Course guide of Economic Mathematics 2 (2391125)

Curso 2022/2023
Approval date: 13/06/2022

Grado (bachelor's degree)

Bachelor'S Degree in Economics

Branch

Social and Legal Sciences

Module

Ampliación de Matemáticas

Subject

Matemáticas para la Economía II

Year of study

2

Semester

1

ECTS Credits

6

Course type

Compulsory course

Teaching staff

Theory

  • María Álvarez de Morales Mercado. Grupo: B
  • Philippe Bechouche . Grupo: D
  • Lidia Fernández Rodríguez. Grupo: A
  • Joaquín Francisco Sánchez Lara. Grupo: C

Practice

  • María Álvarez de Morales Mercado Grupos: 3 y 4
  • Philippe Bechouche Grupos: 7 y 8
  • Lidia Fernández Rodríguez Grupos: 1 y 2
  • Joaquín Francisco Sánchez Lara Grupos: 5 y 6

Timetable for tutorials

María Álvarez de Morales Mercado

Email
  • First semester
    • Tuesday de 10:30 a 12:30
    • Wednesday de 09:30 a 10:30
    • Thursday de 09:30 a 12:30
  • Second semester
    • Tuesday de 10:30 a 13:30
    • Wednesday de 10:30 a 13:30

Philippe Bechouche

Email
  • First semester
    • Monday
      • 10:00 a 15:00
      • 15:00 a 15:30 (Fccee. Desp B02)
    • Tuesday de 15:00 a 15:30 (Fccee. Desp B02)
  • Second semester
    • Monday de 09:00 a 15:00 (Desp 3, 5ª Planta, Etsie)

Lidia Fernández Rodríguez

Email
  • First semester
    • Wednesday de 10:30 a 14:30 (Despacho B03 de la Facultad de CC Económicas y Empresariales)
    • Friday
      • 09:30 a 10:30 (Despacho B03 de la Facultad de CC Económicas y Empresariales)
      • 12:30 a 13:30 (Despacho B03 de la Facultad de CC Económicas y Empresariales)
  • Second semester
    • Tuesday de 18:00 a 20:00 (Despacho de Química de la Facultad de Ciencias)
    • Wednesday de 09:00 a 13:00 (Despacho de Química de la Facultad de Ciencias)

Joaquín Francisco Sánchez Lara

Email
  • First semester
    • Monday de 17:30 a 18:30 (Desp B02 - Fac Empresariales)
    • Tuesday de 17:30 a 18:30 (Desp B02 - Fac Empresariales)
    • Thursday de 10:00 a 14:00 (Desp B02 - Fac Empresariales)
  • Second semester
    • Monday de 18:30 a 19:30 (Desp B02 - Fac Empresariales)
    • Tuesday de 18:30 a 19:30 (Desp B02 - Fac Empresariales)
    • Wednesday de 10:00 a 14:00 (Desp B02 - Fac Empresariales)

Prerequisites of recommendations

Completion of the following courses: Mathematics and Mathematics for Economics I (Bachelor’s Degree in Economics) or Mathematics for Business (Bachelor’s Degree in Business).

Brief description of content (According to official validation report)

• Mathematical programs with equality constraints. Method of Lagrange multipliers. Economical applications.

• Mathematical programs with inequality constraints. Karush-Kuhn-Tucker conditions. Economic interpretation of the multipliers.

• Linear programming. Simplex algorithm. Sensibility and post-optimization analysis.

• Differential and difference equations of greater order. Stability criteria

General and specific competences

General competences

  • CG02. Cognitive comprehension skills.
  • CG03. Ability to analyse and summarise.
  • CG04. Ability to organise and plan.
  • CG08. Problem-solving skills.
  • CG09. Ability to make decisions.
  • CG16. Ability to engage in critical and self-critical reasoning.
  • CG17. Ability to learn and work autonomously.
  • CG18. Ability to adapt to new situations
  • CG19. Creatividad o habilidad para generar nuevas ideas 

Specific competences

  • CE22. Bring rationality to the analysis and description of any aspect of economic reality.
  • CE23. Evaluate the consequences of alternative courses of action and select the best ones given the objectives.
  • CE37. Mathematical optimisation.
  • CE50. Acquire skills in solving optimization problems in the economic field.
  • CE51. Understand the techniques of differential and integral calculus in several variables and their application to economic analysis.
  • CE52. Know and understand how to apply the different methods of Mathematical Optimisation and some of the main dynamic models in Economics.
  • CE55. Understand and operate generic optimisation software and specific linear programming software.

Transversal competences

  • CT01. Through the knowledge and application of concepts learnt in the Bachelor's Degree (Grado), be able to identify and anticipate economic problems relevant to the allocation of resources, both in the public and private sectors.
  • CT02. Know, understand and apply the different economic models to provide rationality to the analysis and description of any aspect of reality, and be able to know the economic choice criteria of the different agents that make up society.

Objectives (Expressed as expected learning outcomes)

• Solve mathematical programs with equality constraints using substitution method and Lagrange multipliers.
• Aply Karush-Kuhn-Tucker multipliers method to solve programs with inequality constraints.
• Understand the economical interpretation of the multipliers.
• Know the utility of Weierstrass theorem and the implication of coercivity to guarantee the existence of solution in
optimization problems.
• Recognize quadratic functions and separate variables functions which are coercive.
• Aply simplex method to solve linear programs.
• Solve problems of production planification, diet, etc.
• Analize sensitivity in a linear program.
• Solve linear difference equations.
• Solve linear differential equations.
• Know stability criteria for dynamical systems.

Detailed syllabus

Theory

• Lesson 1. Ordinary differential equations. 

  • Phase portrait for autonomous differential equations.
  • Linear differential equations.
  • Stability.

• Lesson 2. Ordinary Difference equations.

  • Autonomous difference equations.
  • Linear difference equations.
  • Stability.

• Lesson 3. Linear programming.

  • Simplex method. 
  • Two phases simplex method.
  • Economical applications: Diet problem and production problem.
  • Sensitivity analysis.

• Lesson 4. Optimization with equality constraints.

  • Weierstrass theorem.
  • Coercive functions.
  • Method of Lagrange multipliers.
  • Interpretation of the multipliers.

• Lesson 5. Optimization with inequality constraints.

  • Method of the Karush-Kuhn-Tucker multipliers.
  • Interpretation of the multipliers.

Practice

Not applicable

Bibliography

Basic reading list

  • ARRANZ PEREZ, GARCILLAN Y OTROS, Ejercicios resueltos de Matemáticas para la Economía. Optimización y Operaciones financieras. Ed. AC, 1998.
  • ÁLVAREZ DE MORALES, M. Y FORTES, M. A., Matemáticas Empresariales. Ed. GodelImpresiones Digitales S.L., 2009.
  • GANDOLFO, G., Economic Dynamics, ED. Springer, 2010.
  • GARCIA, J., MARTINEZ, C. Y RODRIGUEZ M.L., Optimización Matemática aplicada a la Economía. Ed.Godel Impresiones Digitales S.L., 2009.
  • STEWART, J. Multivariable Calculus. Cengage Learning, 2012.
  • SYDSATER, K Y HAMMOND, P. J., Further Mathematics for Economic Analysis Ed. Prentice Hall. 2008.
  • SYDSATER, K Y HAMMOND, P. J., Essential Mathematics for Economic Analysis Ed. Prentice Hall. 2016.
  • ZILL, D.G. Ecuaciones diferenciales con Aplicaciones. Ed. Grupo Iberoamérica. 1988

Complementary reading

  • ALEGRE, P. Y OTROS, Ejercicios resueltos de Matemáticas Empresariales 2. Ed. AC,1993.
  • BARBOLLA, S., CERDÁ, E. Y SANZ, P., Optimización (cuestiones, ejercicios y aplicaciones a la economía). Ed. Prentice Hall 2000.
  • BORRELL, J., Métodos matemáticos de la Economía: Programación matemática. Ed. Pirámide, 1987.
  • CABALLERO, R., CALDERON, S. Y OTROS, Matemáticas aplicadas a la economía y a la empresa. Ed. Pirámide, 1993.
  • CHIANG, Métodos fundamentales en Economía Matemática. Ed. McGraw-Hill, 2006.
  • DIAZ, A., NOVO, V. Y PERÁN, J., Optimización. Casos prácticos. UNED Ediciones, 2000.
  • GARCÍA CABELLO J., Cálculo Diferencial de las Ciencias Económicas. Ed. Delta Publicaciones 2008.
  • GASS, S.I, Programación lineal. Ed. Cecsa, 1978.
  • HAEUSSLER, E. Y PAUL, E., Matemáticas para la Administración, Economía, Ciencias Sociales y de la Vida. Ed.Prentice Hall, 1997.
  • PERIS, J.E. Y CARBONELL, L., Problemas de matemáticas para economistas. Ed. Ariel Economía, 1986.
  • SOTO, M.D., Métodos de Optimización. Ed. Delta publicaciones, 2007.

Recommended links

  • Teaching platform Matemapli: http://vvv.ugr.es
  • Web site of the Department of Applied Mathematics: http://mateapli.ugr.es/

Teaching methods

  • MD01. Docencia presencial en el aula 
  • MD02. Estudio individualizado del alumno, búsqueda, consulta y tratamiento de información, resolución de problemas y casos prácticos, y realización de trabajos y exposiciones. 
  • MD03. Tutorías individuales y/o colectivas y evaluación  

Assessment methods (Instruments, criteria and percentages)

Ordinary assessment session

According to University of Granada Assessment and Grading Regulations (see http://secretariageneral.ugr.es/bougr/pages/bougr71/ncg712/!), continuous and single final assessment are proposed for this subject.

Continuous assessment will be the default choice, unless another option be formally requested to the Head of the Department (University of Granada Assessment and Grading Regulations).

Continuous assessment is divided into three blocks. The score of each block is obtained by gathering the score of a partial test and other activities such as exercises, online tests, seminars/workshops, blackboard exhibitions, homeworks, etc. The breakdown of the grades is the following:

  • Block I, related with lessons 1 and 2, will score 4 points maximum.  
  • Block II, related with lesson 3, will score 2 points maximum. 
  • Block III, related with lessons 4 and 5, will score 4 points maximum. 

The final grade will be:

  • The sum of all the block grades if this is greater than or equal to 5 points.
  • If the sum is less than 5 points, students could make an exam of the blocks where the obtained mark is less than 50% of the maximum score (2 points in Block I, 1 point in Block II and 2 points in Block III). The final exam will consist of a global test comprising all the blocks mentioned before with the same score (that is, Block I with maximum score 4 points, Block II with 2 points and Block III with 4 points). If a student takes the part corresponding to one block in the final test, the student drops the previous score in this block. The grade obtained in each block in the final test will substitute the one obtained during the semester. The final grade will be the sum of all the block marks.

Extraordinary assessment session

A single final test on the theoretical and practical contents of the course with a maximum score of 10 points.

Single final assessment

The single final assessment will comprise a single test with a maximum score of 10 points. Every detail on the single final assessment regulations by UGR can be found at the following URL: http://secretariageneral.ugr.es/bougr/pages/bougr112/_doc/examenes%21.

Date and place of the exam will be set by the Faculty (as well as the final exam in the continuous assessment)

Additional information

All aspect related with both continuous and final assesment will be guided by current assessment regulations by UGR 
(http://secretariageneral.ugr.es/bougr/pages/bougr112/_doc/examenes%21)