Implications of a lowered damage trajectory for mitigation in a continuous-time stochastic model

We provide counterexamples to the idea that mitigation of greenhouse gas emissions, and adaptation to climate change, are always substitutes. We consider optimal mitigation policy when climate damages follow a geometric Brownian motion process with positive drift and mitigation is lumpy. Climate damages can be affected by adaptation in two main ways: 1) reduced proportionately for given climate impact; or 2) their growth path down-shifted. In either case expectation and variance of the climate damage are both reduced by adaptation. In case 1, the variance effect (which leads to more rapid mitigation as the option value of waiting is reduced) may dominate over the expectation effect (which reduces mitigation), thus on balance increasing mitigation when damages are reduced. Mitigation and adaptation are then complements. A family of functions relating climate damage to adaptation cost in this way includes the Cobb–Douglas specification. In case 2, mitigation and adaptation are always substitutes.