This paper provides counterexamples to the idea that mitigation of greenhouse gases causing climate change, and adaptation to climate change, are always and everywhere substitutes. The author considers optimal policy for mitigating greenhouse gas emissions when climate damages follow a geometric Brownian motion process with positive drift, and the trajectory for damages can be down-shifted by adaptive activities, focusing on two main cases: 1) damages are reduced proportionately by adaptation for any given climate impact ("reactive adaptation")
and 2) the growth path for climate damages is down-shifted ("anticipatory adaptation"). In this model mitigation is a lumpy one-off decision. Policy to reduce damages for given emissions is continuous in case 1, but may be lumpy in case 2, and reduces both expectation and variance of damages. Lower expected damages promote mitigation, and reduced variance discourages it (as the option value of waiting is reduced). In case 1, the last effect may dominate. Mitigation then increases when damages are dampened: mitigation and adaptation are complements. In case 2, mitigation and adaptation are always substitutes.