PATNA UNIVERSITY SYLLABUS BA ECONOMICS HONS

PATNA UNIVERSITY SYLLABUS BA ECONOMICS HONS

Below is given the Syllabus for Mathematical ans Statistical Methods for Economics for Patna University Distance Education BA Economics Honours course.

Paper-II

 MATHEMATICAL AND STATISTICAL METHODS FOR ECONOMICS

Marks - 100 Group- A

MATHEMATICAL METHODS FOR ECONOMICS

Marks - 50

1.    Preliminaries

Elements of logic and proof: converse and contra positive, necessary and sufficient conditions, proof by contradiction, mathematical induction. Sets and set operations. Ordered pairs, Cartesian products of sets. Relations. Functions: one-to-one and onto functions, composite functions, the inverse function. The real numbers: natural numbers, integers, rational and irrational numbers; absolute value and intervals; inequalities.

2.    Elementary Linear Algebra

2–, 3-, and n-dimensional row and column vectors; vector addition and scalar multiplication; length of a vector, scalar products, orthogonality. Geometric representation, lines and planes in R² and R3 . Linear and convex combinations of vectors. Linear independence. Convex sets.

Matrices and "matrix operations; addition, scalar multiplication, matrix multiplication. The transpose. The inverse of a square matrix. Rank. Elementary row operations and computation of rank. Invertibility and rank of square matrices.

Determinants: definition, properties, minors and cofactors, the Laplace expansion, expansion by alien cofactors; singularity and invertibility; the adjoint matrix and formula for the inverse.

Linear equation systems in matrix and vector notation (m equations, n variables). The rank criterion for consistency (existence of solutions ). Uniqueness of solutions; redundancy and degree's of freedom. The case m = n : homogeneous and inhomogeneous systems. determinantal criteria for consistency and uniqueness, matrix methods of solution and Cramers Rule.

3.   Functions of One Real Variable and Applications of Calculus

Examples (linear functions, polynomials, etc.) and elementary curve types, sets of points in the plane determined by equations or inequalities.

Infinite sequence and series: the concepts of convergence and limits; algebraic properties of limits. Present discounted values and elements of investment analysis.

The limit of f (x) as x—kx. Continuity. The intermediate-value theorem.

The derivative of a function. Differentiability and continuity. Techniques of differentiation; sums. products and quotients of functions; composite functions and the chain rule. Inverse functions. Implicit differentiation. Second and higher order derivatives. Concavity and convexity of functions: Jensen's inequality; the second derivative criterion. Points of inflexion. Differentials and linear approximation. Taylor's theorem and polynomial approximation. Indeterminate forms and L'Hopital's Rule.

Exponential and logarithmic functions. Logarithmic differentiation. Examples of the use of the exp and log functions (proportional rates of change, elasticities. continuous compounding etc.).

Optimization: stationary points, local and global optima, location of turning points and points of inflexion using derivatives; the role of concavity and convexity. Applications.

4.   Functions of Several Variables

[The emphasis throughout should be on functions of two variables (and related geometrical interpretation) without, however, restricting the discussion only to this case].

Geometric representation; level curves. Partial differentiation; plane sections and geometrical interpretation. Tangent planes to a surface. Higher- order partial derivatives, Young's Theorem. Partial derivatives in economics.

Linear approximation and differentials. The chain rule. The implicit function theorem (statement only), first -- and higher — order derivatives of functions defined implicitly, geometric interpretation.

Homogeneous and nomothetic functions. Elasticity of substitution.

Concave and convex functions, Jensen's inequality and characterization in terms of the Hessian (statement only). Convex sets. Quasiconcave and quasiconvex functions.

Maxima and minima, saddle points, unconstrained optimization, necessary and sufficient conditions for local optima.

Constrained optimization (equality constraints). The method of Lagrange multipliers. Interpretation of the necessary conditions and of the Lagrange multiplier; geometrical meaning. Sufficient conditions. Envelope results. Economic examples.

readings:

1.       Knut Sydsaeter and Peter J.  Hammond (2002), Mathematics for Economic Analysis, Pearson Educational Asia: Delhi (reprint of 1^st 1995 edition).

2.    Alpha C. Chiang (1984), Fundamental Methods of Mathematical Economics, McGraw Hill (3^rd edition).

Paper - II

MATHEMATICAL AND STATISTICAL METHODS FOR ECONOMICS

Marks-100 Group- B

STATISTICAL METHODS FOR ECONOMICS

Marks - 50

1.   Elementary Distribution Theory

Univariate Frequency Distributions measures of location, Dispersion, Skewness and Kurtosis; the first four moments about-zero and central moments.

2.   Elementary Probability Theory

Concepts of Sample space and events, probability of an event; addition and multiplication theorems; conditional probability and independence of events. Bayes rule.

Concept of a random variable; Probability distribution, Joint Marginal and Conditional Distributions, Independence of random variables; mean and variance of a random variable; binominal and normal distribution; Law of large numbers and central limit theorem.

3.   Introduction to Estimation and Hypothesis Testing

Methods of sampling; sampling distribution of a statistic; distribution of the sample mean; sampling error and standard error of a statistic with special reference to the mean; Point and interval estimation of parameters; properties of an estimator; unbiasedness, relative efficiency and consistency.

Testing of hypothesis; type I and type II errors, power of a test; large sample tests, t test for the mean; one tail and two tail tests for difference of means; Chi-square test for (i) goodness of fit and (ii) independence of two attributes.

4.  Bivariate Distributions and Simple Linear Regression

Marginal and conditional distributions: discrete case; Covariance and correlation: rank correlation.

Simple linear regression; method of least squares; Derivation of the normal equation; standard error of regression (SER), properties of the least squares estimator, Gauss-Markov Theorem, Simple tests of hypothesis on regression coefficients, linear and exponential trend, point and interval forecasts.

5.   Index Numbers

Concept of an index number. Laspeyer's, Paasche's and Fisher's Index Numbers; Time Reversal, Factor reversal and circular tests, Chain base index; Problems in the Construction of an index number; splicing; base shifting and use of index number for deflating other series.

1.   P.H. Karmel and M. Polasek, Applied Statistics for Economists, (4^th edition), Pitman,
                Australia.

2.        Alien Webster, Applied Statistics for Business and Economics, (3^rd edition), McGraw Hill, International Edition 1998.

3.      M.R. Spiegel (2^nd edition), Theory and Problems of Statistics, Schaum Series.