Syllabus for
Bachelor of Science (Economics, Mathematics)
Academic Year  (2023)

Course Description

This course is designed to give a systematic introduction to mainstream approaches to the study of microeconomics. The course begins by introducing students to the theories and derivation of demand and supply. Then the course proceeds with a systematic introduction to the theories of production. With the understanding of laws of production, cost, revenue, and functioning of various markets are introduced. The course has been designed in such a way that it stimulates awareness on essential variables for the understanding of how consumers and firms derive various decisions.

Course Objectives

The course has been conceptualised in order to help students:

• Develop an understanding of the conceptual foundations and analytical methods used in Microeconomics.
• Familiarise with the basics of consumer behaviour and decision-making criteria.
• Analyse and understand relationships and interactions in various forms of markets.

Theory of Consumer Behaviour: The Cardinal Utility Theory, The Indifference Curves Theory, Derivation of demand curve; The Market Demand: Derivation of the Market Demand- Determinants of Demand -Elasticities of Demand; Market Supply: Individual supply- Derivation of the Market Supply- Determinants of Supply -Elasticities of Supply.

Production Function; Laws of Production: The Law of Variable Proportions, Laws of Returns to Scale; Technological Progress and the Production Function.

The Traditional Theory: Short-Run Costs- Long-Run Costs, Economies and Diseconomies of scale, The 'Envelope Curve'; Modern Theory of Costs: Short-Run Costs, Long-Run Costs, The 'L-Shaped' Scale Curve.

Concepts of Revenue: Total, Marginal and Average; Market structure: Perfect Competition - Output Determination; Monopoly - Price and Output Determination, Price Discrimination; Monopolistic Competition - Price and Output Determination; Oligopoly – Cournot Model, Cartel.

Pindyck, R. S., & Rubinfeld, D. L. (2013). Microeconomics (8th ed.). New York: Pearson Education.

Salvatore, Dominick. (2017). Microeconomics Theory and Applications (5th ed.). Oxford: Oxford University Press.

Samuelson, P. A., & Nordhaus, W.D. (2010). Economics (19th ed.). New Delhi: McGraw-Hill Companies.

This course provides the basics of international trade theory stems from classical to new trade theories, and international economic policies on domestic and world welfare. This course begins with an introduction to international trade. Then the neo classical trade theories and new trade theories are discussed. The course concludes with a discussion on trade policies and its controversies. The course uses the empirical evidences to explain the theories and models in international trade.

Introduction: What is international economics about? An overview of world trade. Stylized facts about international trade, Components of Balance of Payments: Current account and Capital account.

Smith’s absolute advantage theory of trade, Ricardo’s comparative advantage theory of trade, concepts of offer curve and terms of trade; Heckscher-Ohlin theory, Rybczinski and Stolper-Samuelson theorems; factor price equalisation theorem; Leontief Paradox; Krugman’s New Trade Theory.

Instruments of trade policy; tariffs, quotas, export subsidies, voluntary export restraints, Global value Chain (GVC’s).

Political economy of trade policies, Controversies of trade policies, Free trade agreements

Francis Cherunilam. (2020). International Economics, 6th ed. McGraw Hill

Feenstra, R., Taylor, A. (2014). International Economics, 3rd ed. Worth Publishers.

Krugman, P., Obstfeld, M., Melitz, M. (2018). International Economics - Theory and Policy, 11th ed. Pearson Education

Pugel, T. (2015). International Economics, 16th ed. McGraw-Hill.

Soderstein, B and Geoffrey Reed (1999). International Economics, 3rd ed. Palgrave Macmillan

Dominick Salvatore. (2021). International Economics, 13th ed. Wiley

Antweiler, Werner and David Trefler. “Increasing Returns and All That: A View from Trade.” American Economic Review 92 no. 1 (2002): 93–119.

Bernhofen, Daniel M, and Brown. “Testing the General Validity Of the Heckscher-Ohlin Theorem: The Natural Experiment of Japan.” (PDF) University of Nottingham Working Paper, 2009.

Bowen, Harry P, Leamer, et al. “Multicountry, Multifactor Tests of the Factor Abundance Theory.” (PDF - 2.43MB) American Economic Review 77, no. 5 (1987): 791–809.

Dornbusch, R., S. Fischer, et al. “Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods.” American Economic Review 67, no. 5 (1977): 823–39.

Eaton, J., and S. Kortum. “Technology, Geography and Trade.” Econometrica 70, no. 5 (2002): 1741–79.

Broda, Christian, Nuno Limão, and David E. Weinstein. “Optimal Tariffs and Market Power: The Evidence.” American Economic Review 98, no. 5 (2008): 2032-2065.

Limao, Nuno. “Preferential Trade Agreements as Stumbling Blocks for Multilateral Trade Liberalization: Evidence for the United States.” American Economic Review 96, no. 3 (2006): 896–914.

Rose, Andrew K. “Do We Really Know That the WTO Increases Trade?” American Economic Review 94, no. 1 (2004): 98–114.

Course description : This course enables the students to understand the basic techniques and theories of real Analysis.

Course objectives : This course will help the learner to

COBJ1. examine the convergence or divergence of sequences and series.

COBJ2. understand the different types of convergence and their properties.

CO1. Quote and understand the definition of a limit of a sequence or a function in its various forms.

CO2. Demonstrate the convergence or divergence of the geometric and harmonic series and other standard series.

CO3. Apply the basic tests for convergence of infinite series.

CO4. Prove the tests for convergence: Comparison Test, Ratio Test, Cauchy’s Root test, Raabe’s Test, alternating series test etc.

CO5. Understand the differences between convergence and absolute convergence

CO6. Understand and solve binomial , logarithmic and exponential series

Open sets, closed sets, closure of a set, countable and uncountable sets, topology of real line. Sequences: Definition of Sequences, limit of a sequence, algebra of limits of a sequence, convergent, divergent, and oscillatory sequences, problems thereon. Bounded sequences, Monotonic sequences and their properties, Cauchy sequence.

Infinite series, Cauchy convergence criterion for series, geometric series, comparison test, convergence of p-series, D'Alembert's Ratio test, Raabe's test, Cauchy's Root test, alternating series, Leibnitz’s test. Definition and examples of absolute and conditional convergence.

Sequences and series of functions, Pointwise and uniform convergence. Mn - test, M-test, Statements of the results about uniform convergence. Power series and radius of convergence.

Course Description: This course enables the students to understand the basic theory and principles of complex analysis.

Course Objectives​: This course will help the learner to

COBJ1. Understand the theory and geometry of complex numbers.

COBJ2. Evaluate derivatives and integrals of functions of complex variables.

COBJ3. Examine the transformation of functions of complex variables. 

Properties of complex numbers, regions in the complex plane, functions of complex variable, limits, limits involving the point at infinity, continuity and differentiability of functions of complex variable. Analytic functions, necessary and sufficient conditions for a function to be analytic. 

Definite integrals of functions, contour integrals and its examples, Cauchy’s integral theorem, Cauchy integral formula, Liouville’s theorem and the fundamental theorem of algebra, elementary transformations, conformal mappings, bilinear transformations.

2.  J. Bak and D. J. Newman, Complex analysis, 2nd ed., Undergraduate Texts in Mathematics, Springer-Verlag New York, Inc., New York, 2000.

3.  A. Jeffrey, Complex Analysis and Applications, 2nd ed., CRC Press, Boca Raton 2013.

4.  L. V. Ahlfors, Complex Analysis, 3rd ed., McGraw-Hill Education, 2017.

5. S. Ponnusamy, Foundations of Complex Analysis, 2nd ed., Narosa Publishing House, Reprint 2021.

Course Description:

This course provides an introduction to R, statistical language, and an environment that provides more flexible graph capabilities than other popular statistical packages. The course also covers the basics of R for statistical computation and exploratory analysis.

Course Objectives:

This course is to equip the students to visualize and analyse the data using R and to communicate statistical results in correct manner. 

Getting started with R - installing R and R studio - getting help - installing and loading packages - R–markdown-simple arithmetic calculations - Numbers and Vectors - Objects- modes and attributes - Ordered and unordered Factors - Arrays and Matrices.

Constructing and modifying lists - Making Data frames - attach () and detach () - Working with data frame - Reading data from files using read. table () – scan ()

Grouping - Conditional execution: if statements - Repetitive execution: for loops - repeat and while loops - Functions.

Introduction to Statistics - probability and data with R. Visualizing numerical data - graphing systems available in R

Descriptive Statistics - measures of central tendency and dispersion – correlation - transforming data - exploring categorical variables. 

W. N. Venables, D. M. Smith,  An Introduction to R, R Core Team, version 4.0.3, 2020. 

Crawley M. J.,  The R book, John Wiley & Sons, 2012 

Seema Acharya,  Data Analytics Using R, CRC Press, Taylor & Francis Group, 2018

ESE: 50%

Course Description:

This course is designed to teach the basic concepts of random variables, generation functions, and an introduction to inferential statistics. It also gives a brief idea about standard probability distributions, sampling, and how they are applied in real time situations.

Course Objective:

Develop an understanding of random variables, probability distributions, and two-dimensional random variables, as well as sampling distributions, and inferential statistics.

Definition - Discrete and continuous random variables - Probability Mass function and Probability density function - Distribution function and its properties - Two dimension random variables: Discrete and continuous type - Joint Density function

Expectation of single and bivariate random variables and its properties - Conditional expectations - Moments and Cumulants - Moment Generating Function - conditional probability – conditional expectation - independence of variables with illustration.

Uniform - Bernoulli - Binomial - Poisson – geometric distributions along with their properties and applications

Uniform - Normal – Exponential distributions along with their properties and real-life applications. Population and sample - Parameter and statistic – sampling distributions: chi-square, t, F (only definition and statement of applications)

Point Estimators – hypothesis - testing of hypothesis problem -Setting of Hypothesis -Null and alternative hypotheses - Test statistics - Types of errors in hypothesis testing - level of significance – Critical region and p-value - Decision making.

Rohatgi V.K and Saleh E,  An Introduction to Probability and Statistics, 3rd edition, John Wiley & Sons Inc., New Jersey, 2015.

Montgomery D.C and Runger G.C,  Applied Statistics and Probability for Engineers, Wiley India, New Delhi, 2018.

Mood A.M, Graybill F.A, and Boes D.C,  Introduction to the Theory of Statistics, 3rd edition, McGraw Hill, New Delhi, 2017.

Course Description

This course is in continuation to the Introductory Macroeconomics course offered in the second semester. The course first introduces students to the mathematical framework for Keynesian economics – ISLM. Then the links between output, inflation, and unemployment and the effectiveness of policies are discussed from the Keynesian and the Monetarist perspectives. The third unit then introduces students to the open economy framework, and the course concludes with a discussion on the contemporary debates in the field of macroeconomic theory and policies.

Course Objectives

The course aims to:

• enhance the understanding of the learners regarding the macroeconomic dynamics in the short-run closed as well as open economy.
• understand and analyse the nexus between output, inflation and unemployment in both the short-run and in the long-run.
• understand and critically evaluate contemporary macroeconomic policies, create reports and deliver presentations

The goods market and derivation of IS curve; real influences and Shift in IS schedule; the money market and derivation of LM curve; monetary influences and the shift in LM curve; determination of equilibrium income and interest rates; the relative efficacy of fiscal and monetary policy under IS-LM framework; Critiques of IS-LM.

Links between output and unemployment: Okun’s law; Estimates of potential GDP and their limitations; Natural rate of unemployment; Factors affecting natural rate of unemployment; Links between inflation and unemployment: Phillips curve; Friedman-Phelps expectations augmented Phillips curve; Output-inflation trade-off: Keynesian vs. Monetarists view.

The Mundell-Fleming model: assumptions; determining equilibrium output and exchange rate in a small open economy; the monetary and fiscal policy under floating and fixed exchange rates regimes.

Economic Stabilization-Monetary vs. Fiscal Policy; Handling Recession- Higher Spending vs. Tax Cuts; Monetary Policy-Rule vs. Discretion Based; Central Bank Goal: Zero vs. non-zero Inflation; Government Budget - Balanced vs. Unbalanced; Tax Laws for Savings – Reformed vs. Not Reformed.

Froyen, R. (2014). Macroeconomics: Theories and Policies (10th ed.). Pearson Education.

Mankiw, N. G. (2014). Principles of Macroeconomics (7th ed.). Cengage Learning.

Mankiw, N. G. (2015). Macroeconomics (9th ed.). USA: Worth Publishers.

Blanchard, O. (2009). Macroeconomics (5th ed.). New Delhi: Pearson Education.

Heijdra, B. J. & Ploeg, F. V. (2001). Foundations of Modern Macroeconomics. Oxford: Oxford University Press.

McConnell, C. R., & Brue, S. L. (2011). Macroeconomics, Principles, Problems, and Policies.  New York: McGraw Hill Inc.

Moorthy, V. (2017). Applied Macroeconomics. New Delhi: I. K. International Publishing House.

Thomas, A. M. (2021). Macroeconomics: An Introduction. Cambridge: Cambridge University Press.

Public Economics is the study of government policy from the point of view of economic efficiency and equity. This course introduces students to allocation,distribution, stabilisation and regulatory functions of government. The course discusses about concept of public goods, club goods, and merit goods, andanalyses causes of externalities and market failures. It then does a systematic analysis of sources of government revenue, expenditure, public debt which is inclusive of theories on taxation, public expenditure and Economist views on public debts to provide students a broader perspective to analyse such issues. Last unit, provides a thorough understanding on fiscal institutions with a careful analysis of the issues pertaining to budgetary policies in general and Indian experience in particular.

The nature, scope and significance of public economics – Principle of Maximum Social advantage: Approaches and Limitations- Functions of Government - Economic functions - allocation, distribution and stabilization; Regulatory functions of the Government and its economic significance

Concept of public goods - characteristics of public goods, national vs. local public goods; Externality - concept of social versus private costs and benefits, merit goods, club goods; Provision versus production of public goods - Market failure and public Provision.

Concept of tax, types, canons of taxation-Incidence of taxes; Taxable capacity; Approaches to the principle of Equity in taxation -Ability to Pay principle, Benefit Approach; Sources of Public Revenue; VAT, Goods and Services Tax.

Structure and growth of public expenditure; Wagner’s Law of increasing state activities; Wiseman-Peacock hypothesis Different approaches to public debt; concepts of public debt; sources and effects of public debt; Methods of debt redemption- Trends of Public expenditure, Public debt and subsidies in India.

Government budget and its structure – Receipts and expenditure - concepts of current and capital account, balanced, surplus, and deficit budgets, concept of budget deficit vs. fiscal deficit- FRBM Act. Federal Finance: Different layers of the government; Inter governmental Transfer; horizontal vs. vertical equity; Principle of federal finance; Theory of Grants; Finance Commission.

Bhatia A.K. (2018). Public Economics, Wisdom Press, New Delhi.  Chapter -1.

Musgrave, R.A. and P.B Musgrave (1989). Public Finance in Theory and Practice, Tata McGraw-Hill, New Delhi.

Jha, R (2010). Modern Public Economics, Rutledge, London.

Cullis, John G. & Jones, Philip R. (2009). Public finance and public choice: analytical perspectives.  Oxford ; New York :  Oxford University Press

Tyagi B.P., Public Finance, Jai Prakash Nath Pub. Meerut (UP).

Government of India Budget Report, various issues

Citizen Report, various issues

Srivastava, D. K (2000). Fiscal Federalism in India, New Delhi, Har-Anand Publication Ltd.

Finance Commission Reports.

Economic Survey, Government of India, various issues.

State Finances: A Study of Budgets, Reserve Bank of India, various issues.

Course description : This course aims at developing the ability to write the mathematical proofs.  It helps the students to understand and appreciate the beauty of the abstract nature of mathematics and also to develop a solid foundation of theoretical mathematics.

Course objectives : This course will help the learner to

COBJ1. Understand the fundamentals of groups and its theories.

COBJ2. Relate abstract algebraic constructs to more familiar sets and operators

COBJ3. Know about the subgroups and group homomorphisms

COBJ4. Get familiar with the theories on rings, integral domains and fields.

Definition and examples of groups, examples of abelian and non-abelian groups, the group Z_n of integers under addition modulo n and the group U(n) of units under multiplication modulo n, complex roots of unity, groups of symmetries: Equilateral triangle.

Subgroups, the concept of a subgroup generated by a subset and the commutator subgroup of group, examples of subgroups including the center of a group. order of an element, cyclic subgroups, Cosets, Index of subgroup, Lagrange’s theorem, consequences of Lagrange’s theorem, Normal subgroups: their definition, examples, and characterizations, Quotient groups, permutation groups and Symmetric groups – Homomorphism of groups – Kernel of group homomorphisms and theorems thereon – Fundamental theorem of homomorphism of group.

Definition and examples of rings, examples of commutative and non-commutative rings: rings from number systems, Zn the ring of integers modulo n, ring of real quaternions, rings of matrices, polynomial rings, and rings of continuous functions. Subrings and ideals, Integral domains and fields, examples of fields: Zp, Q, R, and C. Field of rational functions.

Course Description:

This course is aimed at enabling the students to appreciate and understand the concepts of mathematics and statistics with the help of Python programming language. Students will learn to use the tools, libraries and packages useful for data analysis.

Course Objectives:

This course will help the learner to:

• gain proficiency in using Python for programming. 
• acquire skills in usage of suitable functions/packages of Python for data analysis.
• acquaint with Numpy and Pandas packages for data manipulating and visualization.
• illustrates use statistics methods to handle data effectively.

Arrays in NumPy, Creating, Indexing, Slicing, Algebraic operations on array, Python Data structures: List, Tuple, Dictionaries. Data series and Data frames, Using Pandas library to read and write data from a CSV file and Excel file.

Plotting data in Python using Matplotlib: 2D plots, bar graph, histogram, box plot, pie chart. Plotting data using Seaborn: Line Plot, Scatter Plot, Box plot, Point plot, Count plot, Violin plot, Swarm plot, Bar plot.

Mean, Median, Mode, Creating a frequency table, Dispersion, Variance, and standard deviation, Correlation between two data sets- Correlation Coefficient, Regression, GroupBy in Python, foundations of predictive analysis.

Jake VanderPlas, Python Data Science Handbook: Essential Tools for Working with Data, 2nd Edition.

This course is designed to prepare students to pursue careers in Actuarial Science. The aim of this course is to provide grounding in Actuarial Mathematics and their applications. Topics covered include the economics of insurance, survival distributions, life tables, and different types of life insurance.

Course Objectives​:

This course will help the learner to acquire fundamental knowledge of  Economics of insurance, Life Tables,Survival Distributions and Life Insurance.

Utility Theory, Insurance and Utility, Elements of Insurance, Optimal Insurance, Models for Individual Claim Random variables, Sums of independent random variables, Approximations for the distribution of sums, Applications to insurance

Probability for the Age-at-Death: The Survival function, Time-until-Death for a Person Age x, Curtate-Future-LifeTime, Force of Mortality. Life Tables: Relation of Life Table Functions to the Survival Function, Life table example, The Deterministic Survivorship Group, Other Life-Table Characteristics, Assumptions for Fractional Ages

Insurances Payable at the Moment of Death, Level Benefit Insurance, Endowment Insurance, Deferred Insurance, Varying benefit Insurance, Insurances Payable at the end of the year of death, Relationships between Insurances Payable at the moment of Death and the End of the Year of Death, Differential equations for Insurances Payable at the Moment of Death

2. Steven Roman, Introduction to the Mathematics of Finance: From risk management to options pricing. Springer, 2004.

This course is designed to help students to apply Calculus in solving Problems in Economics with the aid of FOSS tools.

Course Objective :

         COBJ 1:  Apply optimization techniques of calculus in Economics.

         COBJ 2:  Be familiar with the theory of integral calculus to understand concepts such as  Consumer/ Producer surplus,  Ramsey pricing, etc.

         COBJ 3:Use differential equations in conceptualising simple mathematical models in Economics.

Functions of one variable: Profit maximisation - Concavity and optimization - free rider problem - Comparative statics - elasticity, demand and profit maximisation - Taxation and monopoly - Taxation incidence and supply and demand - Ramsey pricing - Case studies with the help of FOSS tools.

Common integrals and rules of integration - Consumer surplus - Producer surplus - Consumer surplus and welfare - Average and marginal cost - Taxation and consumer surplus - present value - inequality measures - Ramsey pricing - Welfare measures - Case studies with the help of FOSS tools.

First order differential equations - logistic model - The Bernoulli equation - Systems of differential equations - Stability- Case study with the help of FOSS tools.