A biofuel supply chain equilibrium analysis with subsidy consideration

Abstract

Summary We consider a biofuel supply chain problem in which a farmer supplies two downstream refineries with nonidentical crops (corn and energy crop). The problem has been modeled as a multi leader single follower game to derive the farmer's decisions on land use as well as refineries' proposed prices to the farmer. We consider subsidizing the farmer and the refinery that uses the energy crop to study whether a subsidy plan can enhance the advanced biofuel production and meet the mandate of the Environmental Protection Agency (EPA). This mandate requires the production of 36 billion gallons of biofuel, out of which 21 billion gallons should be noncorn‐based biofuel. We solve the problem under four cases based on the willingness of the farmer to sell corn to the food market as well as the availability of land expansion for her. The Nash equilibrium is derived for all cases, and parametric analyses are used to study the effect of subsidies on the profit of the players and the total social welfare of the supply chain. We observe that a government's expenditure can be offset by the increase of the social welfare under certain circumstances. We find the minimum budget requirement to meet the EPA's mandate and show that a specific budget can be distributed in different ways while obtaining the same results.

A study of subsidizing a biofuel supply chain to incentivize the production of advanced biofuel: An equilibrium problem with equilibrium constraints approach

“…Similarly, with the same amount of total subsidy, increases in the total producer and the consumer surplus remain the same regardless of the subsidy distribution between the farmer and the advanced refinery. A similar result has previously been reported by Bajgiran et al, 25 where a biofuel supply chain with a single farmer and a single refinery of each type is considered.…”

“…Hence, refineries can produce more biofuel and are better off under the farmer's increasing marginal cost. Finally, from Figure 2, we observe that the total subsidy payment is not offset by the increase of the total social welfare, although we can sometimes see that happen under some conditions 25 …”

“…Additionally, corn can be sold to a corn market for food. We consider that the farmers in the region form a union and act as a single firm, 25 and there are multiple refineries in both conventional and advanced types that use corn and cellulosic biomass as input, respectively, for biofuel production.…”