A bilevel programming approach to determining tax credits for biofuel production

This paper presents a bilevel programming formulation of a leader±follower game that can be used to help decision makers arrive at a rational policy for encouraging biofuel production. In the model, the government is the leader and would like to minimize the annual tax credits it allows the petro-chemical industry for producing biofuels. The crops grown for this purpose are on land now set aside and subsidized through a di€erent support program. The agricultural sector is the follower. Its objective is to maximize pro®ts by selecting the best mix of crops to grow as well as the percentage of land to set aside. Two solution algorithms are developed. The ®rst involves a grid search over the tax credit variables corresponding to the two biofuels under consideration, ester and ethanol. Once these values are ®xed, nonfood crop prices can be determined and the farm sector linear program solved. The second algorithm is based on an approximate nonlinear programming (NLP) formulation of the bilevel program. An ``engineering'' approach is taken where the discontinuities in the government's problem are ignored and the farm model is treated as a function that maps nonfood crop prices into allocation decisions. Results are given for an agricultural region in the northern part of France comprising 393 farms. Ó 2000 Elsevier Science B.V. All rights reserved.