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OPTIMAL PEST CONTROL IN AGRICULTURE THOMAS CHRISTIAANS THOMAS EICHNER RUEDIGER PETHIG CESIFO WORKING PAPER NO. 1507 CATEGORY 8: RESOURCES AND ENVIRONMENT JULY 2005 An electronic version of the paper may be downloaded from the SSRN website: www.SSRN.com from the CESifo website: www.CESifo.de

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Page 1: OPTIMAL PEST CONTROL IN AGRICULTURE T C CES W P N 1507 · OPTIMAL PEST CONTROL IN AGRICULTURE THOMAS CHRISTIAANS THOMAS EICHNER RUEDIGER PETHIG CESIFO WORKING PAPER NO. 1507 CATEGORY

OPTIMAL PEST CONTROL IN AGRICULTURE

THOMAS CHRISTIAANS THOMAS EICHNER RUEDIGER PETHIG

CESIFO WORKING PAPER NO. 1507 CATEGORY 8: RESOURCES AND ENVIRONMENT

JULY 2005

An electronic version of the paper may be downloaded • from the SSRN website: www.SSRN.com• from the CESifo website: www.CESifo.de

Page 2: OPTIMAL PEST CONTROL IN AGRICULTURE T C CES W P N 1507 · OPTIMAL PEST CONTROL IN AGRICULTURE THOMAS CHRISTIAANS THOMAS EICHNER RUEDIGER PETHIG CESIFO WORKING PAPER NO. 1507 CATEGORY

CESifo Working Paper No. 1507

OPTIMAL PEST CONTROL IN AGRICULTURE

Abstract Based on economic methodology we model an ecosystem with two species in predator-prey relationship: mice feed on grain and grain feeds on a resource. With optimizing behaviour of individual organisms a short-run ecosystem equilibrium is defined and characterized that depends on the farmer’s use of fertilizer and on the mice population which, in turn, is affected by pesticides. In that way, a microfounded agricultural production function is derived. Linking a sequence of short-run ecosystem equilibria yields the growth function of the mice population which is thus derived rather than assumed. In each period the farmer harvests all grain in excess of some given amount of seed. If she maximizes her present-value profits, optimal farming is shown to depend on the prices of pesticide and grain. It is either optimal to use no pesticide or a moderate amount of pesticide or to apply a chattering control. Pest eradication is never optimal. On the other hand, if the farmer takes into account steady state mice populations only, it may be optimal to eradicate mice or to use no or a moderate amount of pesticide depending on prices as well as on the shape of the grain production function which is determined by micro parameters of grain reproduction.

JEL Code: Q24, Q57.

Keywords: pesticides, agriculture, predator-prey, chattering pest control.

Thomas Christiaans University of Siegen

Department of Economics Hoelderlinstr. 3 57068 Siegen

Germany [email protected]

Thomas Eichner University of Siegen

Department of Economics Hoelderlinstr. 3 57068 Siegen

Germany [email protected]

Ruediger Pethig

University of Siegen Department of Economics

Hoelderlinstr. 3 57068 Siegen

Germany [email protected]

Page 3: OPTIMAL PEST CONTROL IN AGRICULTURE T C CES W P N 1507 · OPTIMAL PEST CONTROL IN AGRICULTURE THOMAS CHRISTIAANS THOMAS EICHNER RUEDIGER PETHIG CESIFO WORKING PAPER NO. 1507 CATEGORY

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Page 23: OPTIMAL PEST CONTROL IN AGRICULTURE T C CES W P N 1507 · OPTIMAL PEST CONTROL IN AGRICULTURE THOMAS CHRISTIAANS THOMAS EICHNER RUEDIGER PETHIG CESIFO WORKING PAPER NO. 1507 CATEGORY

CESifo Working Paper Series (for full list see www.cesifo-group.de)

___________________________________________________________________________ 1441 John Whalley, Globalization and Values, April 2005 1442 Denise L. Mauzerall, Babar Sultan, Namsoug Kim and David F. Bradford, Charging

NOx Emitters for Health Damages: An Exploratory Analysis, April 2005 1443 Britta Hamburg, Mathias Hoffmann and Joachim Keller, Consumption, Wealth and

Business Cycles in Germany, April 2005 1444 Kohei Daido and Hideshi Itoh, The Pygmalion Effect: An Agency Model with

Reference Dependent Preferences, April 2005 1445 John Whalley, Rationality, Irrationality and Economic Cognition, April 2005 1446 Henning Bohn, The Sustainability of Fiscal Policy in the United States, April 2005 1447 Torben M. Andersen, Is there a Role for an Active Fiscal Stabilization Policy? April

2005 1448 Hans Gersbach and Hans Haller, Bargaining Power and Equilibrium Consumption,

April 2005 1449 Jerome L. Stein, The Transition Economies: A NATREX Evaluation of Research, April

2005 1450 Raymond Riezman, John Whalley and Shunming Zhang, Metrics Capturing the Degree

to which Individual Economies are Globalized, April 2005 1451 Romain Ranciere, Aaron Tornell and Frank Westermann, Systemic Crises and Growth,

April 2005 1452 Plutarchos Sakellaris and Focco W. Vijselaar, Capital Quality Improvement and the

Sources of Growth in the Euro Area, April 2005 1453 Kevin Milligan and Michael Smart, Regional Grants as Pork Barrel Politics, April 2005 1454 Panu Poutvaara and Andreas Wagener, To Draft or not to Draft? Efficiency,

Generational Incidence, and Political Economy of Military Conscription, April 2005 1455 Maurice Kugler and Hillel Rapoport, Skilled Emigration, Business Networks and

Foreign Direct Investment, April 2005 1456 Yin-Wong Cheung and Eiji Fujii, Cross-Country Relative Price Volatility: Effects of

Market Structure, April 2005

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1457 Margarita Katsimi and Thomas Moutos, Inequality and Relative Reliance on Tariffs:

Theory and Evidence, April 2005 1458 Monika Bütler, Olivia Huguenin and Federica Teppa, Why Forcing People to Save for

Retirement may Backfire, April 2005 1459 Jos Jansen, The Effects of Disclosure Regulation of an Innovative Firm, April 2005 1460 Helge Bennmarker, Kenneth Carling and Bertil Holmlund, Do Benefit Hikes Damage

Job Finding? Evidence from Swedish Unemployment Insurance Reforms, May 2005 1461 Steffen Huck, Kai A. Konrad and Wieland Müller, Merger without Cost Advantages,

May 2005 1462 Louis Eeckhoudt and Harris Schlesinger, Putting Risk in its Proper Place, May 2005 1463 Hui Huang, John Whalley and Shunming Zhang, Trade Liberalization in a Joint Spatial

Inter-Temporal Trade Model, May 2005 1464 Mikael Priks, Optimal Rent Extraction in Pre-Industrial England and France – Default

Risk and Monitoring Costs, May 2005 1465 François Ortalo-Magné and Sven Rady, Heterogeneity within Communities: A

Stochastic Model with Tenure Choice, May 2005 1466 Jukka Pirttilä and Sanna Tenhunen, Pawns and Queens Revisited: Public Provision of

Private Goods when Individuals make Mistakes, May 2005 1467 Ernst Fehr, Susanne Kremhelmer and Klaus M. Schmidt, Fairness and the Optimal

Allocation of Ownership Rights, May 2005 1468 Bruno S. Frey, Knight Fever – Towards an Economics of Awards, May 2005 1469 Torberg Falch and Marte Rønning, The Influence of Student Achievement on Teacher

Turnover, May 2005 1470 John Komlos and Peter Salamon, The Poverty of Growth with Interdependent Utility

Functions, May 2005 1471 Hui Huang, Yi Wang, Yiming Wang, John Whalley and Shunming Zhang, A Trade

Model with an Optimal Exchange Rate Motivated by Current Discussion of a Chinese Renminbi Float, May 2005

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May 2005

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Stages in Enterprise Formation: The “New View” of Dividend Taxation Reconsidered, June 2005

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Trade Impacts of Domestic Policies, June 2005 1481 Edward B. Barbier and Michael Rauscher, Trade and Development in a Labor Surplus

Economy, June 2005 1482 Harrie A. A. Verbon and Cees A. Withagen, Tradable Emission Permits in a Federal

System, June 2005 1483 Hendrik Hakenes and Andreas Irmen, On the Long-Run Evolution of Technological

Knowledge, June 2005 1484 Nicolas Schmitt and Antoine Soubeyran, A Simple Model of Brain Circulation, June

2005 1485 Carsten Hefeker, Uncertainty, Wage Setting and Decision Making in a Monetary Union,

June 2005 1486 Ondřej Schneider and Jan Zápal, Fiscal Policy in New EU Member States – Go East,

Prudent Man!, June 2005 1487 Christian Schultz, Virtual Capacity and Competition, June 2005 1488 Yvan Lengwiler and Elmar Wolfstetter, Bid Rigging – An Analysis of Corruption in

Auctions, June 2005 1489 Johannes Becker and Clemens Fuest, Does Germany Collect Revenue from Taxing

Capital Income?, June 2005 1490 Axel Dreher and Panu Poutvaara, Student Flows and Migration: An Empirical Analysis,

June 2005 1491 Bernd Huber and Marco Runkel, Interregional Redistribution and Budget Institutions

under Asymmetric Information, June 2005

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1492 Guido Tabellini, Culture and Institutions: Economic Development in the Regions of

Europe, July 2005 1493 Kurt R. Brekke and Michael Kuhn, Direct to Consumer Advertising in Pharmaceutical

Markets, July 2005 1494 Martín Gonzalez-Eiras and Dirk Niepelt, Sustaining Social Security, July 2005 1495 Alfons J. Weichenrieder, (Why) Do we need Corporate Taxation?, July 2005 1496 Paolo M. Panteghini, S-Based Taxation under Default Risk, July 2005 1497 Panos Hatzipanayotou and Michael S. Michael, Migration, Tied Foreign Aid and the

Welfare State, July 2005 1498 Agata Antkiewicz and John Whalley, BRICSAM and the Non-WTO, July 2005 1499 Petr Hedbávný, Ondřej Schneider and Jan Zápal, A Fiscal Rule that has Teeth: A

Suggestion for a ‘Fiscal Sustainability Council’ underpinned by the Financial Markets, July 2005

1500 J. Atsu Amegashie and Marco Runkel, Sabotaging Potential Rivals, July 2005 1501 Heikki Oksanen, Actuarial Neutrality across Generations Applied to Public Pensions

under Population Ageing: Effects on Government Finances and National Saving, July 2005

1502 Xenia Matschke, Costly Revenue-Raising and the Case for Favoring Import-Competing

Industries, July 2005 1503 Horst Raff and Nicolas Schmitt, Why Parallel Trade may Raise Producers Profits, July

2005 1504 Alberto Bisin and Piero Gottardi, Efficient Competitive Equilibria with Adverse

Selection, July 2005 1505 Peter A. Zadrozny, Necessary and Sufficient Restrictions for Existence of a Unique

Fourth Moment of a Univariate GARCH(p,q) Process, July 2005 1506 Rainer Niemann and Corinna Treisch, Group Taxation, Asymmetric Taxation and

Cross-Border Investment Incentives in Austria, July 2005 1507 Thomas Christiaans, Thomas Eichner and Ruediger Pethig, Optimal Pest Control in

Agriculture, July 2005