Revisiting the Lucas model

We revisit the influential economic growth by Lucas(1988) ["On the mechanics of economic development." Journal of Monetary Econmomics, 22(1):3-42], assuming that households optimally allocate consumption and education over the life-cycle given an exogenous interst rate and exogenous wages. We show that in such a partial equilibrium setting, the original two-state (physical capital and human capital) optimization problem can be decomposed into two single-state optimal control models. This transformation allows us to rigorously prove the existence of a singular control describing the allocation of education time along a balanced growth path. We derive a constructive condition for a singular control to exist and show that under this condition definitely many singular controls are optimal in the individual household problem. In contrast to the original general equilibrium framework in which an agent always chooses part-time education and part-time work, in our framework such an agent might find it optimal tp allocate her whole available time to education at the beginning of her life and to focus on labor supply only when she is older

Heterogeneous Product & Process Innovations for a Multi-product Monopolist under Finite Life-cycles of Production Technologies.

Bondarev A. Heterogeneous Product & Process Innovations for a Multi-product Monopolist under Finite Life-cycles of Production Technologies. MPRA Paper.; 2012.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

Maximizing tree harvesting benefit from forests under insect infestation disturbances

Mathematical modeling has been recognized as an important tool to advance the understanding of the synergetic effect of coupled disturbances (stressors) on the forest population dynamics. Nonetheless, most of the modeling done on disturbances focus on individual disturbance agents and the modeling research on disturbances interactions uses predominantly descriptive statistical processes. This state of art points to the need for continuing modeling efforts not only for addressing the link among multiple disturbances but also for incorporating disturbance processes. In this paper, we present an age-structured forest-beetle mechanistic model with tree harvesting. We investigate three scenarios involving the beetles equilibrium states (no beetles, beetles in endemic and epidemic states). Optimal control theory was applied to study three different benefit functions involving healthy and dead trees. The numerical simulations show that maintaining the beetle infestation at endemic level instead of eliminating all the beetles is sufficient to ensure the forest has trees with all ages. Furthermore, the numerical simulations shows that the harvesting benefit decreases as the number of beetles increases in all cases except when the benefit functional includes a cost (ecological and harvest implementation) and the value of wood is equal across all trees (healthy harvested trees, trees killed by beetles, and trees that die naturally)