Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change
Economic growth is a function of the interactions between the different productive factors framed in the economic policy of an economy, in particular, it can be expressed in terms of labour force, productive resources (land, capital) and technology, among others. The present work pretends to approxi...
- Autores:
-
Vergel Ortega, Mawency
GALLARDO PÉREZ, HENRY DE JESÚS
Rojas Suárez, Jhan Piero
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2021
- Institución:
- Universidad Francisco de Paula Santander
- Repositorio:
- Repositorio Digital UFPS
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.ufps.edu.co:ufps/755
- Acceso en línea:
- http://repositorio.ufps.edu.co/handle/ufps/755
https://doi.org/10.36260/rbr.v10i5.1287
- Palabra clave:
- economía matemática
crecimiento económico
economías con cambio tecnológico endógeno y exógeno
- Rights
- openAccess
- License
- Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)
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Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| dc.title.translated.none.fl_str_mv |
La economía matemática en la explicación del crecimiento económico en economías con cambio tecnológico endógeno y exógeno |
| title |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| spellingShingle |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change economía matemática crecimiento económico economías con cambio tecnológico endógeno y exógeno |
| title_short |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| title_full |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| title_fullStr |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| title_full_unstemmed |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| title_sort |
Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change |
| dc.creator.fl_str_mv |
Vergel Ortega, Mawency GALLARDO PÉREZ, HENRY DE JESÚS Rojas Suárez, Jhan Piero |
| dc.contributor.author.none.fl_str_mv |
Vergel Ortega, Mawency GALLARDO PÉREZ, HENRY DE JESÚS Rojas Suárez, Jhan Piero |
| dc.subject.proposal.spa.fl_str_mv |
economía matemática crecimiento económico economías con cambio tecnológico endógeno y exógeno |
| topic |
economía matemática crecimiento económico economías con cambio tecnológico endógeno y exógeno |
| description |
Economic growth is a function of the interactions between the different productive factors framed in the economic policy of an economy, in particular, it can be expressed in terms of labour force, productive resources (land, capital) and technology, among others. The present work pretends to approximate a model to explain the economic growth in developing economies, for which a model is proposed that explains this growth in function of the referred factors; then production is proposed in function of capital and work and two models are adjusted, one with exogenous technological change and the other that involves technological change in an endogenous manner. The model is developed with a production function with constant substitution elasticity so that it is applicable to both developed and developing economies, since it is to be expected that in developed economies the substitution elasticity is unitary, which would lead to a Cobb-Douglas-type production function, but it is very probable that in incipient economies the function with constant substitution elasticity better reflects the relationship between production factors and economic growth. The research allows the development of the corresponding mathematical model in each case, the economic and mathematical foundations of each model are presented and validated according to economic theories. The behaviour of variables such as savings, investment, income, consumption, capital and their relationships in each model is analysed. |
| publishDate |
2021 |
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2021-11-08T16:13:39Z |
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2021-11-08T16:13:39Z |
| dc.date.issued.none.fl_str_mv |
2021-05-01 |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://repositorio.ufps.edu.co/handle/ufps/755 |
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https://doi.org/10.36260/rbr.v10i5.1287 |
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http://repositorio.ufps.edu.co/handle/ufps/755 https://doi.org/10.36260/rbr.v10i5.1287 |
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eng |
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eng |
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Revista Boletin Redipe |
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Vol.10 No.5.(2021) |
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109 |
| dc.relation.citationissue.spa.fl_str_mv |
5 (2021) |
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101 |
| dc.relation.citationvolume.spa.fl_str_mv |
10 |
| dc.relation.cites.none.fl_str_mv |
Gallardo Pérez H de J, Vergel Ortega M. La economía matemática en la explicación del crecimiento económico en economías con cambio tecnológico endógeno y exógeno. bol.redipe [Internet]. 1 de mayo de 2021 [citado 7 de noviembre de 2021];10(5):101-9. Disponible en: https://revista.redipe.org/index.php/1/article/view/1287 |
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Revista Boletin Redipe |
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info:eu-repo/semantics/openAccess |
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openAccess |
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Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0) http://purl.org/coar/access_right/c_abf2 |
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application/pdf |
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Journal of Physics: Conference Series |
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https://revista.redipe.org/index.php/1/article/view/1287 |
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Universidad Francisco de Paula Santander |
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Vergel Ortega, Mawencye1db451514df4d6eb054b4e8e3bf1e42600GALLARDO PÉREZ, HENRY DE JESÚS65e8d56df3770f30fa30193266191212600Rojas Suárez, Jhan Piero96cb752d974d2a7f4f66513af6ebbf8d6002021-11-08T16:13:39Z2021-11-08T16:13:39Z2021-05-01http://repositorio.ufps.edu.co/handle/ufps/755https://doi.org/10.36260/rbr.v10i5.1287Economic growth is a function of the interactions between the different productive factors framed in the economic policy of an economy, in particular, it can be expressed in terms of labour force, productive resources (land, capital) and technology, among others. The present work pretends to approximate a model to explain the economic growth in developing economies, for which a model is proposed that explains this growth in function of the referred factors; then production is proposed in function of capital and work and two models are adjusted, one with exogenous technological change and the other that involves technological change in an endogenous manner. The model is developed with a production function with constant substitution elasticity so that it is applicable to both developed and developing economies, since it is to be expected that in developed economies the substitution elasticity is unitary, which would lead to a Cobb-Douglas-type production function, but it is very probable that in incipient economies the function with constant substitution elasticity better reflects the relationship between production factors and economic growth. The research allows the development of the corresponding mathematical model in each case, the economic and mathematical foundations of each model are presented and validated according to economic theories. The behaviour of variables such as savings, investment, income, consumption, capital and their relationships in each model is analysed.El crecimiento económico es una función de las interacciones entre los diferentes factores productivos enmarcados en la política económica de una economía, en particular, puede expresarse en términos de mano de obra, recursos productivos (tierra, capital) y tecnología, entre otros. El presente trabajo pretende aproximarse a un modelo para explicar el crecimiento económico en las economías en desarrollo, para lo cual se propone un modelo que explica este crecimiento en función de los factores referidos; luego se propone la producción en función del capital y el trabajo y se ajustan dos modelos, uno con el cambio tecnológico exógeno y otro que implica el cambio tecnológico de manera endógena. El modelo se desarrolla con una función de producción con elasticidad de sustitución constante de manera que es aplicable tanto a economías desarrolladas como en desarrollo, ya que es de esperar que en las economías desarrolladas la elasticidad de sustitución sea unitaria, lo que llevaría a una función de producción tipo Cobb-Douglas, pero es muy probable que en economías incipientes la función con elasticidad de sustitución constante refleje mejor la relación entre los factores de producción y el crecimiento económico. La investigación permite desarrollar el correspondiente modelo matemático en cada caso, se presentan y validan los fundamentos económicos y matemáticos de cada modelo según las teorías económicas. Se analiza el comportamiento de variables como el ahorro, la inversión, la renta, el consumo, el capital y sus relaciones en cada modelo.application/pdfengJournal of Physics: Conference SeriesRevista Boletin RedipeVol.10 No.5.(2021)1095 (2021)10110Gallardo Pérez H de J, Vergel Ortega M. La economía matemática en la explicación del crecimiento económico en economías con cambio tecnológico endógeno y exógeno. bol.redipe [Internet]. 1 de mayo de 2021 [citado 7 de noviembre de 2021];10(5):101-9. Disponible en: https://revista.redipe.org/index.php/1/article/view/1287Revista Boletin RedipeEsta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.info:eu-repo/semantics/openAccessAtribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)http://purl.org/coar/access_right/c_abf2https://revista.redipe.org/index.php/1/article/view/1287Mathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological changeLa economía matemática en la explicación del crecimiento económico en economías con cambio tecnológico endógeno y exógenoArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85economía matemáticacrecimiento económicoeconomías con cambio tecnológico endógeno y exógenoSánchez P and Prada A 2015 Del concepto de crecimiento económico al de desarrollo de las naciones: una aplicación a la Unión Europea. Revista de Economía Mundial 40 221Castillo P 2011 Política económica: crecimiento económico, desarrollo económico, desarrollo sostenible. Revista Internacional del Mundo Económico y del Derecho 3 1Cuenca M and Penagos I 2014 Crecimiento económico en Colombia: una aproximación empírica fundamentada en la perspectiva capital humano. Apuntes del CENES 33(58) 11Peña A 2010 Contribución de la cultura al crecimiento de la economía regional española. Cuadernos de Economía 29(53) 211Romer P 1986 Increasing returns and longrun growth Journal of Political Economy 94(5) 1002Romer P 1990 Endogenous technological change Journal of Political Economy 98(5) 71Lucas R 1998 On the mechanism of economic development Journal of Monetary Economics 22 3Aghion P and Howitt P 1992 A model of growth through creative destruction. Econometrica 60(2) 323.Grosman G and Hellpman E 1991 Trade, knowledge spillovers, and growth European Economic Review 35(2) 517.Guellec D and Ralle P 1996 Les nouvelles théories de la croissance (París: La Decouverte)Gaviria M 2007 El crecimiento endógeno a partir de las externalidades del capital humano Cuadernos de Economía 26(46) 51.Uzawa H 1995 Optimum technical change in an aggregative model of economic growth International Economic Review 6 18Gallardo H Vergel M and Cordero C 2019 Economic growth model in developing economies Journal of Physics: Conference Series 1388 012033Gallardo H 1993 Una Validación del Modelo de Lucas (Bogotá: Universidad de Los Andes)Romer P 1989 Human capital and growth: Theory and evidence, Carnegie-Rochester Conference Series on Public Policy, Elsevier 32(1) 251ORIGINALMathematical economics in the explanation of economic growth in economies with endogenous and exogenous technological change.pdfMathematical economics in the explanation of economic 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
0000-0001-8285-2968e1db451514df4d6eb054b4e8e3bf1e426000000-0003-4377-390365e8d56df3770f30fa301932661912126000000-0003-2682-988096cb752d974d2a7f4f66513af6ebbf8d600 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