A bilevel programming approach to determining tax credits for biofuel production

Abstract 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 different support program. The agricultural sector is the follower. Its objective is to maximize profits 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 first involves a grid search over the tax credit variables corresponding to the two biofuels under consideration, ester and ethanol. Once these values are fixed, 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.