The tractable general equilibrium model developed by Golosov et al. (2014), GHKT for short, is modified to allow for additional negative impacts of global warming on utility and productivity growth, mean reversion in the ratio of climate damages to production, labour-augmenting technical progress, and population growth. We also replace the GHKT assumption of full depreciation of capital each decade by annual logarithmic depreciation. Furthermore, we allow the government to use a lower discount rate than the private sector. We derive a tractable rule for the optimal carbon price for each of these extensions which contain the GHKT model as a special case. Finally, the GHKT model is simplified by modelling temperature as cumulative emissions and calibrated to Burke et al. (2015) damages. We illustrate our analytical rules with a range of optimal policy simulations.
carbon price tractable rule general equilibrium utility and growth damages technical progress population growth logarithmic depreciation differential discount rules