We study pollution permit markets in which a fraction of permits are allocated to firms based on their output. Output-based allocations, which are receiving increasing attention in the design of carbon markets around the world (e.g., Europe, California, New Zealand), are shown to be optimal under demand and supply volatility despite the output distortions they may create. In a market that covers multiple sectors, the optimal design combines auctioned permits with output-based allocations that are specific to each sector and increasing in its volatility. When firms are better informed about the latter or must self select, the regulator resort to some free (i.e., lump-sum) allocations to sort firms out.
utput-based allocations (OBAs) are typically used in emission trading systems (ETS) with a fixed cap to mitigate leakage in sectors at risk. Recent work has shown they may also be welfare enhancing in markets subject to supply and demand shocks by introducing some exibility in the total cap, resulting in a carbon price closer to marginal damage. We extend previous work to simultaneously include both leakage and volatility. We study how OBA permits can be implemented under an overall cap that may change with the level of production in contrast with a design that deducts OBA permits from the overall permit allocation as is the current practice in the EU-ETS and California. We show that introducing OBA permits while keeping the overall cap fi xed would only increase price uctuations and induce severe welfare losses to non-OBA sectors.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.