Product and Quality Innovations: An Optimal Control Approach

In the suggested paper an attempt to combine two different aspects of innovative activity which are known as product and process innovations is made. The main objective of the paper is to demonstrate the importance of interdependence between these two types of innovative activity through means of a simple one agent model. Research questions which are studied in the paper are as following: 1. Whether it is possible to analyze simultaneously two di.erent aspects of innovations on a continious and dynamical basis. To our knowledge there are no models which would suggest the dynamical analysis of such type. 2. What is the interaction between product and quality innovations and how it may in uence both processes. 3. What is the effect of the degree of diversity of products on the innovative activity. The suggested model contains no uncertainty and only one agent (monopolist) which may invest in expan- sion of variety of products available on the market and into the development of quality of every product which already exists. To develop such a model in continuous time I make use of Infinite-dimensional Optimal Control methods. Main finding of the paper is that interaction between different types of innovative activity significantly changes the dynamics of product emergence to the market as well as the quality of products on the market as incentives of investor are changed. Another important finding is that heterogeneity of products and its nature are fundamental for the outcome of the model. The complementarity of product and process innovations changes our view on technology management and competition in this field.

Games without winners: Catching-up with asymmetric spillovers

Dynamic game with changing leader is studied on the example of R&D co-opetition structure. The leader benefits from higher followers' innovations rate and followers are enjoying a spillover from the leader. Leadership changes because of asymmetric efficiency of investments of players. It is demonstrated that under sufficiently asymmetric players there is no long-run leader in this game and all players act as followers. Moreover this outcome may be the socially optimal one. In decentralised setting additional complex types of dynamics are observed: permanent uctuations around symmetric (pseudo)equilibrium and chaotic dynamics. This last is possible only once strategies of players are interdependent. Cooperative solution is qualitatively similar for any number of players while market solution is progressively complex given all players are asymmetric. Results are extended to an arbitrary linear-quadratic multi-modal differential game with spillovers and the structure necessary for the onset of non-deterministic chaos is discussed

Robust policy schemes for R&D games with asymmetric information

We consider an abstract setting of the differential r&d game, where participating firms are allowed for strategic behavior. We assume the information asymmetry across those firms and the government, which seeks to support newer technologies in a socially optimal manner. We develop a general theory of robust subsidies under such one-sided uncertainty and establish results on relative optimality, duration and size of different policy tools available to the government. It turns out that there might exist multiple sets of second-best robust policies, but there always exist a naturally induced ordering across such sets, implying the optimal choice of a policy exists for the government under different uncertainty levels

Heterogeneous R&D spillovers and sustainable growth: Limits to efficient regulation

This paper introduces heterogeneity of cross-technologies interactions into the double-differentiated R&D-based endogenous growth model. In this model new technologies appear continuously and older are outdated generating structural change. All technologies may interact with each other through knowledge spillovers which are technology-specific and this results in innovations' heterogeneity. The conditions on the shape of these interactions for the existence of the (sustained) growth path in the decentralized economy as well as for the social planner's problem are estab- lished. Next the necessity for government interventions depending on the complexity of these interactions is studied. At last the scale and duration of interventions are demonstrated to be functions of spectral properties of the interactions operator

Heterogeneous product and process innovations for a multi-product monopolist under finite life-cycles of production technologies.

Current paper analyses the influence of the length of production technologies life-cycles on the relative intensity of investments of a multi-product monopolist into different types of innovations. This monopolist is developing new versions of the basic product continuously and simultaneously invests into the production technologies of all these new products. In the paper the finite character of these products' life-cycles is assumed. These finite life-cycles are treated for the purposes of the paper as patents which are granted to the monopolist for the production and upgrading of every new product he/she introduces into the market. It is demonstrated that under the condition of finite-time life-cycles of new products the monopolist prefers to invest into process innovations for already introduced products rather than introducing the new ones in relative measure. It is argued, that this is not the case under infinite life-cycles for all these products where the monopolist invests relatively the same amounts into both types of innovations

Sensitivity of energy system investments to policy regulation changes: Application of the blue sky catastrophe

In this paper we argue, that the interaction of technology and economic policy regulations in the energy sector may be described by the so-called slow-fast class of dynamical systems. It is known that such systems may exhibit the blue sky catastrophe, a special type of bifurcation. Application of this result allows us to argue that caution is needed when updating economic policies in the energy sector to avoid the onset of catastrophic developments in the system's transformation, when energy system dynamics becomes unresponsive to policy updates

Differential games approach to trade with exhaustible resources

The paper presents a model of world economy with two countries where one of them dubbed home sells the exhaustible resource to final producers in both countries, which compete at the final goods market. The interaction between final producers is reached via the sticky price mechanics, whereas price continuously adjusts to produced final product quantities. Production technology in both countries includes the resource as an essential input plus the variety of intermediate products. We demonstrate how opening up to trade of the exhaustible resource may be beneficial for the home economy by promoting technical change and capital accumulation via increased resource rents and relative factor prices movements. This leads to the increase in social welfare due to taste for variety and fosters structural change in the home country

Environmental pollution in a growing economy with endogenous structural change

In this paper we study the impact of environmental pollution in an endogenous growth model that allows for structural change. The model is based on doublydifffferentiated R&D where newer, less polluting technologies gradually replace older ones. The analysis shows that the presence of environmental externalities stimulates structural change but reduces the growth rate of the economy. Further, comparing the models with and without structural change demonstrates that the latter implies stronger environmental damages and, consequently, a lower growth rate than the ffirst one. Finally, levying a tax on the polluting output speeds up structural change, thus, reducing environmental pollution and spurring economic growth. This can give new support for the double dividend hypothesis

Differential games approach to trade with exhaustible resources

The paper presents a model of world economy with two countries where one of them dubbed home sells the exhaustible resource to final producers in both countries, which compete at the final goods market. The interaction between final producers is reached via the sticky price mechanics, whereas price continuously adjusts to produced final product quantities. Production technology in both countries includes the resource as an essential input plus the variety of intermediate products. We demonstrate how opening up to trade of the exhaustible resource may be beneficial for the home economy by promoting technical change and capital accumulation via increased resource rents and relative factor prices movements. This leads to the increase in social welfare due to taste for variety and fosters structural change in the home country

Environmental pollution in a growing economy with endogenous structural change

In this paper we study the impact of environmental pollution in an endogenous growth model that allows for structural change. The model is based on doublydifffferentiated R&D where newer, less polluting technologies gradually replace older ones. The analysis shows that the presence of environmental externalities stimulates structural change but reduces the growth rate of the economy. Further, comparing the models with and without structural change demonstrates that the latter implies stronger environmental damages and, consequently, a lower growth rate than the ffirst one. Finally, levying a tax on the polluting output speeds up structural change, thus, reducing environmental pollution and spurring economic growth. This can give new support for the double dividend hypothesis