A Stock Targeting International Carbon-Tax Rule with Uncertainty and Diminishing Compliance

A rule for setting a tax on carbon emissions to limit their atmospheric stock to a predetermined level is developed for a world inhabited by uncoordinated, myopic, expected utility maximizing agents. In all locations, the mean of the marginal product of the carbon emitting input diminishes and the variance increases as climate deteriorates. The rule is illustrated for a world divided into poor countries and rich countries. The poor countries’ costs of non-compliance with the tax, in terms of per capita utility loss from diminished reputation, are negligible. The rich countries' costs of non-compliance and, consequently, inclination to pay the globally set tax can be substantial but not identical. The number of complying rich countries decreases with the tax level, but at a rate that is moderated by the range of the rich countries’ loss of per capita utility from abstinence.