Course Code: CAL-211
Title: Calculus-II
Credit Hours: 03
Prerequisite: Calculus-I
Objectives:
To prepare the students with the essential tools of calculus to apply the concepts and the techniques in Economics.Course Contents
Partial & Total Differentiation
- Partial Differentiation.
- Marginal Physical Product of Labor and Capital.
- Marginal Utility Functions.
- Money Market Analysis, Demand for Money Function Analysis using Partial Derivatives.
- Income Elasticity of Demand and Cross Price Elasticity of Demand using Partial Derivatives.
Second and Higher Order Derivatives.
- Profit Maximization Condition using Second Derivative.
- Young’s Theorem.
- Partial Derivatives Application on Three Input Production Function Differentials versus Derivatives.
- Point Elasticity using Differentials, Income and Price Elasticity of Demand using Differentials.
Concept of Total Differentials.
- Savings Function and Total Differentials.
- Specific Utility Function and Total Differentials.
Concept of Total Derivatives.
- Specific Production Function with time-dependent Labor and Capital.
- Exponential Functions and Growth.
- Rules of Differentiation of Exponential and Logarithmic Functions.
- Optimal Timing: A Problem of Wine Storage, A Problem of Timber Cutting, A Problem of Land Purchase for Speculation.
- Finding the Rate of Growth using Exponential and Logarithmic Functions.
- Point Elasticity.
- Rate of Growth of Per Capita Employment. Rate of Growth of Profit.
Optimization
Concept of Optimization:Calculus Approach to Optimization
- 1st Order and 2nd Order Conditions.
- Average Cost Minimization Analysis.
Matrix Approach to Optimization (2nd Order)
- Hessian Test
- Profit Maximization Analysis
- Profit Maximization of Technically Related Goods
- Monopolistic Firm Producing Related Goods
- Firm Producing Substitute Goods
- Short Run Production Function Analysis
Optimization of More than one Choice Variable
- Economic Application
- Multi-product Firm
- Multi-plant Firm
- Price Discrimination by Monopoly
- Price Discrimination by Monopsony
- Input Decision of a Firm
- Profit Maximization of Two-Product Firm.
Comparative-Static Aspects of Optimization
- Rationale for Constrained Optimization.
- Finding Stationary Values using Substitution-Elimination Method.
- Finding Stationary Values Method of Lagrange Multiplier.
- Interpretation of the Lagrange Multiplier.
- Second Order Condition: The Bordered Hessian. Convexity and Concavity using Second Order Derivative.
- Economic Applications:
- Utility Maximization
- Law of Equi-marginal Utility using Lagrangian Multiplier
- Production Function Maximization
- Logarithmically Transformed Production Function.
Integral Calculus
- Dynamics and Integration.
- The Nature of Indefinite Integrals.
- Basic Rules of Integration.
- The Substitution Rule
- Rule of Integration by Parts.
- Economic Applications of Integrals:
- Finding Total Functions from Marginal Functions
- Investment & Capital Formation
- Utility Function
- Definite Integrals
- Major Properties of Definite Integral
- A Definite Integral as an Area Under a Curve
- Improper Integrals
Consumer Analysis using Integrals
- Applications of Definite Integrals:
- Consumer’s Reservation Price using Differential Equations
- Consumer Willingness to Pay using Integrals
- Consumer Surplus using Integrals
- Differential of Consumer Surplus using Integrals
- Producer & Social Surplus using Integrals
- Producer Surplus with Tax using Integrals.
Firm Related Microeconomic Applications of Integrals
- Wine Storage Problem with Storage Costs.
- Breakeven Analysis of a Firm. Scale of Production Analysis.
- Mobile Production Analysis.
- Firm’s Average Profit Analysis.
- Firm’s Average Cost Analysis.
- Average Production Analysis.
- Average Inventory Analysis.
- Advertisement Analysis.
- Profit over Useful Life of Machine.
- Oil Extraction Analysis, Dynamics of Labour Cost.
Miscellaneous Microeconomic Applications of Integrals
- Efficiency Analysis using Integrals.
- Cost Effectiveness Decision using Differential Equations.
- Depreciation Analysis using Integrals.
- Retirement Annuity Analysis using Integrals.
- Wage Differential using Integrals.
- Present Value of Cash Flow.
- Present Value of a Perpetual Flow.
Macroeconomic Applications of Integrals
- Gini Index using Integrals.
- Depletion of Energy Resources Analysis using Integrals.
- Present Value of Gold Mine using Integrals.
- Balance of Trade Analysis using Integrals.
- Demand Analysis of Oil using Integrals.
- Demand Analysis of Oil using Integrals.
- Domar Growth Model: Framework, Solution and Numerical.
Recommended Books:
- Chiang A.C. Fundamental Methods of Mathematical Economics McGraw Hill –Latest
- Weber E. Jean, Mathematical Analysis, Business and Economic Application (latest edition).
- Bradley, T. Essential mathematics for economics and business. Latest edition. John Wiley & Sons.
- Dowling, E. T. Theory and Problems of Introduction to Mathematical Economics. Latest Edition, McGraw-Hill, New York.
- Hoffman, L. D., & Bradley, G. L. Calculus for business, economics, and the social and life sciences. McGraw-Hill. Latest edition.
- Kolman, B., & Beck, R. E. (1995). Elementary linear programming with applications. Academic Press.
- Sydsæter, K. and Hammond, P. Essential Mathematics for Economic Analysis. Latest edition., Pearson Education Limited, England.