government’s jurisdiction (Lemma 3). We turn, next, to the optimal location choices of firms with harmonized taxes in place. Proposition 8. Consider a situation when both governments have agreed to harmonize taxes. Suppose that sA > sB . In this situation, LA is a dominant strategy for both F1 and F2 and {LA , LA } is the unique Nash equilibrium of the location game. Proof: See Appendix Proposition 8 establishes, like Proposition 5, the attractiveness of the stronger government for both firms. However, contrasting Proposition 8 with Proposition 6, we see that the result in Proposition 8 holds for all φ ∈ [ 21 , 1]. Intuitively, tax harmonization destroys the attractiveness of the weak government for the weak innovator. In Proposition 6, the firm less likely to innovate finds it attractive to locate with the weaker government to take advantage of the lower tax and, consequently, reap the benefits of public theft by a roving bandit. With harmonized taxes, this public theft can no longer occur and the weak innovator has no benefit from forging an alliance with the weak government. 6. Conclusion In the standard economic analysis of intellectual property, the government is an agent for the collective will of the people as they seek to resolve the market failure problem of R&D investment (Arrow, 1962) by creating and enforcing an institutional mechanism to maximize their collective welfare by creating the incentive of monopoly rents through the mechanism of intellectual property rights. This formulation makes sense within a single nation state, but in a global economy of creative goods and services in which agents who produce ideas can locate anywhere, and who gain by expanding the size of their market beyond the boundaries of the nation state, then this implies a fundamentally different understanding of the nature of intellectual property. Rather than a monopoly rent to resolve a market failure problem within a nation state, intellectual property rights are a form of exchange relation between an entrepreneur and a strong government who offers legal rights in exchange for a share of total revenue from an expanded market (tax). We have developed a formal model that examines the relationship between the innovativeness and location of firms, the strength of governments (ability to governments to enforce intellectual property), and international tax setting. The standard social contract-based theory of intellectual property and intellectual property rights, on the other hand, does not identify these linkages in a precise manner. The propositions developed in the paper highlight the importance of the exchange view of innovation in understanding the nature of innovative activity and intellectual property in a global context. In doing so, we hope to provide some impetus for an empirical investigation of the importance of a regulatory strength for explaining the trends and location of innovative activity. Appendix I Proof of Proposition 1. (a) This follows directly from Lemma 1(a); specifically, tAI > < tB iff σ

φ > sB rearranged either to yield 1− φ < sA or, equivalently,

φ >< sAs+AsB .

> <0

. The condition σ

> <0

can be

(b) From Lemma 1(b), d1I > d2I if (3 − 2φ )sA + 2(1 − φ )sB > 0, which is true since φ < 1. Similarly, we have that dˆ2I > dˆ1I if (3 − 2(1 − φ ))sB + 2φ sA > 0, which always holds. (c) From Lemma 1(c), we have that: pI1 − pI2 = 29 (3sA v + σ ) and pˆI2 − pˆI1 = 29 (3sB v − σ ) Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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So, when σ > 0, pI1 − pI2 > 0 holds. However, pˆI2 − pˆI1 > 0 requires that 3sB v > σ , which translates to (1 − φ ) > Similarly, when σ < 0, pˆI2 − pˆI1 > 0 is true, but pI1 − pI2 > 0 is true only if φ >

sB −3sA sA +sB .

sA −3sB sA +sB .

I I (d) Suppose σ > 0. Then, tAI > tBI (part (a) above) and d1I > d2I (part (b)); consequently, T RIA > T RIB . For T RB > T RA to be I I I I I I I I I I I ˆ ˆ ˆ ˆ ˆ true, we need that tB d2 > tA d1 ; but, while d2 > d1 holds (part (b)), we have that tB < tA (part (a)), so that tB d2 > tA dˆ1I need not necessarily hold. To examine this further, we note that d1I = 61θ (tAI + 3sA v − 3σ ) and d2I = 61θ (tBI − 3sA v + 3σ ). Plugging I I I I s −3s this back into the definitions of T R and T R and simplifying, we see that T R > T R holds only (1 − φ ) > A B . Analogous B

A

B

arguments hold when σ < 0. (e) This follows directly from Lemma 1(e) and part (b) of this proposition. 

A

sA +sB

∂tI ∂ tBI φv Proof of Proposition 2. (a) From Lemma 1(a): ∂ sA = φv 3 > 0 and ∂ sA = − 3 < 0. Similar results hold for changes in sB . A ∂ dI

∂ d1I 1 ∂ sB = 9θ v (1 − φ ) ≥ 0. Thus, the innova∂ dI ∂ dI tor’s share improves when either bandit has greater strength. For the non-innovator, ∂ s 2 = − 181θ v(3 − 2φ ) < 0 and ∂ s 2 = B A

(b) Suppose F1 innovates. From Lemma 1(b): ∂ s 1 = A

1 18θ

v(3 − 2φ ) > 0 and

− 91θ v(1 − φ ) ≤ 0. Similar arguments hold when F2 innovates. ∂ pI

∂ pˆI

(c) Consider F1 . From Lemma 1(c), ∂ s 1 = 19 v(3 + φ ) > 0 and ∂ s 1 = 19 vφ > 0. So, F1 charges a higher price when the A A strength of its stationary bandit rises, irrespective of whether F1 innovates or not. Similar analysis holds for F2 . (d) Consider GA . If F1 (the firm in GA ’s jurisdiction) innovates the ex post tax revenues are T RIA and T RIB for GA and GB , respectively. From Lemma 1(d):

∂ T RIA ∂tI ∂ d1I = d1I A + tAI >0 ∂ sA ∂ sA ∂ sA ∂ T RIB ∂tI ∂ d2I = d2I B + tBI <0 ∂ sA ∂ sA ∂ sA The signs above follow directly from parts (a) and (b) of this proposition. This proves the first part of the proposition. Suppose now that F2 (the firm in GB ’s jurisdiction) innovates. I

∂tI ∂ dˆ1I ∂ TRA φv = dˆ1I A + tAI =− ( 9θ + 3sB v + 4σ ) < 0 ∂ sA ∂ sA ∂ sA 54θ I

∂tI ∂ dˆ2I ∂ TRB φv = dˆ2I B + tBI = ( 9θ − 3sB v − 4σ ) ∂ sA ∂ sA ∂ sA 54θ I

I

∂ TR

∂ TR

While we can sign ∂ s A given our modeling assumption that 3θ > 53 v, this condition is not sufficient to sign ∂ s B for all A A parametric ranges. The impact of a change in sA on equilibrium revenues of GB is, therefore, indeterminate. Similar arguments hold for a change in sB . (e) This follows directly from Lemma 1(e) and part (b) of this proposition.  Proof of Proposition 4. We show this for Case III. Analogous arguments hold for Case IV. ∂ t III

(a) From Lemma 3(a) and (d): ∂ sA = − 21 v < 0 A ∂ pIII

∂ pˆIII

∂ pIII

∂ pˆIII

∂ d III

∂ dˆIII

∂ d III

∂ dˆIII

(b) From Lemma 3(c): ∂ s1 = ∂ s2 = − 61 v < 0 and ∂ s2 = ∂ s1 = − 56 v < 0 A A A A (c) From Lemma 3(b): ∂ s1 = ∂ s2 = 61θ v > 0 and ∂ s2 = ∂ s1 = − 61θ v < 0 A A A A ∂π III

∂ d III

∂ πˆ III

∂ dˆIII

From Lemma 3(e): ∂ si = 4θ diIII ∂ si and ∂ si = 4θ dˆiIII ∂ si , so changes in profits have the same sign as changes in deA A A A mand.  Proof of Proposition 5. Given the assumptions in the proposition, we begin by noting that σ = 2v (sA − sB ) > 0 and that σ  = 2v (sB − sA ) < 0. LA is a (strict) dominant strategy for F1 when (i) and (ii) below hold: (i) E {π1I } > E {π1IV } (ii) E {π1III } > E {π1II } Consider (i) first. E {π1I } > E {π1IV } is true when:

      θ d1I − d1IV d1I + d1IV + dˆ1I − dˆ1IV dˆ1I + dˆ1IV > 0

Based on the equilibrium values of demand:

      (s − s )v θ d1I − d1IV d1I + d1IV + dˆ1I − dˆ1IV dˆ1I + dˆ1IV = A B [18θ + (5sA + 13sB )v] > 0 324θ

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So, E {π1I } > E {π1IV } holds. Similarly, E {π1III } − E {π1II } > 0 holds when:

      θ d1III − d1II d1III + d1II + dˆ1III − dˆ1II dˆ1III + dˆ1II > 0

At the equilibrium levels of demand:

      (s − s )v θ d1III − d1II d1III + d1II + dˆ1III − dˆ1II dˆ1III + dˆ1II = A B [18θ + (13sA + 5sB )v] > 0 324θ Thus, LA is a dominant strategy for F1 . In a similar fashion, it can be shown that the following hold: (i) E {π2III } > E {π2I } (ii) E {π2II } > E {π2IV } which implies that LA is a dominant strategy for F2 . Consequently, {LA , LA } is the unique dominant strategy Nash equilibrium of the location game. Proof of Proposition 6. Consider F1 to begin with. Given that F2 chooses strategy LA , we first show that F1 ’s best response is to choose LA for all possible values of φ . This is true if E {π1III } > E {π1II } for all possible φ ∈ ( 12 , 1]. As in Proposition 5:

E {π1III } − E {π1II } = 2θ

       φ d1III − d1II d1III + d1II + (1 − φ ) dˆ1III − dˆ1II dˆ1III + dˆ1II

For any φ , we have that:

      φ d1III − d1II d1III + d1II + (1 − φ ) dˆ1III − dˆ1II dˆ1III + dˆ1II

      = 3241θ 2 φ 3v(sA − sB ) + 2σ  18θ + v(3sA + 3sB ) − 2σ  + (1 − φ ) 2σ  18θ − 6sA v − 2σ 

Given that φ ∈ ( 21 , 1], it follows that (d1III − d1II ) = (3v(sA − sB ) + 2σ  ) > 0; moreover, it is evident that (d1III + d1II ) > (dˆ1III + dˆ1II ) > 0. Thus, φ (3v(sA − sB ) + 2σ  )(18θ + v(3sA + 3sB ) − 2σ  ) > 0 for any given value of φ ∈ ( 12 , 1]. Now, if σ  ≥ 0 is true, then (1 − φ )2σ  (18θ − 6sA v − 2σ  ) ≥ 0 holds as well and E {π1III } > E {π1II } follows directly. On the other hand when σ  < 0, (dˆ1III − dˆ1II ) < 0. In this case, the relative magnitudes of φ (d1III − d1II )(d1III + d1II ) and (1 − φ )(dˆ1III − dˆ1II )(dˆ1III + dˆ1II ) are important. To gage this, we first note that φ > (1 − φ ) and (d1III + d1II ) > (dˆ1III + dˆ1II ) always hold. So, E {π1III } > E {π1II } is still true whenever(d1III − d1II ) = (3v(sA − sB ) + 2σ  ) > |2σ  | = |(dˆ1III − dˆ1II )| holds; that is, if (3v(sA − sB ) + 2σ  ) > −2σ  holds. Substituting σ  = (φ sB v − (1 − φ )sA v), this inequality reduces to sA (3 − 4(1 − φ ) ) > sB (3 − 4φ ), which is obviously true given sA > sB and φ > 12 . Thus, E {π1III } > E {π1II } holds when σ  < 0 as well. Now consider F2 . Given that F1 chooses strategy LA , F2 will deviate from the Nash equilibrium when E {π2III } < E {π2I }. We have that:

       θ φ d2III − d2I d2III + d2I + (1 − φ ) dˆ2III − dˆ2I dˆ2III + dˆ2I = 3241θ 2 [−φ (2σ )(18θ − 6sA v + 2σ ) + (1 − φ )(3v(sA − sB ) − 2σ )(18θ + v(3sA + 3sB ) + 2σ )] E {π2III } − E {π2I } =

Given our assumptions that sA > sB and φ > 12 , σ = φ sA v − (1 − φ )sB v > 0. Moreover, it is evident that (18θ − 6sA v + 2σ ) > 0. Thus the first expression in the equation above is negative, that is, [−φ (2σ )(18θ − 6sA v + 2σ )] < 0. s −s Now, the second expression is negative when (3v(sA − sB ) − 2σ ) < 0, which occurs when φ > ( 21 + sA +sB ). As long as sA < 3sB , there exists a feasible interval φ ∈ ( 12 + s −s

sA −sB sA +sB , 1]

A

B

where (3v(sA − sB ) − 2σ ) < 0. Thus, F2 being weak enough

(φ > 12 + sA +sB ) and GA is being not too strong (sA < 3sB ) is sufficient for F2 to prefer strategy LB when F1 chooses stratB A egy LA .  Proof of Proposition 7. Consider F1 first. Suppose F2 chooses strategy LB . In a manner similar to the proof of Proposition 5 it can be seen that E {π1IV } > E {π1I }, and LB is the best response for F1 . Similarly, if F2 chooses strategy LA , E {π1III } > E {π1II } and LA is F1 ’s best response. Thus, {LA , LB } and {LB , LA } cannot be equilibrium outcomes. Conducting the same exercise for F2 , we see that E {π2III } < E {π2I } and E {π2II } > E {π2IV }. So, LB is F2 ’s best response to LA , and LA is F2 ’s best response to LB . Thus, {LA , LA } and {LB , LB } cannot be equilibrium outcomes. It follows that there is no pure strategy Nash equilibrium for the location game at T = 1. Proof of Proposition 8. LA is a (strict) dominant strategy for F1 if: (i) E {π1IH } > E {π1IV } (ii) E {π1III } > E {π1IIH } Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018

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For (i), from Lemmas 5 and 4 we have:

1 (3θ + sA v ) and dˆ1IH = 6θ 1 = (3θ + sB v) and dˆ1IV = 6θ

d1IH = d1IV

1 ( 3θ − sB v ) 6θ 1 ( 3θ − sB v ) 6θ

It follows directly that E {π1IH } > E {π1IV }. Similarly, it can be shown that E {π1III } > E {π1IIH }, making LA a dominant strategy for F1 . Parallel arguments hold for F2 , and Proposition 8 follows. References Adnan, A., 2013. Competition and post-innovation strategies: imitation, masking and licensing. Masking and Licensing. University of New South Wales Unpublished Thesis. Antonipillai, J., Lee, M. (2016). Intellectual property and the us economy: 2016 update. https://www.uspto.gov/sites/default/files/documents/ intellectual propertyandtheUSEconomySept2016.pdf. Arrow, K., 1962. Economic welfare and the allocation of resources for invention. In: Nelson, R. (Ed.), The Rate and Direction of Inventive Activity. Princeton University Press, pp. 609–626. Athreye, S., Yang, Y. (2011). Disembodied knowledge flows in the world economy. WIPO Economic Research Working Paper No. 3, December 2011. Available at https://www.wipo.int/edocs/pubdocs/en/wipo_pub_econstat_wp_3.pdf. 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Please cite this article as: S. Davidson, V. Mohan and J. Potts, Location, taxation and governments: An exchange theory of intellectual property, Journal of Economic Behavior and Organization, https://doi.org/10.1016/j.jebo.2019.11.018