0000000000113128
AUTHOR
Lisa Morhaim
Monotone Concave Operators: An application to the existence and uniqueness of solutions to the Bellman equation
We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.
Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital
Abstract This paper develops a method for proving the existence of competitive equilibrium in a distorted/non-optimal one-sector economy–a discrete time variant of the Romer model–without conditions on the equilibrium value of the marginal product of capital. Existence is obtained under weaker conditions than in Le Van et al. (2002) . Moreover, we provide an existence result for an economy with a regressive tax studied in Santos (2002) . The proofs rely on ideas of Becker and Boyd (1997) .