Intergenerational Inequality Aversion, Growth and the Role of Damages; Occam's rule for the global carbon tax

We use the Euler equation to put forward a back-on-the-envelope rule for the global carbon tax based on a two-box carbon cycle with temperature lag, and a constant elasticity of marginal damages with respect to GDP. This tax falls with time impatience and intergenerational inequality aversion and rises with population growth and prudence. It also falls with growth in living standards if inequality aversion is large enough or marginal damages do not react much too GDP. It rises in proportion with GDP if marginal climate damages are proportional to output and has a flat time profile if they are additive. The rule also allows for mean reversion in climate damages. The rule closely approximates the true optimum for our IAM of Ramsey growth, scarce fossil fuel, energy transitions and stranded assets despite it using the more complicated DICE carbon cycle and temperature modules. The simple rule gets close to the social optimum even if damages are much more convex than in DICE.