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Course Code: CAL-211 Title: Calculus-II Credit Hours: 03 Prerequisite: Calculus-I


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.


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.

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