Entrepreneurship, management services and economic growth

We model the joint production of entrepreneurs and workers where the former provide both entrepreneurial (strategic) and managerial (coordination, motivation) services, and management services are shared with individual workers in an output maximizing way. The static equilibrium of the model determines the endogenous share of entrepreneurs in the economy in a given moment of time. The time dynamics of the solution implies that a given growth rate in quality of entrepreneurial services contributes to productivity growth proportionally to the share of entrepreneurs at the start of the period and improvement in quality of entrepreneurial services is convergence enhancing. Model predictions are tested with data from OECD countries in the period 1970-2002. We find that improvements in quality of entrepreneurial services over time explain up to 100% of observed average productivity growth in these countries.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .