When does eco-efficiency rebound or backfire? An analytical model

•Examine eco-efficiency and its relationship with the rebound.•Provide the analytic conditions for different kind of rebounds.•Highlight the possibility of a reverse rebound effect. It is known that an eco-efficiency strategy, which saves resources in the production process, may be offset by a rebound effect; it may even backfire. Less known are the exact conditions under which eco-efficiency rebounds or backfires. This article fills the gap by providing an analytical model of the rebound and backfire effects. We propose an optimal control framework of dynamic pricing and eco-efficiency investment, for which eco-efficiency reduces the unit production cost and boosts the demand of environmentally concerned consumers. Results, which hold with a general demand formulation, examine the analytic conditions for the rebound and backfire effects. They also highlight the possibility of a reverse rebound effect. Such results pave the way to sounder sustainability strategies.