Competing Stochastic Thresholds: The Green Transition as a Race Between "The Good" and "The Ugly"

We derive policy rules for a highly aggregated fossil-based world economy with two competing stochastic thresholds or tipping points. Current production generates emissions that add to a stock of GHGs that affect the probability distribution of hitting a climate threshold with severe consequences (the "ugly" scenario). The fossil-intensive output is used for current consumption and as investment in knowledge production, with the stock of knowledge affecting the probability distribution for hitting a "good" threshold or having a technological breakthrough (the "good" scenario). The new technology will provide a clean emission-free substitute to fossil energy. Given that no threshold has been hit, the decision rules are being continuously revised due to the induced changes in the derived probability distributions. To avoid the ugly scenario, while pushing for the good one, we find that the conditional expected marginal benefit or willingness-to-pay for knowledge will increase over time, with a non-decreasing rate of R&D investment and non-increasing rate of consumption. Implementation of this strategy requires a global organization with coercive power, equipped with instruments to tax the negative stock externality and to eventually subsidize the provision of a public good; the stock of knowledge. The optimal carbon tax is derived and shown to depend on the hazard rate for a climate change, modified by the "odds ratio" for a technological breakthrough.