Major elective · Economics · Semester 6 · TY BA · 4 credits · 100 marks · 60 hours
Module 1: Advanced Calculus for Economic Modeling (15 Hours)
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Multivariable Optimization: Functions of several variables. Partial derivatives and second-order partial derivatives. Unconstrained optimization for functions of two variables (using Hessian Determinant).
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Constrained Optimization: The Lagrange Multiplier Method for problems with equality constraints. Economic applications: Utility Maximization subject to a budget constraint; Cost Minimization subject to an output constraint. Interpretation of the Lagrange multiplier as a shadow price.
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Production Functions: Homogeneous production functions and returns to scale. Introduction to the Cobb-Douglas production function and its properties.
Module 2: Integral Calculus and Dynamic Analysis (15 Hours)
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Techniques of Integration: Integration by substitution and by parts, Definite integrals and the concept of area under a curve.
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Dynamic Economic Applications: Capital Formation - Finding the total capital stock from a net investment flow, Present Value of Cash Flows - Calculating the present value of a future sum and a continuous income stream, Consumer’s and Producer’s Surplus - Precise calculation using integration.
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Introduction to Differential Equations: Meaning and formation. Solving simple first-order differential equations. Application: The Harrod-Domar Growth Model.
Module 3: Statistical Inference and Regression Analysis ( 15 Hours)
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Introduction to Statistical Inference: Concept of a sampling distribution. Point and Interval Estimation.
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Hypothesis Testing: Formulating Null (H₀ ) and Alternative (H₁ ) hypotheses, Concepts of Type I and Type II errors, p-values, and level of significance, conducting a t-test for a single population mean.
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Simple Linear Regression: Moving beyond correlation to causation, The Classical Linear Regression Model (CLRM), Ordinary Least Squares (OLS) method: Derivation and interpretation of slope and intercept coefficients, Goodness-of-fit: Understanding and interpreting R-squared.
Module 4: Economic Indices and Applied Data Analysis: (15 Hours)
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Index Numbers: Construction of simple and weighted index numbers: Laspeyre’s, Paasche’s, and Fisher’s Ideal Index. Consumer Price Index (CPI) and Wholesale Price Index (WPI): Uses and limitations. Concepts of splicing, deflating, and real income.
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Sampling Methods: Probability vs. non-probability sampling methods (Simple Random, Stratified, Systematic). The role of sampling theory in economic data collection.
Reference Books
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1
Chiang, A. C., & Wainwright, K. (2005). Fundamental Methods of Mathematical Economics (4th Edition). McGraw-Hill.
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2
Sydsaeter, K., Hammond, P., Strom, A., & Carvajal, A. (2016). Essential Mathematics for Economic Analysis. Pearson.
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3
Dowling, E. T. (2004). Introduction to Mathematical Economics (Schaum's Outline Series). Tata McGraw-Hill.
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4
Gujarati, D. N., Porter, D. C., & Gunasekar, S. (2017). Basic Econometrics (5th Edition). McGraw-Hill.
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5
Wooldridge, J. M. (2015). Introductory Econometrics: A Modern Approach (6th Ed.). Cengage Learning. (Chapters on Regression and Hypothesis Testing)
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6
Gupta, S. C. & Gupta, A. (2022). Statistical Methods (Sultan Chand & Sons).
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7
Sancheti, D.C. & Kapoor, V.K. (2014). Statistics: Theory, Methods and Applications. S. Chand.
