Metodos dinamicos en economia / Dynamic Methods in Economy: by Irma Beatriz Rumbos Pellicer, Hector Lomeli Ortega

By Irma Beatriz Rumbos Pellicer, Hector Lomeli Ortega

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Extra info for Metodos dinamicos en economia / Dynamic Methods in Economy: Otra busqueda del tiempo perdido / Another Search of Lost Time (Spanish Edition)

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20 Resolver las ecuaciones dadas las condicioplemente el valor presente de los dividendos nes iniciales: futuros del activo, descontados a una tasa r. 0 c) Definir el valor fundamental del activo como p∗ = dr y probar que se cumple lim pe (t) = p∗ . a) x ¨ − x = 0, x(0) = x(0) ˙ = 1. b) 2¨ x − 5x˙ + 6x = 0, x(0) = 3, x(0) ˙ = 7. t→∞ c) x ¨ + 2x˙ + 2x = 0, x(0) = 1, x(0) ˙ = 0. d) Probar que p = p∗ + αr (p − pe ), susd) x ¨ − 6x˙ + 9x = 0, x(0) = 1, x(0) ˙ = 0. 21 Encontrar la solución general de las sirado como el precio convergen al valor funguientes ecuaciones: damental del activo.

A1 t + a0 ) aeαt cos βt + beαt sin βt tk (An tn + . . + A1 t + A0 ) tk Aeαt tk (A cos βt + B sin βt) eαt tk (An tn + . . 1: Soluciones particulares comunes. El método tiene que modificarse ligeramente si la función f (t) o alguna de sus derivadas es solución de la ecuación homogénea. , tk f (n) (t) , donde k es el mínimo exponente tal que ningún elemento del conjunto es solución de la ecuación homogénea. 1 muestra la forma de una solución particular para algunas formas funcionales de f. El siguiente ejemplo muestra estas consideraciones.

9) está dada por Y (t) = YT + BT t δ(s)ds B(t). 10). 1 Una curiosidad: la transformada de Laplace La llamada transformada de Laplace se utiliza constantemente en economía, no obstante que la mayoría de los usuarios desconocen su existencia. Hacemos aquí este pequeño paréntesis pues en la sección anterior acabamos de utilizar de manera inadvertida esta famosa transformada. En general una transformada integral es una relación de la forma ∞ K(s, t)f (t)dt, F (s) = 0 en donde una función f es transformada en otra función F por medio de una integral.

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