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Course of Study

Module 4700
Mathematical Economics (for Agricultural Economists)


Prof. Xiaohua YU Ph.D., University of Göttingen
Email: xyu@gwdg.de; Tel: 0551-3919574

Course Description

Some basic math techniques are crucial for a proper understanding of the current economic theory and methods, which also applies to agricultural economics.

This course is designed to help graduate-level students at the University of Göttingen and the Doctoral Certificate Program in Agricultural Economics understand some basic math tools (mainly optimization techniques) and their application to resource and environmental economics.

Course Outline

  1. Introduction
  2. Differentiation and Implicit Function
    • Differentiation
    • Partial Differentiation
    • Comparative Static Analysis
    • Implicit Function
    • Homogenous Functions
    • Homothetic Functions
    • Maclaurin and Taylor Series
  3. Optimization without constraints
    • First-Order Condition
    • Second-Order Conditions
    • Concavity and Convexity
    • Envelope Theorem
    • Duality and Theorem
  4. Optimization with Equality constraints
    • Lagrange-Multiplier Methods
    • Second-Order Conditions
    • Quasiconcavity and Quasiconvexity
  5. Optimization with Inequality constraints
    • Kuhn-Tucker Conditions
    • Constraint Qualifications
    • Sufficiency Theorems in Non-linearity
  6. Discrete Dynamic Programming
    • Bellman Equation
    • Overlap-Generation Model
  7. First-order Differential Equations
    • First-Order Linear Differential Equations
    • Exact Differential Equations
    • Random Matching Theorem
  8. Optimal Control Theory
    • Alternative Terminal Conditions
    • Infinite Time Horizontal
    • Calculus of Variations
  9. Some Numeric Methods
    • Newton’s Method
    • Runge-Kutta Method

Teaching Method: Lectures + Presentations
Language: English
Credits: 3

Reading List

Part I Development Economics

*1, Mortensen D.T. and C.A. Pissarides (1994) “Job Creation and Job Destruction in the Theory of Unemploment,” Review of Economic Studies, 61:397-415.
*2, Lucas R. (2004), Life Earnings and Rural-Urban Migration, Journal of Political Economy, 2004, vol. 112, no. 1, pt. 2
*3, Hanse G. and E. Prescott (2002), Malthus to Solow, American Economic Review, 1205-1217
4, Atkeson A. and A.T. Burstein (2010) “Innovative, Firm Dynamics and International Trade,” Journal of Political Economy, 118:435-484.
5, Holmstrom B. 1979, “Moral hazard and Observabililty”, the Bell Journal of Economics, 10:74-91.
6, Gary S. Becker; Robert J. Barro (1988) “A Reformulation of the Economic Theory of Fertility” The Quarterly Journal of Economics, Vol. 103, No. 1. (Feb., 1988), pp. 1-25.

Part II Environmental and Resource Economics

7, *Wu J., 2006, Environmental amenities, urban sprawl, and community characteristics, Journal of Environmental Economics and Management 52 (2006) 527–547
8, *Andersen P. 1982, Commercial Fisheries Under Price Uncertainty, Journal of Environmental Economics and Management, vol. 9:11-28.
9, *Tahvonen O, and S. Salo (1999) “Optimal Forest Rotation with in Situ Preferences”. Journal of Environmental Economics and Management, vol. 37:106-128.
10, Tahvonen O., Seppo Salo and Jari Kuuluvainen (2001) Optimal forest rotation and land values under a borrowing constraint, Journal of Economic Dynamics and Control, 25:1595-1627.