OPTIMAL CONTROL OF DESENSITIZING INPUTS:THE CASE OF PAYLEAN DEVENDRA CANCHI,NING LI,KEN FOSTER,PAUL V. PRECKEL, ALLAN SCHINCKEL, AND BRIAN RICHERT We examine production economic implications of a specialized input to which a biological system (e.g., an animal) becomes desensitized over time, but its marginal productivity can be restored by increasing the dosage level. Optimal dosage levels and their timing become choice variables and may substitute or complement other inputs. This analysis is demonstrated for the case of Paylean in swine production. Use of a step-up approach to optimal Paylean use is shown to return substantial value, especially in market structures that reward producers for lean carcass value, and in cases where the health status of the animals is compromised. Key words: desensitizing inputs, livestock production, optimal replacement. JEL codes: Q10, Q16. Production economists have extensively stud- ied the problem of optimal input use in man- aging the growth of a biological system. The standard static model of typical production input response reflects high marginal response at low levels of input use and diminishing marginal response as the level of input use increases. Over time, the marginal response may change as the biological system matures. A pharmacological input may desensitize the biological system (e.g., animal), causing a pre- cipitous drop in marginal productivity. 1 How- ever, unlike ordinary inputs to production, the marginal productivity of a desensitizing input can often be revitalized by increasing the dosage. From a production economics perspective, the diminishing response over time associ- ated with desensitization is interpreted as a declining marginal product at a fixed dosage, and leads to rapidly diminishing returns as the period of use is extended. This feature Devendra Canchi is a graduate research assistant and Ken Foster and Paul Preckel are professors in the Department of Agricul- tural Economics at Purdue University. Ning Li is an analyst at Citigroup, and Allan Schinckel and Brian Richert are a professor and associate professor, respectively, in the Department of Animal Sciences at Purdue University. The authors appreciate the helpful comments and suggestions of Peter Berck and three anonymous referees whose assistance greatly improved this manuscript. 1 Desensitization refers to the adaptation of the biological sys- tem to the administration of the pharmacological treatment that reduces the effectiveness of a constant dosage over time. of desensitizing inputs limits the optimal sup- plementation period for any given concen- tration level, leads to optimal strategies that potentially adjust the levels of input use over time, and creates an interdependence between decisions regarding both the level of input use and the timing of its administra- tion. The problem is that limited knowledge about the management of desensitizing inputs exists among economists and farm manage- ment practitioners. Desensitization occurs as the result of down- regulation mechanisms in the animal’s or plant’s metabolism toward chemical interven- tion (Mills and Liu 1990). The phenomenon is somewhat rare in standard production pro- cesses, but similar phenomena do occasionally occur in agricultural production. A comparable though not exactly parallel situation occurs in the context of pest management. Commonly, widespread, long-term usage of a pesticide leads to an increase in the resistant population of insects or weeds (Regev et al. 1983). In this manner, the pesticide input becomes ineffec- tive over time. The difference with the present case is that population resistance develops over generations,whereas desensitization occurs for the individual organism over time. Desensiti- zation is also a potential concern for antibi- otic use in livestock and in some human drug therapies (Lanzara 2004; Kim et al. 2003). In this article, we focus on the case of a swine Amer. J. Agr. Econ. 92(1): 56–69; doi: 10.1093/ajae/aap016 Received October 2008; accepted August 2009 © The Author (2010). Published by Oxford University Press on behalf of the Agricultural and Applied Economics Association. All rights reserved. For permissions,please e-mail: journals.permissions@oxfordjournals.org at Purdue University Libraries ADMN on July 24, 2014 http://ajae.oxfordjournals.org/ Downloaded from