Abstract:

The innovations related to new directions of scientific research usually include relatively low return for labor investment in the beginning, when a new branch starts its activity. Thus even superior branches (which would generate higher returns to labor input when enough investment is done) may have a difficulty in their initial development due to a conflict between individual and group interests. This paper studies the evolution of scientific schools in the general equilibrium framework, incorporating non-constant returns to scale (convex-concave), network externalities and continuum of overlapping generations. A neoclassical model of the microeconomics of growth of research sectors has been proposed. Among the crucial assumptions is convex-concave production function, which generates network externality for the employee of this sector, and the fixed cost of studying. Although a similar model can be written for finite number of overlapping generations, the continuum of them makes the model both more realistic and analytically simpler. The paper is focused on the transition dynamics across schools after emergence of a new school. It is endogenous and is generated by optimal choices of all agents, who take into account the rational behavior of the others. The equilibrium wage dynamics exhibits the property of wage inequality across sectors along the whole transition path. The phenomenon of a cascade, when a big group of scientists shifts in one moment across sectors, can also be observed in this model. When agents are heterogeneous also with respect to their learning skills of different subjects, then the choice of a school depends both on these skills and the future wage path in this sector. The dynamics of demand for teaching different subjects, emerging from this choice, is shown to be governed by an integral equation, which in some cases can be transformed into second order differential equation. Thus, not only the complexity of demand evolution is described analytically, but also some quantitative recommendations can be given to universities about the evolution of the relative weight of different subjects across time. The results may be applied for the forecasting and planning of the transition paths for research development and education, consistent with equilibrium or optimality. The problem of difficulty in the initial period of any new research school is also discussed. Sometimes the entry there can be blocked by old school. The centralized policy may be either superior or inferior in the comparison with free market outcome, depending on the objective function of planner. The slow-down of growth of new research sector can result in slow-down of the stream of innovations, and hence the whole growth path of the economy.

Keywords:

innovation, scientific schools, transitions, cascade effect, modelling.