# Mathematical Methods for Economics

** Course Objectives **

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

** Teaching Methodology **

- Friendly introduction to new and apparently complicated topics before exploring more rigorous methods.
- Use of real world data in econometric techniques which reinforces the idea with a real example.
- 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
- Continuous assessment through quizzes and problem solving challenges.

** Course Outline **

Sr.No. | Topic | Hours |

1 |
Functions and Graphso 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 Mathematicso 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 methodso 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 calculuso 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 Optimizationo 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 differentiationo 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 Optimizationo 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 calculuso 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 |