Symbiosis International University Symbiosis School for Liberal Arts

Mathematical Methods for Economics

 Course Objectives 

  1. Understand the rationale behind the use of mathematics in economics and in other fields of study.
  2. Appreciate the scientific method employed by the economic models.
  3. Explore more complex and abstract concepts presented through the use of mathematics.
  4. Contrast and compare different methods for approaching the same problem.
  5. Apply the models learned in economics in practical and everyday affairs such as financial thinking.
  6. Draw economic and policy inferences based on a given data by applying the techniques learnt.

 Teaching Methodology 

  1. Friendly introduction to new and apparently complicated topics before exploring more rigorous methods.
  2. Use of real world data in econometric techniques which reinforces the idea with a real example.
  3. Stress on not only solving given problems but also reverse engineering those problems to make new ones while exploring the limitations of any given technique
  4. Continuous assessment through quizzes and problem solving challenges. 

 Course Outline 

Sr.No. Topic Hours
1 Functions and Graphs
o Understanding meaning and idea of functions. How to visualize functions through graphs. Interpreting graphs and drawing causal relations.
o Inverse functions. Budget constraint.
o Solving for values for given functions and construct functions with given information.
o The idea of slope or rate of change of a function from which the idea of marginal is derived in economics. The meaning of intercept.
o Meaning of limits. What it means for a function to be continuous.
o Comparative statics and the reduced form of an economic model.
o Solving for multiplant monopoly and price discrimination.
o Quadratics and Polynomials.
10
2 Financial Mathematics
o The idea of timeline and differing values of money due to cost of capital in the economy.
o Present value, future value, compounding and discounting.
o Annuities, series of payments, equated monthly installments.
o Stock markets and the idea of returns on capital.
o The concept of real cost through discounting. The difference between a nominal value and real value of any economic parameter.
10
3 Econometric methods
o Basic idea of arithmetic mean, mode and median. Their limitations and validity.
o Choosing independent and dependent variables and its meaning.
o Data series of two variables and its dependence on and relation with each other.
o Variance, covariance and standard deviation.
o Regression – the method of ordinary least squares, coefficient of determination, accuracy of the model, correlation and its coefficient.
o Look at non-linear regression models.
10
4. Introduction to calculus
o Differential calculus and the idea of slope reconsidered.
o Rules of differentiation. Ease of determining slope with differentiation.
o Deriving various economic functions such as marginal cost, marginal revenue from TC and TR curves.
o Idea of profit maximization.
o Point elasticity, tax yield, Keynesian multiplier and other applications.
5
5. Unconstrained Optimization
o First order conditions for minimum and maximum of a function.
o Second order conditions for minimum or maximum.
o Comparative statics – effect of taxes.
5
6. Partial differentiation
o Marginal product and production functions of various types.
o First and second order partial derivatives.
o Applying PD on non-linear models discussed.
7
7. Constrained Optimization
o Constrained optimization via substitution.
o Lagrange’s multiplier: Constrained optimization with two variables.
o Second order conditions and Lagrange’s multiplier.
o Constrained minimization.
o Constraint optimization with more than two variables.
8
8. Further topics in calculus
o Chain rule, product rule and quotient rule.
o Marginal revenue productivity theory of demand for labor.
o Point elasticity for non-linear functions.
o Integration – definite and indefinite integrals.
5
  Total 60