Borradores de Economia
Número:
230
Publicado:
Clasificación JEL:
C02, C20
Palabras clave:
Concavity, Monotonicity, Lipschitz, Continuity
Lo más reciente
Bernardo Romero-Torres, Gerson Javier Pérez-Valbuena, Andrés Felipe García-Suaza, Jaime Alfredo Bonet-Moron
Olga Lucia Acosta Navarro, Andrés Felipe Chitán-Caes, Ana María Iregui-Bohórquez, Ligia Alba Melo-Becerra, María Teresa Ramírez-Giraldo, Jorge Leonardo Rodríguez Arenas
Alejandro Ome, Laura Giles Álvarez, Gerson Javier Pérez-Valbuena, Cristhian Larrahondo
The following is proven here: let W : X × C ? R, where X is convex, be a continuous and bounded function such that for each y?C, the function W (·,y) : X ? R is concave (resp. strongly concave; resp. Lipschitzian with constant M; resp. monotone; resp. strictly monotone) and let Y?C. If C is compact, then there exists a continuous extension of W, U : X × Y ? [infX×C W,supX×C W], such that for each y?Y, the function U(·,y) : X ? R is concave (resp. strongly concave; resp. Lipschitzian with constant My; resp. monotone; resp. strictly monotone).