Module Code and Title:        MTE101 Mathematics for Economics

Programme:                          BA in Development Economics

Credit Value:                          12

Module Tutor:                       Tshering Lhamo Dukpa

General objective: The module aims to provide the knowledge of basic mathematics that enables the study of economic theory, and its application in core theoretical modules such as microeconomics, and macroeconomics. In this module, the students will learn and apply mathematical tools such as functions, differential equations, integration, optimisation and matrices.

Learning outcomes – On completion of the module, students will be able to:

1. Apply the concepts of functions, continuity and limit.
2. Interpret slope of the curves
3. Model economic scenario as a mathematical problem
4. Calculate the derivatives of a function and extreme point.
5. Solve unconstrained optimization problems involving functions of a single or multiple variables. 
6. Apply the notions of a partial derivative of a function of several variables.
7. Solve matrix operations and systems of linear equations.
8. Apply the Leontief input-output model to solve real-world problems.

Learning and Teaching Approach: 

Assessment Approach:

Each student will submit an assignment before the midterm examination. It will test problem-solving skills, ability to identify a problem, and decide why and how a particular mathematical device can be applied to find solution for economic problems. The assignment will have maximum limit of 200-300 words. 

3    Ability to understand a problem

3    Identify appropriate mathematical device to solve the problem

6    Finding solution

3    Interpretation of the findings

Two written tests will be conducted (each worth 10 marks), that will comprise 45 minutes duration and cover units II and IV. The tests will contain 4 questions- 2 on the conceptual understanding, and 2 on problem solving.

Group size: 4-6 students. Audio-Video presentations on the task to test conceptual understanding of given mathematical concept, and identify economic situations in which they can be applied. The group members will work on one component of the problem, and provide a consolidated work. The assignment should have a maximum limit of 400-500 words. 

1    Group work plan

3    Individual work

2    Review of individual work by team members

4    Synthesis of individual work in a joint report 

Students will take a written exam of 1.5-hr duration covering topics up to the mid-point of the semester. The exam will comprise structured questions like MCQ, fill-in-the-blanks, matching, definition, as well as open-ended essay questions.

Students will take a written exam of 2.5-hr duration encompassing all the subject matter covered in the semester. This assessment is comprehensive and summative in nature, and will comprise structured questions like MCQ, fill-in-the-blanks, matching, definition, as well as open-ended essay questions.

Overview of assessment approaches and weighting

Pre-requisites: None

Subject matter:

(Apply the concepts of demand and supply functions, consumption function and growth rates)

1. Review of graphs of common functions
2. Elementary types of functions: linear, quadratic, polynomial, power, exponential, logarithmic 
3. Continuous functions: characterizations, properties with respect to various operations and applications
4. Differentiable functions: characterizations, properties with respect to various operations and applications; second and higher order derivatives: properties and applications    

(Apply cost, revenue and profit functions)

1. Review of slope calculation and interpretation: slope of tangent and derivatives, rate of change and their economic significance
2. Simple rules for differentiation of sums, products and quotients
3. Second and higher order differentiation: generalised power rule, Chain rule, polynomial approximations, elasticity
4. Limit, continuity, continuity and differentiation

(Apply concepts of growth models and market equilibrium)

1. First order difference equations: existence and uniqueness theorem, with constant coefficient
2. Compound interest, present discounted values, mortgage repayments
3. Linear equations with variable coefficient
4. Second order equations, with constant coefficients, stability

1. Unit IV: Optimization
2. (Apply the concepts of consumer and producer behaviour)
   1. Single variable Optimisation: geometric properties of functions, first derivative test, convex functions, their characterizations and applications 
   2. Multivariable optimisation: local and global optima: value theorem, geometric characterizations (concave/convex functions, conditions for concavity /convexity, quasi concave/convex functions) 
3. Unit V: Integration of functions

(Apply the concept of income distribution)

1. Areas under curves, case when f (x) has a negative value 
2. Indefinite integrals
3. The definite integral, integration by parts, Integration by substitution, economic applications of integrals 

(Apply IS-LM model)

1. Linear transformations: properties, matrix representations and elementary operations
2. Systems of linear equations: properties of their solution sets; determinants: characterization, properties and applications
3. Leontief Input -output model

Reading List:

Essential Reading

Chiang, A.C. (2017). Fundamental Methods of Mathematical Economics. New York: McGraw Hill. 

Hoy,M; Livernois,J; Mckenna,C; Rees,R and Stengos,T (2011). Mathematics for Economics. MIT press

Simon, K.P. & Blume, L. (1994). Mathematics for Economists. W.W. Norton, New York. London.

Sydsaeter, K., & Hammond, P. (2018). Mathematics for Economic Analysis. Delhi: Pearson Educational Asia.

Additional Reading

Allen, R.G.D. (1974). Mathematical methods for Economics. McGraw Hill.

Rosser, M. (1993). Basic Mathematics for Economists (1st ed.). Routledge.

Warner, S. & Costenoble, S.R. (2010). Finite Mathematics and Applied Calculus. Thomson, Brooks/Cole.

Date: June 2022