Trade-off between research risk and major innovations: a theoretical discussion to understand optimal R&D

The activities of research and development have been transforming our society for the last centuries and nowadays their importance is even greater due to the high level of technology required by all players in the economy. It is important to firms, since R\&D represents the key for profits in many growing sectors, such as the microelectronic, the automobile and the pharmaceutical ones; to customers, who have `modern' needs that can be satisfied only with high standards of technology, such as the need to be constantly online, as it is proved by the spreading of social media, to receive real-time information, and to use the internet to perform everyday-tasks, such as online shopping with home delivery; and to public institutions, since technological development may be an engine for growth and welfare improvements. It is no surprise that many economic papers, published mainly between the end of the 1980s and the beginning of the 2000s, have addressed the topic of R\&D from various perspectives and enriched our knowledge in this regard; a survey of such literature is not repeated here because is provided throughout the following chapters. More specifically with the present thesis I plan to contribute to the literature concerning the field of R\&D risk, that is the risk of conducting an R\&D investment without producing any innovation, from both private producers and social planner perspectives. Focusing on the private aspect, the possibility for a research activity to fail represents a negative factor able to decrease profits of firms, especially when the amount of investment in R\&D is considerably high. On the other hand many firms decide to embark on risky projects because they have greater potential in delivering ground-breaking innovations. In other words firms may be willing to take greater risk to obtain better innovations, at least to a partial extent; in fact a growing number of firms is forming research consortia with the objective to share the risk related to R\&D and to aim at major innovations. As for the social perspective, the government has a limited availability of public funds and should carefully address resources in a welfare-maximising way. It is common in the real world to dispense subsidies to researching firms in order to foster technological development and to obtain welfare gains. In particular governments may decide to grant subsidies to either safer research projects that have larger probability to produce an innovation or riskier projects which might deliver larger benefits to the population. It is the case for instance of the millions of dollars that governments invest into the pharmaceutical sector for the discovery of new medicines against dangereous deseases, which are worth investing even if a large share of the funded projects inevitably do not deliver the expected results. The present dissertation represents an opportunity to discuss these topics and other related to the activity of research and development. The approach followed in the thesis is theoretical since it is based on a benchmark model of industrial organization in which two firms operate in the same sector and compete à la Cournot over the quantity of a homogeneous good. At the pre-competitive stage producers can decide to invest in research and development, where the research output is an innovation that raises firm efficiency. A peculiarity of the model is the presence of technological spillovers: the investment of one firm is likely to benefit the rival, at least to a partial extent, due to the possibility of observing and replicating innovations. The incentive of firms to invest is thus lowered if the spillover rate is large, since the rival can free-ride on technological development and obtain a large benefit at no extra cost. To overcome this issue firms have the possibility to sign a cooperative agreement: in this case they form a research cartel and choose the level of investment to maximise the joint level of profits of cartel members. From this kind of model, largely adopted in the literature, it is possible to show that cartels are willing to invest more than non cooperative firms and thus are welfare-improving, provided that the spillover rate is sufficiently large. On the contrary if spillovers are low research cartels invest lower amount of resources and are welfare-reducing. In chapter 1 I add the element of research risk to the benchmark model. The R\&D activity needs not deliver an innovation to the firms, which thus face a certain risk level represented by the negative event of research failure. Hence there are two possible outcomes: the research activity produces either an innovation or nothing. Firms may select the optimal risk rate by choosing among different research projects, which thus differ in their `degree of ambition'. The trade-off for greater risk is represented by higher marginal returns: given the level of investment riskier projects might deliver better innovations and higher gains in efficiency. The focus of the chapter is the solution of such trade-off between R\&D risk and ambition for profit-oriented firms. I show that such solution depends on the presence of technological spillovers. In general they may serve as an insurance instrument to firms, which can implement a new technology even when own R\&D fails provided that the rival's is successful. If spillovers are sufficiently large, the insurance effect fosters the adoption of riskier research projects. However I show that this argument may be overturned when firms form a research cartel due to the impact of spillovers on investment: cooperative firms prefer to increase their level of investment when spillovers are large and thus are less keen to take greater risk, contrary to the previous expectation. Chapter 2 represents the natural evolution of chapter 1: I consider the optimal research project that a firm should undertake from the perspective of a social planner, thus the focus shifts from the private scope to the social one. This model develops upon the previous one by adding a government that sets subsidy policy to affect the decisions of the firms and obtain welfare improvements. In particular it may grant as many types of subsidy as the actions of the firms: one per unit of output supplied at the competitive stage and one per dollar of investment in R\&D conducted at the pre-competitive stage. In the paper I show that in the first-best scenario with high spillovers the government desires firms to develop riskier projects due to the spillover-insurance argument, which preserves the average level of efficiency in the industry. Conversely in case of low spillovers safer activities are more likely to be welfare-improving. In the second-best case, where output subsidies are not available to the government and the output level cannot be influenced towards efficient values, simulations suggest that riskier activities are likely to be welfare-maximising also when spillovers are low because they may foster efficiency and hence production. In chapter 3 I depart from the risk analysis to address strategic trade policy issues concerning research subsidies. The model is simplified relative to the ones adopted in chapter 1 and 2 by removing the element of R\&D risk, but is also enriched by the presence of two different countries, say home and foreign, that freely trade in the international market; such model may thus be suited to describe trade policy between two European countries. The main difference between the two countries is the degree of intervention of the respective social planners, because only the home government is allowed to conduct policy and to dispense research subsidies to the domestic firm so as to increase the domestic level of welfare. I explore the relationship between level of subsidy, degree of research cooperation and amount of international spillovers. In general a large level of international spillover is able to transfer knowledge from one country to another, so that the foreign firm may take advantage from the domestic subsidy. Moreover if the two firms sign an international cooperative agreement the domestic subsidy is likely to benefit the foreign firm because the home firm pursues cartelwide profits maximisation. In principle both elements may lower the effectiveness of research subsidy policy by the government. In the paper I show that the optimal level of research subsidy is always non-negative when the two firms carry their research activities in a non-cooperative fashion. When spillovers are large the incentive to invest in R\&D is so low that the government is willing to grant a positive subsidy even if it benefits foreign rivals. When firms form an international R\&D cartel instead the subsidy is positive only when the spillover rate is sufficiently low. On the other hand, if it is large the government may optimally raise an R\&D tax on the domestic firm which still maintains high level of efficiency due to international cooperation. As a consequence the presence of an international cartel is always welfare-maximising and its creation should be encouraged through suited policy. At the beginning and the end of each chapter I dedicate specific introduction and concluding remark sections. Moreover the reader may find a chapter-specific appendix to check assumptions and mathemetical methods.