Module 4700
Mathematical Economics (for Agricultural Economists)

Instructor

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

Lecture Room: Online Course with ZOOM (Zoom meeting information will be sent later)

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
   • Example: Market Power Estimation
   • Comparative Static Analysis
   • Implicit Function
   • Homogenous Functions
     • Example: Consumer Theory and Production Theory
   • Homothetic Functions
   • Maclaurin and Taylor Series
     • Example: Cobb-Douglas and Translog Production Function
   • Uncertainty
     • Example: Firm Theory and Insurance
3. Optimization without constraints
   • First-Order Condition
   • Second-Order Conditions
   • Concavity and Convexity
   • Envelope Theorem
   • Duality and maximization 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
     • Example: Exact Welfare Measure
   • Exact Differential Equations
   • Random Matching Theorem
8. Optimal Control Theory
   • Alternative Terminal Conditions
     • Example: None-renewable resource use
   • Infinite Time Horizontal
     • Example: Renewable resource use
   • Calculus of Variations
9. Some Numeric Methods
   • Newton’s Method
   • Runge-Kutta Method

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

• Chiang A. and K. Wainwright, Fundamental Methods of Mathematical Economics, (4ed.) McGraw-Hill. 2004.
• Dixit A. Optimization in Economic Theory, Oxford University Press, 1990.
• Takayama A. Analytical Methods in Economics, U Michigan Press, 2000.
• Sundaram R. K. A First Course in Optimization Theory, Cambridge U. Press, 2007.

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.

7, Bao T., Dai Y. and X. Yu (2018) Memory and Discounting: Theory and Evidence Journal of Economic Dynamics and Control. Volume 88, March 2018, Pages 21-30

8, Chen, Y. and X. Yu (2018), Does the centralized Slaughtering Policy Create Market Power for Pork Industry in China, China Economic Review. Vol. 58:59-71.

Part II Environmental and Resource Economics

9, *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.

10, *Tahvonen O, and S. Salo (1999) “Optimal Forest Rotation with in Situ Preferences”. Journal of Environmental Economics and Management, vol. 37:106-128.

11, 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.

12, Koemle D., Dieter Koemle, Yves Zinngrebe and Xiaohua Yu (2018), Highway Construction and Wildlife Populations: Evidence from Austria. Land Use Policy.Vol.73:447-457.

Time table

Time	Monday	Tuesday	Wednesday	Thursday	Friday
8:30-10:00	Lecture 1	Lecture 5	Lecture 19	Lecture 13	Lecture 17
10:30-12:00	Lecture 2	Lecture 6	Lecture 10	Lecture 14	Lecture 18
13:30-15:00	Lecture 3	Lecture 7	Lecture 11	Lecture 15
15:15-16:45	Lecture 4	Lecture 8	Lecture 12	Lecture 16

Venue: ZOOM online course