Subsidies and rebound effect with incomplete carbon pricing: An application to biogas and livestock

Bioenergies from dedicated crops or wood have faced substantial criticisms due to their significant land requirements. Certain bioenergy pathways, such as biogas generated from crop residues, manure, or food waste, appear to be exempt from this criticism. However, these feedstocks are byproducts of agricultural activities that generate emissions not covered by current climate policies in most countries. We analyze the optimal biogas subsidy in a second-best framework featuring food–energy market interactions and incomplete pricing of emissions from food production and fossil natural gas. We show analytically how the indirect effect of the biogas subsidy on food production should be taken into account, as well as the welfare implications. We provide numerical simulations calibrated on the French dairy market and anaerobic digestion of livestock manure. We compare a second-best situation in which dairy emissions are not taxed with a first-best situation in which they are taxed. This illustration indicates that for a small Social Cost of Carbon, the rebound effect on milk production is moderate, and the optimal subsidy departs from the Pigouvian one accordingly. The second-best quantity of biogas is slightly larger than the first-best one. For a large Social Cost of Carbon, the rebound effect is important, and the gap between the first-best and second-best widens considerably.