The User Innovation Paradigm: Impacts on Markets and Welfare

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Citation Gambardella, Alfonso, Christina Raasch, and Eric von Hippel. “The User Innovation Paradigm: Impacts on Markets and Welfare.” Management Science (April 4, 2016).

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Alfonso Gambardella, Christina Raasch, Eric von Hippel

To cite this article: Alfonso Gambardella, Christina Raasch, Eric von Hippel (2016) The User Innovation Paradigm: Impacts on Markets and Welfare. Management Science Published online in Articles in Advance 04 Apr 2016 . http://dx.doi.org/10.1287/mnsc.2015.2393

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INFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org MANAGEMENT SCIENCE Articles in Advance, pp. 1–19 ISSN 0025-1909 (print) ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.2015.2393 © 2016 INFORMS

The User Innovation Paradigm: Impacts on Markets and Welfare

Alfonso Gambardella Department of Management and Technology and Center for Research in Innovation, Organization and Strategy, Bocconi University, 20136 Milan, Italy, [email protected] Christina Raasch TUM School of Management, Technische Universität München, 80333 München, Germany, [email protected] Eric von Hippel MIT Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, [email protected]

nnovation has traditionally been seen as the province of producers. However, theoretical and empirical research Inow shows that individual users—consumers—are also a major and increasingly important source of new product and service designs. In this paper, we build a microeconomic model of a market that incorporates demand-side innovation and competition. We explain the conditions under which firms find it beneficial to invest in supporting and harvesting users’ innovations, and we show that social welfare rises when firms utilize this source of innovation. Our modeling also indicates reasons for policy interventions with respect to a mixed user and producer innovation economy. From the social welfare perspective, as the share of innovating users in a market increases, profit-maximizing firms tend to switch “too late” from a focus on internal research and development to a strategy of also supporting and harvesting user innovations. Underlying this inefficiency are externalities that the producer cannot capture. Overall, our results explain when and how the proliferation of innovating users leads to a superior division of innovative labor involving complementary investments by users and producers, both benefitting producers and increasing social welfare. Keywords: user innovation paradigm; user–producer interactions; social welfare; complementarities; division of innovative labor, externalities History: Received June 14, 2012; accepted July 4, 2015 by Lee Fleming, entrepreneurship and innovation. Published online in Articles in Advance.

1. Introduction and Overview Despite increased understanding of the importance of Innovation has traditionally been seen as the province the phenomenon, innovation by users and particularly of producers who invest in product and service devel- by end users—consumers—has not yet been incor- opment to sell their innovations. However, extensive porated into standard microeconomic thinking and theoretical and empirical research has now led to an modeling of markets for innovative products and ser- understanding that users are also a major source of vices (Syam and Pazgal 2013). Our objective in this innovation development, where users are deﬁned as paper is to begin this major task. We ﬁrst describe entities that develop novel products and services for processes that occur within what we term the user use rather than sale. and producer innovation “paradigms,” and then we Over the last three decades, user innovation by describe the four types of interactions between them. With this description in hand, we next analyze the Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. individual citizens has moved from being considered an anomaly to being recognized as an activity conducted impact of paradigm interactions in an analytical model by many millions of users that results in the creation of a market where both producers and users innovate, of many individually and commercially important and we then develop and discuss theoretical, policy, new products and services (von Hippel 2005, Bogers and managerial implications. et al. 2009, von Hippel et al. 2012). Further, it is now In overview, we explain that consumer innovators understood that the range of innovation opportunities have two linked attributes from the point of view of pro- viable for innovation by users, acting both individually ducers, one positive and one negative. On the positive and collaboratively, is increasing over time (Baldwin side, they can develop new product designs of potential and von Hippel 2011). commercial value. On the negative side, their ability to

self-provision can reduce the producer’s market. Exam- a side effect of these investments is loss of potential ples are legion: users develop and self-provision video market via increased self-provisioning capabilities and game and software “mods” to commercial products activities among innovating users. they use, with some of these later being commercialized As our second major finding, we show that as the by vendors (Jeppesen and Frederiksen 2006). Users also proportion of innovating users in a market grows, firms develop and self-provision hardware products, such as generally switch “too late” to investing in supporting “customized” cars and motorcycles, with producers user innovation from the social welfare perspective. later commercializing some of the features they develop That is, social welfare would be better served if firms (Harley-Davidson 2016). switched when the share of user innovators in the In our model, we explore the interplay of two key market is smaller than profit maximization would variables. The first is the share of user innovators in a dictate. Underlying this inefficiency are externalities producer marketplace; i.e., users who can innovate, that the producer cannot capture, e.g., what we will self-provide, and/or buy as they prefer. The second describe as a “tinkering surplus” that accrues to users. describes producers’ choice between two archetypal Third, we find that any government policies that modes of organizing for innovation: The first is the tra- have the effect of raising the productivity of innovating ditional mode in which producers invest in research and users encourage firms to switch to the user-augmented development (R&D) without paying much attention to mode and do not reduce welfare. By contrast, govern- user innovation. They view their R&D as “exhaustive” ment policies such as intellectual property rights and in the sense that it covers all the facets—from design R&D subsidies that specifically support producer R&D to technology—that need to be addressed to serve the increase the proclivity of producers to switch to an market. Thus, their R&D substitutes for any potential open innovation mode too late, or even encourage firms contributions from the user domain because even if to switch back to the traditional producer-innovation the users innovate, firms have developed competing mode and thereby may reduce welfare. solutions internally. The second archetypal mode for In net, the contributions of our paper are among producers to organize innovation involves a more the first to integrate the user and producer paradigms “open” approach whereby they design their R&D to be and their interactions in one modeling framework. complementary with user innovation activities. In this In our microeconomic model, what is traditionally mode, firms take into account that users can innovate viewed as the demand side of the market becomes a and seek to conduct in-house R&D activities that are source of innovative designs and products. We show complementary to user innovation. how the interactions between the user and producer Our major findings are three. First, we explore the paradigms affect the creation and distribution of value optimal producer strategies—traditional versus open— in a market relative to the standard model of producer and welfare effects associated with a rise in the propor- innovation only. The model leverages standard welfare tion of innovating users in a market from near-zero economics with externalities to analytically capture to a higher fraction. We find that when the propor- and analyze the paradigm shift toward innovation tion of innovating users in a producer market is very by individual users. This approach produces results, low, profits are maximized by producers choosing the such as the policy theorem (the third finding described traditional, producer-centric mode of innovation, sub- just above), that are not straightforward based on stituting for any innovative contributions the few user standard welfare economics. It also yields novel testable innovators could make and not investing in supporting predictions, e.g., about the level of producer investment them in any way. The added number of commercially in support of user innovation and about the relationship valuable innovations users could produce is too low between the share of innovating users and producer to justify the producer investments and the risk of profits. Finally, we identify tinkering surplus as a third information spillovers to additional users who could component of social welfare in addition to profits and then also potentially choose to self-provision. consumer surplus in markets with user innovation and When the proportion of innovating users in a market- self-provisioning.

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. place increases from low to moderate levels, it becomes Overall, our paper advances the concept of a division increasingly attractive for producers to switch to the of labor in innovation between users and producers. user-augmented mode of innovation that is based We find that more labor shifted to users than produc- on user–producer complementarity, and to invest in ers would find optimal maximizes value creation in providing innovating users with tools to support their markets for innovation. If users’ capabilities to inno- efforts. At a tipping point identified via the model, the vate are expanding in many industries, as has been benefit in commercially valuable innovations spilled argued (Baldwin and von Hippel 2011), innovation over from innovating users to producers makes this sec- tasks can and should increasingly be shifted to the ond strategy more profitable than an exclusive focus on demand side. To stay competitive, companies should commercially performed R&D. This is so even though carefully observe market trends, especially the share of Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 3

potential user innovators, and be prepared to shift to or service to sell to its customers (von Hippel 2005, the user-augmented mode of innovation. Baldwin and von Hippel 2011). The remainder of the paper is structured as follows: A design is a set of instructions that specify how to In §2 we describe what we term the user and producer produce a novel product or service. These instructions innovation “paradigms” and the evidence for each. can be thought of as a recipe for accomplishing the In §3 we describe four types of interactions between functional requirements of the design (Baldwin and the user and producer paradigms and the evidence for Clark 2006, Baldwin and von Hippel 2011). In the these. In §4 we present a model to theorize the impact case of products or services that themselves consist of of user innovation on producer profits and social information such as software, a design for an innovation welfare. In §5 we discuss our findings and suggest can be virtually identical to the usable product itself. implications for research, policy, and practice. In the case of a physical product, the design recipe must be converted into a physical form before it can be used. 2. User and Producer Innovation Free revealing occurs when an innovator gives up Paradigms exclusive intellectual property rights to an innovation In this section, we first provide some key definitions design, and all interested parties are given access to integral to the user and producer innovation paradigms. it—the information becomes a public good (Harhoff Then we describe and contrast the functioning of these et al. 2003). two paradigms. Self-provisioning occurs when a user makes a copy of a product or service for him- or herself independent of 2.1. Key Definitions producers. Innovating users self-provision when they A single user innovator is a single firm or individual that build a working copy of their innovation for their own creates an innovation in order to use it. Examples are a use. Adopting users self-provision when they build a single firm creating a process machine in order to use copy of a user innovation—or a producer product—for it, a surgeon creating a new medical device in order to their own use. use it, and an individual consumer creating a new piece of sporting equipment in order to use it (von Hippel 2.2. The User Innovation Paradigm 2005). In this paper, as was mentioned previously, we The sequence of activities carried out by individual focus on user innovations by individuals only. innovating users within the user innovation paradigm A producer innovator is a single firm or individual is represented by the broad arrow shown in the top anticipating profiting from their designs by selling half of Figure1. It is important to emphasize that design information or products based on that “recipe” from left to right, it involves user activities only; no to others: by definition, they obtain no direct use-value producers are involved. At the left side of the arrow, from them. Examples of producer innovators are a firm we see users developing new products and services or individual that patents an invention and licenses to serve their own in-house needs. In any given inno- it to others and a firm that develops a new product vation category, they often begin to innovate before

Figure 1 (Color online) The User and Producer Innovation and Diffusion Paradigms User innovation and diffusion

Innovation Collaborative evaluation/ Peer-to-peer by users replication/improvement diffusion

Market R&D Production Market research diffusion

producers do, as shown by the leftward positioning to scope, individual innovating users have been found of the arrow. This is the case especially in instances to be active developers in all consumer product fields where innovations offer functional novelty relative to inquired about to date, ranging from sports, to cloth- existing products, because users are then in a better ing, to vehicles, to dwellings. Whereas innovations by position to perceive an innovation opportunity before consumers are developed for their own use, typically producers do. This is because of the sticky informa- without consideration of their possible value to others, tion they possess regarding their needs and context individuals’ needs are often similar. For this reason, of use (von Hippel 2005). Users then may elect to many of their innovations are, in fact, of value to others freely reveal their innovation designs to any and all as well (de Jong et al. 2015). without compensation. As shown at the center of the It has been shown that about half of consumer inno- arrow, when users in addition to the innovator have vators are willing to share their designs with others free an interest in the innovation, this can trigger an open of charge (de Jong et al. 2015, de Jong 2016). As shown collaborative user innovation process (Baldwin and in Table1, only a small fraction of innovating con- von Hippel 2011). Such processes involve contributors sumers protect their designs by acquiring intellectual who share the work of developing a new product or property. As can be seen in Table2, empirical research service and who also reveal the outputs from their on representative samples of user innovators finds that individual and collective design efforts openly for 44% of innovating individual users in Finland and 66% anyone to use. Free diffusion of innovation-related in Canada are willing to freely reveal their innovations information to non-innovators via peer-to-peer transfer to any and all without compensation. A further 40% in also occurs and is shown at the right end of the user Finland and 22% in Canada are willing to reveal with- innovation paradigm arrow. out charge but selectively (de Jong et al. 2015, de Jong The necessary condition underlying both user 2016). Research on users participating in communities improvement activities and straight adoption activities with a shared innovation interest, such as the design of by users peer to peer is that adopters have the capa- sporting equipment or software, have found essentially bility to produce copies of a user-created innovative 100% of those communities are willing to freely reveal design for themselves. This capability is increasingly their innovations (Franke and Shah 2003, Harhoff and extant among individual users with respect to both Mayrhofer 2010). software (where the “recipe” is the product) and hardware designs. With the proliferation of digital products 2.3. The Producer Innovation Paradigm and services and also the rise of three-dimensional The bottom broad arrow in Figure1 is a schematic printing and other modes of decentralized production, representation of the “linear” producer innovation increasing numbers of innovating and noninnovating paradigm. By our earlier definition, producer innovators users will be able to self-provision without producer invest in creating a new design to profit by selling intermediation (Baldwin and von Hippel 2011). instantiations of it; they obtain no direct use-value from Studies of national representative samples of individ- it. In the sequence of activities shown in the producer ual citizens in five developed countries document the innovation paradigm, producers begin their innovation scale of the sequence of innovation activities described process by studying user needs, and then they perform in the user innovation paradigm (see Table1). These R&D as required to develop and produce novel prod- studies find that from 3.7% to 6.1% of citizens report ucts and services. On the right-hand side of the broad having engaged in developing or modifying consumer arrow, we see that they then diffuse what they have products to better serve their own needs. This involves created via sales in the marketplace. Because producers millions of citizens collectively investing billions of would lose profits if other producers adopted their dollars annually in product development. With respect innovations without payment, innovating producers

Table 1 National Survey Data on the Scale of Product Development by Users

United Kingdom United States Japan

% consumer innovators in the population aged ≥ 18 6.1 5.2 3.7 Number of consumer innovators aged ≥ 18 (million) 2.9 16.0 4.7 Annual expenditures by average consumer innovator ($) 1,801 1,725 1,479 Estimated total expendituresa by consumer innovators on consumer products per year (billion) $5.2 $20.2 $5.8 Estimated consumer product R&D expenditures funded by companies per year (billion) $3.6 $62.0 $43.4 % consumer innovations protected by IP 2 9 0 % consumer innovations that diffuse to commercializers and/or peers 17 6.1 5

Note. Data sources include von Hippel et al. (2012) and Ogawa and Pongtanalert (2013), Table 4. aTotal expenditures include out-of-pocket expenditures and time investment evaluated at average wage rate for each nation. Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 5

Table 2 Innovators’ Willingness to Freely Reveal Their Innovations users to modify (MacCormack et al. 2006, Balka and Raasch 2014), or they may provide users with kits Finland Canada Finland (n = 176) Canada (n = 539) of tools to enable them to make their own designs more easily (von Hippel and Katz 2002, Franke and Willingness to share “for free” Piller 2004). Moreover, firms often engage in boundary Yes, with everyone 44% 66% spanning activities and invest the working time of Yes, selectively 40% 22% (e.g., friends, relatives, employees in supporting innovating users (Henkel business contacts, 2008, Colombo et al. 2013). people in my network) No 16% 12% 3.2. User Innovation Spillovers to Producers Note. Sources of data are de Jong et al. (2015) and de Jong (2016). In this case, the interaction between user and producer is the transfer of user-created innovative designs to the generally do not freely reveal their innovation designs. producer. Transfer is typically for free, but sometimes Indeed, they often try to prevent design information it may also involve a market transaction of buying or spillovers via such means as secrecy and intellectual licensing a user design (Antorini et al. 2012, de Jong property rights. et al. 2015). Designs that producers find of commercial The “producer innovation paradigm” is today deeply value are then supplied to the market at large. Evidence embedded in research, public policy, and governmental from a Finnish nationally representative survey of statistics. With respect to research, almost all academic consumer innovators shows that 6% of innovation work on innovation is based on improving our under- designs developed by consumers for their own use are standing of and management of producer innovation adopted and commercialized by existing producers, and (Schumpeter 1943/2003, Bush 1945, Godin 2006, Aghion an additional 2% are commercialized by user-formed et al. 2013). With respect to public policy, the producer start-up ventures (de Jong et al. 2015). innovation mode is the central theoretical pillar that The literature shows that user innovation spillovers justifies public policies granting subsidies or intellectual can be exceedingly valuable to producer firms (Lilien property rights to producers (Penrose 1951, Teece 1986, et al. 2002, Smith and Shah 2013). In studies from Gallini and Scotchmer 2002). several industries, the best user-generated solutions and product concepts have been found to be more novel and to offer higher customer benefit than the 3. Interactions Between User and best producer-generated ones (Poetz and Schreier 2012), Producer Innovation Modes which translates into higher sales revenues and gross Drawing on academic literature, this section distin- margins (Lilien et al. 2002, Nishikawa et al. 2013) and guishes four pure types of interaction between the longer product life cycles (Nishikawa et al. 2013). user and producer innovation modes: As indicated by the transparent arrows in Figure1, (1) producers may 3.3. User-Complemented Markets supply information, tools, and platforms that make From Figure1 we can see that the user and producer user innovation and modification easier. (2) Via free or innovation and diffusion channels can operate inde- selectively free or compensated revealing, users may pendently, creating and diffusing innovative designs. transfer innovative designs to incumbent or start-up In some cases, an innovation diffused for free by users producers. Further, innovative outputs diffusing peer complements one or more innovations diffused by pro- to peer in the user paradigm, and via the marketplace ducers, creating what we term a user-complemented in the producer paradigm, both (3) compete with and market. The key characteristic of a user-complemented (4) complement each other. All four pure types of market is that one or more users self-provision comple- interaction will be explicated in §§3.1–3.4, and hybrids ments to a product offered on the market by a producer. will be considered in §3.5. The distinction that matters here is self-supply and not the source of the innovative design being pro- 3.1. Producer Support for User Innovation duced. A user may have invented the design himself,

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. When users innovate, or when producers wish them to or adopted it from another user, with or without further do so, producers may want to invest to support them to modiﬁcation, or even from a producer in the market increase their levels of activity and also to direct them for complements. toward design activities of potential commercial value User-complemented markets can involve products to the producers. The empirical literature describes that are separate from but complementary to producer a plethora of such producer investments: producers products and/or can involve modiﬁcations or other may sponsor a user innovation community (West and complements built onto or into producer products or Lakhani 2008, Bayus 2013) or a design contest (Füller platforms. In either case, they are user-created comple- 2010, Boudreau et al. 2011). They may also “open ments that are diffused peer to peer. With respect to the up” their product designs to make them easier for former, consider that techniques for using products are Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 6 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

useful or even essential complements to producer prod- from the existence of an open source alternative, unless ucts, and they are often developed by users (Hyysalo it forces proprietary firms to exit the market (Kuan 2009, Morlacchi and Nelson 2011, Hinsch et al. 2013). 2001, Baldwin and Clark 2006, Casadesus-Masanell For example, whitewater kayakers develop and non- and Ghemawat 2006, Lin 2008). commercially diffuse novel kayaking techniques that are essential complements to whitewater kayaking 3.5. Hybrids equipment (Hienerth 2016). With respect to comple- Note that to this point we have distinguished and ments built into or onto producer products, consider explained four pure types of user–producer interactions. software modifications and additions that complement However, real-world interactions may well be hybrids the value of basic commercial software products in of these. For instance, a pure case of user innovation fields ranging from music software to computer gaming spillovers occurs when a user creates a design and software (Jeppesen and Frederiksen 2006, Prügl and transfers it to a producer for commercialization without Schreier 2006, Boudreau and Jeppesen 2015). making a copy for in-house use (Füller 2010). A hybrid The evidence for the widespread presence of case of spillovers plus user-contested market would user-complemented markets runs counter to the involve a user(s) making a copy(s) and also transferring conventional assumption that only producers provide innovation design information to a producer (e.g., complements, although users may select and assem- de Jong and von Hippel 2009). ble them (Sanchez and Mahoney 1996, Schilling 2000, The very fact that real-world user–producer inter- Jacobides 2005, Adner and Kapoor 2010, Baldwin 2010). actions are often hybrids is a source of complexity, requiring strategic decision making by producer firms 3.4. User-Contested Markets with respect to balancing off multiple effects. For exam- Again referring to Figure1, we can see that the user and ple, producer firms making decisions with respect producer innovation and diffusion channels can oper- to investing in user innovation support versus their ate independently, creating and diffusing innovative own R&D must consider effects both with respect designs. In some cases, an innovation diffused for free to user likelihood of developing complementary and by users substitutes for one or more products diffused with respect to substitute innovations. To improve our by producers, creating what we term a user-contested understanding of producer decision making and its market. The key characteristic of a user-contested mar- consequences for user innovators, noninnovating users, ket is that one or more users via self-provisioning and society at large, we next proceed to formalize these build for themselves substitutes to a product offered considerations in an analytical model. on the market by a producer. Recall that the factor that matters is user self-supply of a full or partial 4. Model Setup and Findings substitute for a commercial offering and not the source In this section, we provide both needed model con- of the innovative design being self-provisioned. As textual “setup” information and related findings in illustration, the market for recreational sailboats is a combination. user-contested one. Some sailors can and do build their own innovative or noninnovative boats rather than 4.1. User Types and Tinkering Surplus purchasing a boat supplied by a producer (Raasch We divide a producer’s potential market into two et al. 2008). types of users: innovating users and noninnovating Some dynamics underlying user-contested markets users. Innovating users find it viable to develop and have been explored in the context of innovation and self-provision innovative designs related to the pro- competition among “open source” and “closed source” ducer product, e.g., improvements, customizations, software suppliers (Casadesus-Masanell and Ghemawat and complements. They can also viably self-provision 2006, Sen 2007). According to this literature, “open homemade copies of the producer product itself and source projects” supply their code for free; they do not so can choose whether to buy the product from a firm behave strategically in competition with commercial or to make it themselves. Noninnovating users do not

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. substitutes. Users can choose to contribute to the have a viable option of innovating. Their costs may supply of open source software code, to free ride on be too high, for example, because they lack needed the effort of others, or to buy the producer software. skills or access to tools, or because they have a high Their choices are determined by heterogeneity in users’ opportunity cost for their time. However, it is viable for willingness to pay, development capabilities, adoption noninnovating users to make copies and self-provision costs, and impatience for a solution meeting their products based on designs developed by user inno- needs. Conclusions of this literature are that open vators at some level of quality ranging from equal to source projects can establish themselves as competitors innovating users down to zero. to closed software producers; producers lose proﬁt The share of innovating users is , and we regard because of this competition; and consumers beneﬁt this share as exogenous and static; users cannot change Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 7

their type. For simplicity, we normalize the size of the Features that only producers will find viable to market to 1, so that and 1 − are also the number develop include those that offer limited value to many of users of each respective type. individual users. No individual user would find it With respect to the utility users derive from inno- viable to develop such a feature, but producers can vating, we note that empirical research finds that aggregate demand across buyers and thereby recoup innovating users derive utility both from using the inno- their investment (Baldwin and von Hippel 2011). Fea- vation they have created and from innovation “process tures in this category may include, e.g., product engi- benefits” they gain from engaging in the innovation neering for greater durability and ease of use, a more process itself, such as fun and learning (Lakhani and elaborate design, a manual to accompany the prod- Wolf 2005, Franke et al. 2010, Raasch and von Hippel uct, etc. By contrast, features b that both individual 2013). Users seek to maximize their utility from inno- users (typically “lead users”) and producers can viably vating, which we call h, by determining the optimal develop require smaller investments, compensated for amount of resources, such as time, t, to devote to by larger benefits to individual user innovators. They innovation projects: provide high functional novelty and solve important, hitherto unmet user needs (von Hippel 2005). As the max h ≡ + 41−/5x1−t + 1 − t0 (1) t needs of lead users foreshadow demand in the market at large (cf. definition of lead user), noninnovating In Equation (1), the parameter represents a user inno- users, too, will predictably benefit from solutions to vator’s utility, net of all innovation-related costs, from these problems with the passage of time. go-it-alone innovation projects, i.e., when producers We assume that all users tend to have more similar do nothing to support him. The second term of (1) assessments of the features we call b that innovative represents the user innovator’s additional utility when users may get involved in developing than of the a firm conducts x projects to support his endeavors. features v that the producer has to develop on its own. Examples of such support are the development of Capturing this idea of less heterogeneity with regard design tools for users and gamification to make product to b but simplifying our analysis, we assume that design activities more enjoyable to users. The parameter users differ only in their valuations of v (v ∼ U601 17), ∈ 401 15 captures whether innovating users’ utility is whereas they all like b to the same degree. In our mostly determined by the time they invest (high ) or model of innovation and production by users and by the extent of firm support (low ). The parameter producers, we focus on innovations of type b, following > 0 captures the productivity of this process. The last our assumption that producers are the only ones to term, 1 − t, captures the value of the user innovator’s invest in v. Innovations with regard to b are assumed remaining time that he can spend on other matters, to depend on two activities. when the total time he has available is normalized to 1 First, the volume of innovations of type b depends and he has decided to spend t on innovation projects. on the aggregate effort T exerted by all innovating We derive from (1) that the user’s utility-maximizing users, to the extent that it is useful to the firm (e.g., net time investment in innovation is t = x, which yields of redundancy). To streamline our analysis, we assume utility h = + 441 − 5/5x + 1. We call this expres- that the aggregate usable effort is simply proportional sion capturing users’ net benefit from innovating the to the total efforts t of the innovating users; that tinkering surplus (TS), where TS is the aggregate net is, T = 0t, 0 > 0. (We could use more complex benefit that all users gain from innovating and self- aggregations, allowing for increasing or diminishing provisioning. It consists of benefits from the use of the returns to the number of innovating users, but our self-provisioned innovation, plus innovation process results would remain materially unchanged.) Assuming benefits, as mentioned above, minus costs. When the identical innovating users, and employing the optimal investment of firms in user innovation support is zero, expression for t, t = x, we obtain aggregate user effort innovating users still get their go-it-alone tinkering surplus; h = + 1 > 0. If firms do invest (x > 0), TS T = x1

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. increases as a function of the level of that investment. where = 0 comprises any factor that raises the 4.2. Shared vs. Producer-Only Innovation ability of the firms to take advantage of the produc- We decompose the value that all buyers derive from tivity of the innovating users’ efforts to improve b. the producer product into two parts: value v that they As explained earlier, the firm can influence aggregate derive from features and components that only the user effort T through x projects to develop tools and producer firm will develop and produce and value b platforms that support and leverage innovating users. that buyers derive from features and components that The projects affect the time t users want to spend on can be developed and produced by firms and users, innovation projects, which then affects the value of the jointly or in isolation. innovative product b via aggregate effort T . Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 8 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

Second, innovations of type b are a function of some producers on developing innovations that increase commitment of resources Y carried out by the firm. To product reliability and user convenience (Riggs and fix ideas, Y can be commercial R&D projects or any von Hippel 1994, Ogawa 1998). A good example in other product creation or development activity. We the software field is RedHat. That firm’s commercial define offerings are based on open source software code such Y = 41 − s5y1 ≥ 01 as Linux and Apache software, developed by users, to where y is the total number of innovation projects which RedHat adds convenience features such as “easy of the firm. The firm allocates a share s to projects installation” software scripts. that support innovating users (that is, x = sy), and To streamline our analysis, we assume that each firm the remainder, 41 − s5y, goes to traditional commercial can pick its preferred innovation option but not the R&D projects (either in-house or external). Projects that specific level of . A fully endogenous would add support innovating users are of little commercial value, complexity without substantial new insight. In practice, per se, but indirectly produce value by attracting more its value will depend on the industry in question, the user innovation activities. The parameter measures technologies available to the firm, and best practices the productivity of the firm’s commercial R&D. for integrating innovating users in R&D. Taking into account these two drivers of innovation— aggregate user effort T and producer R&D activ- 4.4. Individual Market Demands of ity Y —let the value of the innovative product to Innovating Users and Noninnovating Users users be Next, we need to understand the demand for the b = 4T + Y 51/1 > 01 producer product from noninnovating users and from innovating users given user contestability, user-created which we can rewrite as complements, and spillovers, i.e., the different types of interactions that we developed in §3. b = 6s + 41 − s571/y = by1˜ Starting with innovating users, we expect that they where ≡ and b˜ ≡ 6s + 41 − s571/ is the will buy the product from a firm only if their consumer productivity of all the firm’s y projects taken together. surplus is positive and exceeds their surplus from self-provisioning, i.e., if 4.3. User and Producer Innovation Activity as Substitutes or Complements v + b − p + h ≥ b + h1 v ∼ U601 171 0 ≤ ≤ 10 (2) The parameter plays an important role in our analysis. It captures two options that firms can choose from, The term v + b − p is the consumer surplus, where each of which involves a distinct form of organizing v + b is our value decomposition of the producer tasks and resources for innovation. The first option is product (cf. §4.2) and p is its price. In case of self- such that the efforts of innovating users, T, and those provisioning, a user innovator will not get utility v, of the producer, Y, are substitutes. Take, for instance, which is provided by the firm only. Of utility b that all the writing of new software code. Suppose that both innovating users cocreate with the firm, he will get the producer and users can work on each of two tasks: only the “walk-away value” b that he can realize by (1) novel functionality or (2) the creation of convenience- learning from this cocreation process and trying to build enhancing features such as “user-friendly” installation features akin to b on his own. The quality 0 ≤ ≤ 1 of scripts. The more effort the producer spends on each of his self-provisioned version of b will depend on several these tasks, the lower the innovation impact that users factors, such as the extent and format of information can make, and vice versa. One effort tends to substitute spillovers from the firm to the user innovator, his for the other. In our model, this situation is captured “absorptive capacity” for the spillovers, and his skills by > 1, which implies that the marginal impact of T to build the information into a usable artifact. In the on b decreases as Y increases, and vice versa. case of software programming, for instance, where The second option, by contrast, structures R&D for the producer opens up his source code for users to

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. complementarity between user and producer inno- codevelop, will be close to 1, if and as the essential vation activities. In our example, suppose that users design information required to replicate functionality b write novel code and producers develop “convenience is fully revealed. In this example, if the producer shares features.” The more effort users put into coding, the only part of his source code, is depressed accordingly. higher the impact that producers can make, and vice Finally, recall the user innovator’s surplus h from her versa. In our model, this situation is described by own innovation activities, including those extensions 0 < < 1, which implies that the marginal impact of T and customizations that the ﬁrm is not interested on b increases as Y increases, and vice versa. Research in. The user innovator is assumed to get this sur- has shown that user innovators tend to focus on devel- plus h—the tinkering surplus—regardless of whether oping innovations providing novel functionality, and or not she buys the producer product. Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 9

Turning to noninnovating users, recall that they do 4.5. Profit Maximization by Firms not innovate; they simply buy a producer-provisioned The aggregate demanded quantity of 1 − noninnovat- product via the market or, to the extent that they are ing users and innovating users is able, can elect to replicate a design developed and then shared peer to peer by a user innovator. Building on q = 41−541−p+41−5b5+41−p+41−5b5 what we said earlier about v, b, and p as constituents = 1−p+b1 with ≡41−541−5+41−50 (4) of demand, we expect that noninnovating users will buy on the market if Solving for p, inverse demand is v + b − p + 0h ≥ b + 0h1 0 ≤ 1 0 ≤ 1 (3) p = 1 + b − q0 (5) and self-provision otherwise. The parameters and 0 in (3) capture the nonin- With N symmetric firms in the market, aggregate PN novating users’ ability to obtain knowledge of the in- demand is q = j=1 qj , and q/N is the demand faced by novating users’ designs (which will depend on the one firm. Firm profits çi are given by the number of innovating users’ propensity to diffuse design infor- units sold by firm i, qi, times the profit margin, given mation), to replicate them, and to benefit from them. by price p minus marginal cost of production , and Whereas 0 refers to a noninnovating user’s ability to minus the cost of y innovation projects: benefit from an individual user innovator whose design 2 they adopt, captures their trickle-down benefits from çi = 4p − 5qi − y 1 > 01 (6) what the user innovator has learned from the producer as well as other innovating users during the cocre- where we assume diminishing returns to running y ation process of b. Of course, when the noninnovating projects. users buy from the firms they enjoy b incorporated in To maximize profits, firms make several interrelated the firms’ product, whereas they enjoy b when they decisions in the following sequence: First, they decide obtain the product from the innovating users through on the organization of their R&D. Specifically, they peer-to-peer diffusion. We expect noninnovating users pick one of two options available to them: the orga- to have imperfect knowledge of the innovating users’ nization of R&D such that user and producer inputs, designs, to be less skilled at self-provisioning them, T and Y, are substitutes ( > 1) or the organization for and to benefit less from using them ( ≤ and 0 ≤ 1). complementarity (0 < < 1). It will take firms longer to With respect to imperfect knowledge and higher costs change their organizational structure and capabilities in of self-provisioning, consider that innovating users may R&D than to change the number of projects, which is well regard careful design documentation for the bene- why we model this as the first choice. Next, the firms fit of potential adopters to be an unprofitable chore in pick their total number of R&D-related projects (y). the case of freely revealed designs (de Jong et al. 2015, Then they decide on the share of projects (1 − s) to von Hippel et al. 2014). With respect to lower levels of allocate to traditional producer R&D. The remainder of benefit, consider that the designs were developed to the projects, share s, will be devoted to user-innovation precisely suit the innovating users’ individual tastes. support and thus indirectly increase the flow of new Finally, it is crucial to note the trade-off that our product ideas available to the firm. Finally, firms decide

model implies for the producer: Firms beneﬁt from on the quantity to produce and sell on the market (qi). learning from innovating users about how to make a We use backward induction to derive the producers’ better product b for both innovating and noninnovating optimal decisions. In this section, we look at the optimal

customers; to that end they want to invest in x to choices of qi, s, and y, in this order. In §4.7, we will involve users more extensively. At the same time, study the choice of innovation mode (). this comes at the cost of facilitating self-provisioning 4.5.1. Choice of qi. We take the derivative of (6)

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. by both innovating and noninnovating users. As the producer invests in tools and tool kits, modularizes the with regard to output quantity (qi) and obtain the + − −PN − = product, or reveals design knowledge such as source first-order condition (foc): 1 b j=1 qj qi 0. In code to facilitate user innovation, he also makes it symmetric equilibrium, this produces profit-maximizing easier for both innovating and noninnovating users to quantity, price, and profits, respectively: self-provision rather than buy. Our model assumes that the producer cannot entirely avoid this side effect of qi =41+b−5/4N +151 (7a) enhanced user contestability, even while choosing a p =41+b−5/4N +15+1 (7b) mode of supporting user innovation that best serves 2 2 2 2 his goals. çi =4p−5 −y =641+b−5/4N +157 −y 0 (7c) Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 10 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

4.5.2. Choice of s. To determine the share of the respectively. At the same time, aggregate demand is firms’ projects aimed at supporting user innovation, s, (4), with = 1 rather than 41 − 541 − 5 + 41 − 5. we maximize b˜ yielding foc s−1 − 41 − s5−1 = 0. The second innovation mode is characterized by the To determine the optimal s, a case distinction is required. firm organizing its R&D for complementarity with In the case of complementarity between user efforts user innovators (0 < < 1) and then making a positive and producer R&D, i.e., if 0 < < 1, the second-order investment in user innovation support (optimal s = condition (soc) is negative, which implies that there is an /4 + 5 > 0). We call this the user-augmented 4U 5 intermediate project allocation 0 < s < 1 to user support mode. In this mode, firms actively leverage user-created that maximizes innovation output b˜ (specifically, s = spillovers for innovation and organize their R&D to /4 + 5, with ≡ /41 − 55. As can be seen from exploit the complementarity between the two sources of the expression for , this optimal project share allocated innovation. Users contribute to raising the use value b to user innovation support increases in the share of of the product, which enhances the demand of both the innovating users in the market and their productivity in noninnovating users and the innovating users. At the

terms of commercially valuable ideas (s 1 s > 0, where same time, ﬁrms’ support of innovating users creates from now on we use subscripts to denote derivatives), user contestability with regard to features b 41 ≥ 05. and decreases with the productivity of producer R&D To summarize, the trade-off between the U versus P

(s < 0). In the case of substitution between user and modes pivots on producers investing to facilitate user producer innovation efforts, i.e., if > 1, the soc is innovation and reap spillovers but, by this action, positive, which implies that the optimal allocation to simultaneously and unavoidably boosting user self- user support, s, is either 0 or 1, depending on whether provisioning to a degree that may be small or large. the productivity of the user contribution in b˜, that is , is greater or smaller than the productivity of the firm 4.7. Choice of Innovation Mode 45 contribution, . Continuing our earlier process of backward induction to understand outcomes in markets with innovating 4.5.3. Choice of y. The foc of (7c) with respect to y users, we now consider the very first producer decision, ˜ 2 is 241 + b − 5b/4N + 15 − 2y = 0, which yields the choice of innovation mode. Our goal is to under- 2 2 ˜ y = 41 − 5z/64N + 15 − z 7, where z ≡ b. Note that stand under what conditions a producer will prefer the soc implies 4N + 152 − z2 > 0 such that the profit- the producer mode over the user-augmented mode, or maximizing investment y is always positive. It is also vice versa. Additionally, and importantly, we examine easy to see that y increases with z. under what conditions the increasing prevalence of innovating users that we observe in many markets 4.6. The Producer vs. User-Augmented (cf. Baldwin and von Hippel 2011) renders user inte- Innovation Modes gration the profit-maximizing innovation strategy for From our findings from the previous section relating to producers. the distribution of innovation projects by the firm (s), Our first theorem below explains the choice of inno- we see that there are two modes of innovating and vation mode by a producer firm. It establishes that, that firms will want to choose between them. The first subject to two conditions, firms in markets with an mode is characterized by > 1 and s = 0. That is, in increasing share of innovating users will find it in this mode firms choose to organize their R&D such that their own best interest to switch to the user-augmented user and producer efforts are substitute inputs and then mode. In switching, firms are aware that they are allocate their entire budget to their own commercial strengthening user contestability, but they also real- R&D efforts, not supporting user innovation activities ize that, overall, this is more profitable than a closed in any way. We call this the producer (P) innovation innovation approach. mode. In this mode, firms ignore the innovating users To find the profit-maximizing mode of innovation, it and organize the creation of b solely around closed is convenient to rewrite expression (7c) for the profits commercial R&D. of the firms as

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. As a consequence of being closed, ﬁrms need not fear information spillovers to innovating users ( = 0) ç = 641 + zy − 5/4N + 1572 − y20 (9) and on to noninnovating users ( = 0). In the producer mode, therefore, the demands of the noninnovating This expression captures proﬁts in both the P and U users and the innovating users simplify to modes, which differ only in z. (In particular, in the P mode, zP = P b˜ P , with P = 1 and b˜ P = ; in the v − p + b + 0h ≥ 0h (8) U mode, zU = U b˜ U , with U = 41 − 541 − 5 + 41 − 5 and b˜ = 4 + 51/.) Given the optimal choices of s and and y, as derived in §4.5, this implies that çP ≥ çU v − p + b + h ≥ h1 (8’) if and only if zP ≥ zU . In other words, we can check Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 11

whether profits are higher in the P or U mode simply by the bottom curve, a switch to the U mode will never by checking whether z is higher in one or the other. be attractive to firms. We find that when there are very few innovating The second necessary condition for the switch to users ( close to zero), profits in the P mode are occur is that the complementarity between user and always higher than profits in the U mode (çP > çU ). producer efforts T and Y must be strong enough. 1 1 Thus, when there are very few innovating users, firms Specifically, < 1 (i.e., 0 < < 2 ) must hold. In other choose the P mode. The intuition is that from the firms’ words, the contribution of the innovating users must perspective, the user innovation spillovers that they be strong enough to trigger a significant increase in b can harvest, the upside of conducting projects x to that outweighs the negative impact on profits from support user innovation, are low. At the same time, the intensified user contestability; otherwise, firms will downside is considerable, as the information and tools prefer to stay in the producer mode. that the firms supplies to the few innovating users can Theorem (Choice of Mode). If the innovative contri- enable innovating users to develop a competing design 1 bution of the innovating users is sizable (0 < < 2 ) and and share it peer to peer, knocking off a good part of user contestability ( and ) is not too high, a critical the producer’s demand. The magnitude of this loss, mass of innovating users ( > ∗) makes profit-maximizing and thus the downside of switching to the U mode, will firms prefer the user-augmented mode of innovating to the depend on and , users’ ability to self-provision b. producer mode. As the share of innovating users increases, profits stay the same in the P mode but increase in the U Proof. See Appendix A. mode. (This is true under two conditions that we will It should be noted that whereas firms may find it explain below.) Firms will switch from the P to the U profitable to switch to the U mode at threshold ∗, mode when the share of innovating users is larger they may switch back again to the P mode at a high . than a threshold ∗, beyond which çU > çP . This is (As illustrated in Figure2, çU reaches a maximum and illustrated in Figure2. then declines, potentially even falling below the çP The first condition relates to and . When user con- line.) This is particularly likely at higher levels of testability is very weak (as indicated by the uppermost and (cf. Figure2). The reason is the following: by curve for which = = 0), the producer can switch to our assumption of ≥ , innovating users are more the user-augmented mode free of risk. On this curve, capable than noninnovating users of self-provisioning; when the share of innovating users is = 0, profits i.e., they exhibit a superior outside option and thus are equal for both modes of innovating. Then, as lower demand for the product of the firm. When the increases, the U mode outpaces the P mode in terms share of innovating users gets quite large, this not of firm profits. Intuitively, in this case firms benefit only means extensive user innovation spillovers to from the contribution of innovating users without firms but also implies that the share of noninnovating risking the rise of self-provisioning and concomitant users—those who benefit the most from these spillovers reduction of demand for the firms’ product. When user by getting to buy a superior product—is small. Having contestability is more pronounced (as illustrated by the many innovating users implies having low demand, second and third curves), we see that the threshold ∗ particularly if is large. This detracts from the attrac- at which the switch to the U mode can occur shifts to tiveness of the U mode and may make firms prefer the right; that is, a higher share of innovating users in to switch back to the P mode where they can better the market is needed for the producer to prefer the U capture demand. We will leave this issue for future mode. If spillovers or are very large, as illustrated research to investigate in more detail, since our core objective is to understand the initial switch from the producer mode to the user-augmented mode when the Figure 2 Firms’ Profits Under the U and P Modes prevalence of innovating users increases. ΠP, ΠU 4.8. Welfare and Policy = = 0

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. In this ﬁnal section, we consider the welfare impli- ΠU cations of ﬁrms choosing either to “go it alone” in Lower or Πp 1 The ratio of the marginal products of b = 4T + Y 51/ with respect to T and Y is equal to 4Y /T 51−. With small, T is small, and therefore Y/T is likely to be larger than 1. As a result, a lower makes the impact of T on b higher relative to the impact of Y on b. Since a higher makes T higher and Y lower because the optimal s increases, the condition 0 < < 1 says that the contribution of the higher T on 2 b has to be strong enough to compensate by a sizable amount the * * * 1 2 3 1 negative effect on b because of a lower Y. Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 12 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

the producer mode of innovating or to integrate user The first term is the aggregate profit of all the pro- inputs in the user-augmented mode. We need to under- ducers. The second term is the aggregate surplus of all stand whether firms’ choice of mode is efficient from a noninnovating users, calculated from societal perspective and, if not, whether policy is likely Z 1 Z p−41−5b to improve economic outcomes. 41−5 4v−p+b+0h5dv+ 4b+0h5dv 0 Calculations of social welfare that include user inno- p−41−5b 0 vation are different from the standard mode of calculat- The third term derives from ing welfare. Conventionally, social welfare is calculated as profits (PS) plus consumer surplus (CS). When Z 1 Z p−41−5b 6v−p+b+h7dv+ 4b+h5dv 0 innovating users develop and build a new product for p−41−5b 0 their own use, welfare calculations must be modified to include their full costs and benefits. In particular, we These expressions will differ, depending on whether need to take into account their tinkering surplus TS, the U mode or the P mode is being chosen by firms. which is the aggregate net benefit that all users gain Our analysis of welfare produces two main results from self-provisioning, if they choose to do so. To give that we summarize in two theorems. The first theorem 1 an example, if a user self-provisions a newly designed states that, given our condition 0<< 2 , higher firm product at a cost of 10 dollars and receives a monetized profits in the U mode imply higher welfare in the U use value of 30 dollars, her tinkering surplus equals 20 mode, but the reverse is not true. That is, whenever dollars. Recall that benefits to tinkering can also accrue firms’ profits are higher in the U mode, welfare is in the form of process value (Franke and Schreier 2010, aligned; by contrast, when firms’ profits are higher in Raasch and von Hippel 2013), e.g., enjoyment of or the P mode, welfare may not be aligned. Specifically, learning from the innovation process itself, or social there are levels of , the share of innovating users in status in the user community. Our model is agnostic a market, such that profits are higher in the P mode to the composition of these benefits. It only presumes but welfare is higher in the U mode. As a result, to them not to be profit based, in line with the definition the extent that the decision to switch belongs to the of a user innovator. We will consider generalizations of producers, as we modeled it, producers will remain this aspect in the Discussion section. in the P mode even though the share of innovating Incorporating these considerations, then, welfare in users is substantial and social welfare would be better markets containing both user and producer innovators served in the U mode. The reason is that firms do not should be computed as internalize the key externalities of our model—that is, the increase in tinkering surplus (h) accruing to W = PS + CS + T S1 (10) users because of firms’ investment in user support (x) and also facilitation of self-provisioning that firms where PS and CS are the standard producer, and bestow on innovating users (b) and, subsequently, consumer surplus and TS are the tinkering surplus. b How significant is the omission of the tinkering surplus noninnovating users ( ) even if they do not buy the in conventional analyses? The answer depends on product. the extent of user self-provisioning in a market. If Theorem (Welfare). Under the conditions of the many users self-provision (as is common across an choice-of-mode theorem, if firms’ profits are higher in the increasing range of markets, especially markets for user-augmented mode, so is welfare, but the reverse is digital products; cf. Baldwin and von Hippel 2011), not true. the omission can be substantial. In some cases, it may Proof. See Appendix B. dwarf traditional components of welfare. In our model, the tinkering surplus for a user innova- Our second result regards policy. We show that tor equals h, whereas for noninnovating users, it is 0h, policies that increase the productivity of innovating which stems from their ability to tap into peer-to-peer users can never reduce welfare, provided that the costs diffusion from the innovating users. Computing the of such policies do not outweigh their benefits. By

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. components of welfare as they accrue to producers contrast, policies that increase the productivity of R&D (aggregate profits, PS), noninnovating users (consumer within firms may reduce welfare. surplus, CSnui plus tinkering surplus TSnui), and inno- Examples of policies that raise the productivity of vating users (CSui plus tinkering surplus, TSui5, we innovating users, , are subsidized access to design have tools and maker-spaces. If innovating users become more productive, both profits and welfare rise under PS =Nç1 the U mode but not under the P mode, which, after CSnui +TSnui =41−5641−p+41−5b52/2+b+0h71 all, does not leverage users’ productivity. As firms’ profits in the U mode increase, they may come to ui ui 2 CS +TS =641−p+41−5b5 /2+b+h70 exceed profits in the P mode. We know from the Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 13

previous theorem that if profits are higher in the U users ( increasing from a low level), as found in many mode, welfare is also higher. markets. Policies that increase the productivity of producer Our principal findings were three. First, as the share R&D, , include R&D subsidies and tax exemptions as of innovating users in a market increases beyond a well as publicly funded applied R&D. Increases in firms’ certain threshold, firms’ profit-maximizing strategy is research productivity raise profits in both the P and to switch from the traditional producer-only innovation the U modes. We show that, unless complementarity approach to an innovation mode that harnesses user between user and producer efforts is high, increases in innovators. Subject to two intuitive conditions relating induce a larger increase in profits in the P mode than to the innovative and competitive impact of user in the U mode.2 This means that policies that support activities, welfare is higher in this user-augmented traditional producer R&D may induce a switch back to mode than in traditional producer-only innovation the P mode. Since welfare is sometimes lower in the P mode. All of the constituencies—producers, innovating mode even while firms prefer it, increases in may users, and noninnovating users—benefit. render the P mode more attractive to the firms in spite Second, any firm that elects to switch to integrating of the fact that welfare is higher in the U mode. In innovating users definitely augments social welfare, other words, such increases may induce a switch to but firms generally switch too late. Thus, markets the P mode even though welfare is higher in the U containing both user and producer innovators tend mode, or they may prevent a welfare-increasing switch to fall short of their theoretical optimum in terms to the U mode. of value creation because producers are too slow, To summarize, policies that support producer innova- from a social welfare perspective, to embrace user tion productivity may reduce welfare. The mechanism innovation. Thus, producers’ optimal R&D strategies is that such policies encourage firms to adopt a closed yield a suboptimal division of innovative labor between producer innovation mode, whereas welfare may be users and producers at the societal level. Underlying higher in an open user-augmented mode. By contrast, this inefficiency are externalities that the producer policies that support the productivity of the innovating cannot capture, e.g., the tinkering surplus that accrues users can never reduce welfare. This is because they to users, a novel component of social welfare. can only encourage a switch to the U mode, and this is Third, policies that raise the productivity of inno- never welfare reducing because whenever firms prefer vating users encourage firms to switch to the user- the U mode welfare is higher in this mode. augmented mode and can never reduce welfare. By contrast, policies that raise firms’ research productiv- Theorem (Policy). Under the conditions of the choice- ity encourage firms to switch back to the traditional of-mode theorem, policies that raise the productivity of producer-innovation mode and thereby may reduce innovating users, , encourage firms to adopt the user- welfare. augmented mode and can never reduce welfare. By contrast, if the complementarity between user and producer innovation ∗ ∗ 5.1. Assumptions, Robustness, and activities, T and Y , is weak (> , with <1/2), policies Generalizability of Findings that raise firms’ research productivity, , encourage firms Our model rests on several assumptions that can be to adopt the producer innovation mode, which may reduce usefully investigated via further research. welfare. First, as we mentioned at the start of the paper, Proof. See Appendix C. innovating users are defined as individuals or firms developing innovations to use rather than sell. In this paper, we have focused on individual consumer innova- 5. Discussion tors only. We have done this to highlight the contestable In this paper we analyzed the effects of user innovation nature of their demand and to emphasize that con- by consumers on standard outcomes in markets for testability can occur in markets for consumer goods. innovation. Our special focus was on understanding the However, follow-on research could develop a similar

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. implications of the increasing prevalence of innovating model focused on or including user firms creating, for example, process innovations for their own use rather 2 The intuition is that increases in have a direct positive impact than for sale. on Y in both the P and U modes. In addition, in the U mode, Second, we note that there are fields and markets in increases in reduce s, which raises Y and reduces T. However, a which some types of innovations originate only from higher generates a more pronounced drop in s relative to (1−s) innovating users—a situation with s =1 in terms of because when complementarity is strong, the increase in Y does not our model. This is often the case, for example, with produce a strong decline in T as a result of the feedback produced by complementarity. As a result, when complementarity is weak, respect to the development of specialized techniques. increases in produce a stronger increase in b in the P than in Producers often find it impossible to profitably develop the U mode. and market unprotectable techniques, and they tend Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 14 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

to leave that vital arena entirely or almost entirely to a nationally representative survey in Finland shows, users (Hienerth 2016). In this paper we explored the innovating users typically do freely reveal their innova- importance of user innovation in markets that include tions; our assumption of no payment is based on that producer innovation as well. However, further work situation (de Jong et al. 2015). In a different model, our could explore the nature of markets characterized by variable x could be seen as the cost of user royalties to user innovation only. the firm, and implications for market outcomes could Third, for simplicity, our model assumed that all be explored. innovating users will be able to benefit from a pro- Sixth, we have modeled producer support of user ducer’s investment in user innovation support and innovation as increasing the amount of time (or that the producer will be able to observe the efforts of resources more generally) that users wish to spend all innovating users and be able to reap any valuable on activities that benefit producers. Gamification of spillovers. This is clearly not the case in practice—users contributions and the setting up of a user community will be differentially affected, and producers will not were examples in point. It is also conceivable, however, be able to observe or capture all spillovers generated that producer support, e.g., in the form of better tools, by users. However, the same modeling logic and the will enable users to save time while innovating. Such same findings apply if our assumptions are true only kinds of producer support could attract additional for a subset of users. users to contribute, i.e., those who were previously Fourth, we assume that producers can choose the noninnovators. This would endogenize the share of level of investment in support of innovating users that user innovators, , in a market, which we have taken will maximize their profits. In the real world, users are to be exogenous in our model. It would be interesting independent actors who often have power to “push for future research to explore the outcomes of this back” against producer plans and actions. They also extended model, especially with regard to the optimal can initiate user innovation activities in ways that choice of producer strategy . producers do not expect. An example of investment Finally, our model treated all producers symmetrically, in supporting user innovation not going according having all of them choose either a user-substituting to producers’ profit-maximizing plans is the case of or a user-complementing innovation strategy. Future Xara, a proprietary software company. In 2006, Xara research can usefully generalize from this limiting invested in opening a large percentage of the source assumption. In the real world, we observe the coexis- code of Xara Xtreme, a vector graphics package, as a way to invite user innovation. However, Xara did tence of producers of both types. A key reason, we not open a small, commercially critical part of the think, is that reorganizing and restructuring R&D to source code. This omission caused a boycott among exploit user-created innovation spillovers can be quite user programmers, and in the end, Xara yielded and costly. Established firms with a legacy of producer- opened more of the code than it would have preferred centric innovation will, therefore, be hesitant to switch, absent pressure from innovating users (Willis 2007). whereas new entrants without a commitment to the It would be valuable and interesting for follow- traditional model will likely find it economically more on research to address situations such as the above. viable to choose the user-augmented innovation mode. Whereas in this paper we assumed that producers Such constraints and switching costs could usefully be decide unilaterally to what extent they want to support analyzed regarding their effects on strategic heterogene- and complement user innovation activities, we could ity and firm- and market-level outcomes. For instance, think of a game in which innovating users can possess in markets with a growing share of user innovators, we the power to determine the extent of user support, s, should observe that new entrants and incumbents that and potentially even the degree of complementarity, . are more flexible in organizing their R&D are more We expect that, in such a game, when the power to profitable. make both decisions lies with innovating users, they will pick higher levels of user support and complemen- 5.2. Implications for Theory tarity than producers would. Unless users pick very It has been argued, on the basis of theoretical and

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. high levels of s, this should lower producer profit but empirical literature on user innovation, that we are in increase welfare overall. Future research could further the middle of a paradigm shift. User innovation has explore this and also consider situations in which the moved from being considered an anomaly to being decision power with regard to s and is distributed recognized as a new paradigm that challenges and between innovating users and producers. extends our traditional view of innovation (von Hippel Fifth, it is noteworthy that user innovators in our 2005, Baldwin and von Hippel 2011). Both theory model receive no remuneration from producer firms. building and empirical research are needed to marry In the real world, successful user innovators sometimes the two paradigms and build a new and consistent receive payments for valuable contributions (such is structure. Our general objective in this paper has been the case with Lego and many app stores). Still, as to contribute to this major task. More specifically, Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 15

this paper contributes to theory building in several with users yield a superior outcome from a welfare important ways. point of view. This now becomes a clear opportunity Our paper leverages standard welfare economics compared to the traditional producer-centric innovation with externalities to analytically capture and analyze world. There is reason, we argue, to review existing the paradigm shift in innovation toward user and open policies that assume producer innovation only and to innovation. We explore the nature of these externalities develop new innovation policies that incorporate an and find they have strategic implications: companies understanding of both user and producer innovation. can raise profits by producing more externalities, even Our model tells us that five aspects particularly though they cannot capture them in full. Our model require new policy measures. First, we have found that also produces results, such as the policy theorem, which producers choose R&D strategies that are too conser- are not straightforward based on standard welfare vative, from a welfare point of view, with insufficient economics. It yields novel testable predictions, e.g., specialization and complementarity with innovating about the level of producer investment in support of users (choice of in our model). The reason is that part user innovation and about the relationship between the of the value generated by their investment slips to users share of innovating users and producer profits. Future in the form of tinkering surplus and higher consumer research should assess these predictions empirically surplus (two externalities). New policy measures can be and identify additional contingency factors. designed to address these failures. We showed that such While deriving these insights, we found that con- policy measures could never reduce welfare (provided ventional concepts were not sufficient for the analysis they are effective) and would often increase it. of markets containing innovating users. Conventional Second, policy measures supporting firm investment microeconomics does not conceive of individual con- should be designed to distinguish carefully between sumers as a source of innovation and production. Our investments that complement and substitute for user distinction of four pure types of user–producer inter- innovation activities. They should favor a division actions in innovation translates central aspects of the of labor between users and producers and seek to richness of real-world user–producer phenomena into support users and producers each in what they do best. a language that supports strategic analysis. We devel- Our model shows that public incentives for corporate oped new concepts such as user-contested demand R&D can reduce welfare if they cause firms to be less and tinkering surplus. In markets with user innovation open to innovating users. Such policies can crowd out and self-provisioning, tinkering surplus constitutes a firm support of user innovation and keep firms in the third component of social welfare, next to profits and producer-only innovation mode. consumer surplus. Future studies can adopt and further Third, for historical reasons, producers are likely to develop these concepts to analyze firm strategizing and mostly possess R&D capabilities and beliefs ( in our outcomes in markets where users are a major source of model) that support go-it-alone innovation programs innovation and atomistic demand-side production. rather than programs designed to complement user Overall, our paper advances the concept of a division innovation such as user tool kits and employment of of labor in innovation between users and producers. personnel who know how to effectively interact with We find that more labor shifted to users than producers innovating users. This raises the question whether firms would find optimal maximizes value creation in mar- would quickly switch to complementary technologies kets for innovation. If users’ capabilities to innovate as innovating users start populating their markets or are expanding in many industries, as has been argued could be stuck in a substitution equilibrium. Our model (Baldwin and von Hippel 2011), innovation tasks can shows that the share of innovating users in a market and should increasingly be shifted to the demand side. and their productivity from the producers perspective Our findings also elucidate the boundaries for pro- have to be significant for producers to change their R&D ducers to invest in such a division of innovative labor with users. Its viability from the producer’s perspec- strategy and begin to collaborate with innovative users. tive is partly exogenous, determined by technological If firms are stuck in an inferior equilibrium, temporary conditions as well as the characteristics of innovating policy measures to reduce producers’ switching costs to Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. users in the market, and partly endogenous to the the welfare-superior strategy of complementing user producer’s own decision making. Through their own innovation could be valuable. investment in specialization and complementarity with Fourth, our findings suggest that policy measures users, producers can, and may, find it in their own best directed at elevating the share of innovating users interest to partly outsource innovation to users. ( in our model) will increase welfare even further. This is true until the welfare-maximizing share of 5.3. Implications for Policy innovating users in the market is reached (which, as It is increasingly clear that the world significantly we show, is clearly greater than 0): if a market has contains user innovation as well as producer innova- too few or too many, either it does not have enough tion. We have shown that, in such a world, synergies production of valuable spillovers or does not have Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 16 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

enough noninnovating users that benefit from them, To illustrate how this can be done, consider how and thus welfare is not optimized. In essence, in a Harley-Davidson Motorcycles invested to capture more world with synergistic investments of firms and users, profit from the widespread activity of motorcycle you need both innovating users and noninnovating customization by consumers. It created websites to users who benefit from their efforts to maximize wel- enable users to share their designs and learn from each fare. Although everyone, including producers, would other—and to make the user designs visible to Harley. gain from measures that turn noninnovating users into The user design spillovers are evaluated for commercial innovating users up to the levels described above, pro- potential. To reduce loss from self-provisioning, Harley ducers may nonetheless not undertake such measures offers custom production of new bikes according to on their own. The types of investments required often users’ designs and also offers postproduction parts have the character of investment in a public good, that can be installed by the user who is customizing a which typically results in private underinvestment. bike he already owns. This enables Harley to capture They involve education, easy access to cheap design increased profits from this type of complementary user creation, sharing and production technologies, and self-provisioning as well (Harley-Davidson 2016). the promotion of a “maker culture” (Baldwin and As a second illustration, consider that Lego sponsors von Hippel 2011). many events where fans are invited to meet and engage Finally, our findings emphasize that the impact of in joint design activities. It also supports fan websites users on market outcomes hinge on users having access where fans can post their novel constructions made of to innovation design and self-production technologies Lego bricks (Antorini et al. 2012). The Lego-sponsored that are economically viable from their perspective. This website allows Lego to directly observe the popularity brings rapidly improving user production capabilities of user-created designs in terms of download counts. into the limelight of future research and policy. Whereas If a design appears to be very popular, Lego can the extant literature investigates the antecedents of user benefit from the information spillover, build it into a design creation in some detail, user self-provisioning kit product, and sell it to consumers. has received much less attention (cf. Kleer and Piller In both these cases, consumers were innovating, 2013). Our analysis highlights that the creation of creating complements, and modifying products without innovative designs is not sufficient for the existence company involvement or approval prior to official of user-contested and user-complemented markets; company responses. The goal of producer investments self-provisioning is also required. was then to enhance the benefits the producer obtained 5.4. Implications for Producer Firms from these activities. If firms learn how to “direct” users better toward the type of innovation activity As noted earlier, the range of innovation opportunities where single and collaborative user innovation is viable that is valuable to firms, value capture by producers is steadily increasing (Baldwin and von Hippel 2011). increases. This means that the user contestability of many markets To conclude, we began with the observation that will increase, as will users’ ability to create design theoretical and empirical research now shows that spillovers and complements to producer products. individual users—consumers—are a major and increas- Our findings imply that, because of these techno- ing source of new products and services. To develop logical and societal shifts, producers should carefully the implications, we built a microeconomic model observe market trends to understand if or when their of a market that incorporates innovation by both markets will reach the tipping point beyond which users and producers. We think this initial work has the user-augmented innovation mode is their profit- shown and analyzed important interactions between maximizing strategy. Recall that our findings show that the user and producer paradigms. We suggest that when the share of user innovators in a market reaches further explorations of this topic can provide major a certain threshold, producers increase their profits new insights into the nature and functioning of markets by leveraging user innovators, as long as the share for innovative products and services. of users contesting the producer market does not get

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. very high and the contestability, in our model, does Acknowledgments not get too strong. The switch from a producer-centric, The authors are greatly indebted to Carliss Baldwin for her user-substituting R&D strategy to user-complementing generous support and insightful feedback on this paper. The paper has also benefited greatly from many conversations R&D involves a major reorganization of R&D functions with Andrea Fosfuri, Joachim Henkel, Cornelius Herstatt, and the development of new capabilities that will Richard Nelson, Claudio Panico, and Gianmario Verona, derive benefits from valuable user-created spillovers as well as the feedback from the Open and User Innova- and reduce losses from user self-provisioning of the tion community. A. Gambardella gratefully acknowledges firm’s product. Producers are well advised to choose financial support from the Italian Ministry of University their approach carefully at any given time and to Research [Project CUP B41J12000160008]. Financial support prepare to adjust early on to remain competitive. for this project by DFG (Deutsche Forschungsgemeinschaft) Gambardella, Raasch, and von Hippel: The User Innovation Paradigm Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS 17

[RA 1798/3-1 and, subsequently, SFB 768] is gratefully The terms in the first two square brackets are the number acknowledged by C. Raasch. of users who buy times their surplus plus the number of users who do not buy times their surplus. This also explains why 0≤p−41−5b ≤1 and 0≤p−41−5b ≤1. Beyond these Appendix A. Proof of the Choice-of-Mode Theorem 1 + 0 U P P U boundaries, the surplus of the noninnovating user is 2 b As noted, z ≤z →ç ≥ç , and vice versa. Moreover, + 0 1 + + or 4 5b and 2 h or b h for the innovating users. As affects ç only through z, and therefore, we can study the a result, b4p−41−5b5, b4p−41−5b5≥0, and it is easy impact of on ç by studying the impact of on z. We first to see that hU −hP ≥0. Sum the first terms in the first two show that at =0, zU ≤zP , which establishes that at =0, square brackets, weighed, respectively, by 41−5 and , and firms choose the P mode. We then show that and if 0<< 1 , 2 subtract 1 41−p+b52. This yields U P U ˜ U 2 z ≥z 1∀ <0, with 0 <1. For the first point, compare b with P b˜ P =. At =0, U ≤P and b˜ U =b˜ P =. As a result, 1 − + − + − − + − + ≥ 2 41 p b541 p b5 41 p b541 p b5 0 =0 implies zU ≤zP . For the second point, it is not difficult P U ˜ U U U ˜ U ˜ U because ≤1 and 1−p+b ≥0 because is a weighted to see that z =0, and z =b 4 + b /b 5. Recall that U ˜ U ˜ U average between 41−5 and 41−5, and 4p−41−5b5≥0. ≤0, and it is easy to see that b /b = /64 + 57. This expression is positive, and if <1 or 0<< 1 , it is very high Since all the other terms in the expression for W U –W P are 2 ∗ when →0. Moreover, it declines as increases, and, given nonnegative, this establishes that at , W U ≥W P . U U P ≥, declines. All this implies that when is close to zero, The next step is to show that W ≥W . The expression U U ˜ U ˜ U for W P is (10) using the specific expressions for PS, CSnui, z >0, because the positive value of b /b outweighs the U U U ui = = negative . As increases, z declines; that is, z <0. This and CS , with 0 and p, b, and h computed for the P U ˜ U U U ˜ U ˜ U ˜ U U U ˜ U ˜ U = ˜ is because z =b 4 + b /b 5+b ¡4 + b /b 5/¡, mode, which means that x 0, and , b, and y are obtained where based on what we have just said, the last derivative from the problem of the firm under the P mode. It is easy U U ˜ U ˜ U U ˜ is negative. Then, when + b /b =0—that is, z =0— to see that in this case, does not affect , b, and y, and U U P = − 0 P z <0, which in turn means that z reaches a maximum therefore W 41 5h . For the U mode, when zU =0, and it then starts declining. This explains U = U + − − + − − + − the shape of our curves in Figure2. We have discussed W N ç 41 5 41 p 41 5b54 p 41 5b 5 0 U in §4.7, and it is easy to see that when ===0, then +b + h çU =çP . Then, as çU increases faster than çP as increases, + − + − − + − + + U a higher , with ==0, implies çU >çP . This establishes 41 p 41 5b54 p 41 5b 5 b h that a switch can take place if or is sufficiently small. + 41−p+41−5b52 −41−p+41−5b52 /2 U P ∗ Finally, differentiate z −z with respect to or at = . 0 U U P ∗ ∗ +4−5b+41− 5h 1 We know that z −z >0, and therefore, the sign of or is the opposite of the sign of zU −zP or zU −zP , which are U U where apart from ç and h , we suppressed all the super- both negative because and affect these expressions only scripts U. If 0<< 1 and is close to zero, çU ≥0. More- U ∗ 2 through . As a result, increases with or , and if U P U P over, h −h ≥0. Thus, to establish the sign of W −W 1 or is too high, the switch does not take place. Q.E.D. we need to show that all the other terms of the expres- U sion for W are nonnegative. Start with the last term. Appendix B. Proof of the Welfare Theorem Rewrite the difference of squares as the product of the ∗ The strategy to prove this theorem is to show, first, that , sum and difference of the two terms, and collect 4−5b. U − P ≥ U − P ≥ W W 0 and then that W W 0. Under the conditions We obtain 4−5b4p−41−4+5/25b5≥0, because ≥ U P of the choice-of-mode theorem, ç ≥ç . This means that at − − + = 1 − − + − − ∗ and 4p 41 4 5/25b5 2 4p 41 5b p 41 5b5, and , when the firms switch from the P to the U mode, welfare we already established that 4p−41−5b5, b4p−41−5b5 is higher in the U mode, and for larger , welfare does not ≥0. Finally, 41−p+41−5b54−p +41−5b 5+b =41−p+ switch back to the P mode. 41−5b54−p +b 5+b 4p−41−5b5. We know that 41− To show that W U −W P ≥0, evaluate p+41−5b5≥0, 4p−41−5b5≥0, and −p +b =−4 b+ U P W −W b 5/4N +15+b =− b/4N +15+b 61−/4N +157≥0. This ˜ ˜ U P U U U 0 U is because ≤0, b =b y+by ≥0, and 1−/4N +15>0 =N 4ç −ç 5+41−5 1 41−p +41−5b 52 +b + h 2 because ≤1. We obtain a similar result for the analogous P P 0 P − 1 41−p +b 52 − h U P 2 term in . This establishes that W ≥W . Q.E.D. + 1 − U + − U 2 + U + U − 1 − P + P 2 − P 2 41 p 41 5b 5 b h 2 41 p b 5 h

Downloaded from informs.org by [18.51.1.88] on 06 July 2016, at 07:52 . For personal use only, all rights reserved. at ∗, where çU −çP =0 and zU yU =zP yP , which implies Appendix C. Proof of the Policy Theorem pU =pP and zU =zP . The latter equality implies yU =yP , and Like in the previous theorem, the strategy to prove this therefore U bU =bP . We can rewrite W U −W P at ∗ using all theorem hinges on the fact that, as shown in the previous ∗ U P U P this information, suppressing for simplicity the superscript U , theorem, at , W −W ≥0, and then we study how ç −ç U P and rearranging terms, and W −W vary as we change or . The logic is to check U P whether, under the conditions of the choice-of-mode theorem, W −W changes in çU −çP and W U −W P go in the same direction. = − 1 − + − − + + − − U P 41 5 2 41 p 41 5b541 p b5 b4p 41 5b5 In W −W , changes in do not affect any of the variables U U + 1 − + − − + + − − in the P mode. They raise ç and h . The expression for 2 41 p 41 5b541 p b5 b4p 41 5b5 U U W is equivalent to W in the proof of the previous theorem, + 1 − − 1 − + 2 + − 0 + U − P 2 41 5b 2 41 p b5 41 5 4h h 50 without the last two terms and with subscripts instead of Gambardella, Raasch, and von Hippel: The User Innovation Paradigm 18 Management Science, Articles in Advance, pp. 1–19, © 2016 INFORMS

U P . Thus, to show that W −W ≥0, we need to show that Baldwin CY, Clark KB (2006) The architecture of participation: the second and third terms are nonnegative. Analogously to Does code architecture mitigate free riding in the open source the proof of the previous theorem, the second term can be development model? Management Sci. 52(7):1116–1127. written as 41−p+41−5b54−p +b 5+b 4p−41−5b5. We Baldwin CY, von Hippel E (2011) Modeling a paradigm shift: From producer innovation to user and open collaborative innovation. − + − ≥ − − ≥ − U + know that 41 p 41 5b5 0, 4p 41 5b5 0, and p Organ. Sci. 22(6):1399–1417. U U U b =b 41− /4N +155≥00 The same applies to the third Balka K, Raasch C (2014) The effect of selective openness on value term, which establishes that at ∗, where çU −çP =0 and creation in user innovation communities. J. Product Innovation U P U P ∗ Management 31(2):392–407. W −W ≥0, W −W ≥0. This means that at increases in raise çU beyond çP , which induces firms to switch to Bayus BL (2013) Crowdsourcing new product ideas over time: An analysis of the Dell IdeaStorm community. Management Sci. the U mode. At the same time, welfare, which at ∗ is higher 59(1):226–244. in the U mode, cannot turn to be smaller than in the P mode. Bogers M, Afuah A, Bastian B (2009) Users as innovators: A review, ∗ Consider now increases in . We first show that if > critique, and future research directions. J. Management 36(4): ∗ 1 U − P ≤ U − P = U − with < 2 , then ç ç 0. To see this, z z ë 1, 857–875. ≡ + 41−5/ 1 Boudreau KJ, Jeppesen LB (2015) Unpaid platform complemen- where ë 61 4/5 7 . If 0< <1, or 0<< 2 , then U ≤1, but ë ≥1. However, →0 implies that ë becomes tors and the network effect mirage. Strategic Management J. very large, and =1 implies that ë =1. Moreover, ë declines 36(12):1761–1777. Boudreau KJ, Lakhani KR, Lacetera N (2011) Incentives and prob- =− −2 0 + monotonically with . Consider ¡logë /¡ logë lem uncertainty in innovation contests: An empirical analysis. 0 0 641−5/764/5 /ë 7log4/5, where ë ≡61+4/5 7. This Management Sci. 57(5):843–863. expression is negative because we study cases in which Bush V (1945) Science the endless frontier: A report to the president. ∗ ∗ 1 / <1. As a result, there is a threshold <1, or < 2 , Report, United States Government Printing Office, Washing- ∗ U P ∗ ton, DC. http://www.nsf.gov/about/history/vbush1945.htm. such that > →z −z <0, and vice versa. Thus, at = , increases in induce a switch to the P mode. Casadesus-Masanell R, Ghemawat P (2006) Dynamic mixed duopoly: To check for W U −W P , using the logic of the proof of the A model motivated by Linux vs. Windows. Management Sci. 52(7):1072–1084. previous theorem, we can write Colombo MG, Piva E, Rossi-Lamastra C (2013) Authorizing employees to collaborate with communities during working hours: U = + − − + − − + W N ç 41 561 p 41 5b54 p b 5 When is it valuable for firms? Long Range Planning 46(3):236–257. +b 4p+41−5b5+0h 7 de Jong J (2016) The empirical scope of user innovation. Harhoff D, Lakhani K, eds. Revolutionizing Innovation: Users, Communities, and Open Innovation, Chap. 4 (MIT Press, Cambridge, MA). + 41−p+41−5b5 −p +b +b 4p+41−5b5+h 71 de Jong J, von Hippel E (2009) Transfers of user process innovations where for simplicity we suppressed the superscripts U. to process equipment producers: A study of Dutch high-tech P firms. Res. Policy 38(7):1181–1191. The expression for W is the same with ==h =0, and the variables are all evaluated at the P mode. 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