Borradores de Economia
Número:
230
Publicado:
Clasificación JEL:
C02, C20
Palabras clave:
Concavity, Monotonicity, Lipschitz, Continuity
Lo más reciente
Miguel Sarmiento, John Sebastian Tobar-Cruz, Andrés Esteban Casas-Fajardo, Eduardo Yanquen-Briñez
Jaime Alfredo Bonet-Moron, Jaime Andrés Collazos-Rodríguez, Karen Astrid Rubio-Ramírez, Adolfo Ramírez-Moreno, Andrés Felipe Parra-Solano
Julián Alonso Cárdenas-Cárdenas, Deicy Johana Cristiano-Botia, Eliana Rocío González-Molano, Carlos Alfonso Huertas-Campos
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).