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Rewarding countries for taxing fossil fuel combustion: optimal mechanisms under exogenous budgets

Consider a global institution with an exogenous budget that can reward each developing country based on its tax rate on the combustion of a given fossil fuel. I develop a model in which countries differ in the co-benefits that they derive from emissions reductions and also in their aversion to taxing carbon. Assuming a uniform type distribution and linear demand functions for the fossil fuel, I provide an explicit solution for the optimal mechanism. It can be implemented through a reward payment function of the following form: each country is rewarded based on how much (if at all) its carbon tax exceeds a certain reference level. The reward payment is quadratic in this amount if the global institution's budget is small. For large budgets, there is an additional term that is linear in the amount that the carbon tax exceeds the reference level. Empirical calibrations suggest that carbon pricing reward funds could play a valuable role if the world mobilizes substantial additional funding for supporting emissions reductions in developing countries.