We investigate the optimal policy response to the possibility of abrupt, irreversible shifts in system dynamics. The welfare cost of a tipping point emerges from the policymaker's response to altered system dynamics. Our policymaker also learns about a threshold's location by observing the system's response in each period. Simulations with a recursive, numerical climate-economy model show that tipping possibilities raise the optimal carbon tax more strongly over time. The resulting policy paths ultimately lower optimal peak warming by up to 0.5 • C. Different types of post-tipping shifts in dynamics generate qualitatively different optimal pre-tipping policy paths.JEL: Q54, D90, H23

The benefits and costs of increasing solar electricity generation depend on the scale of the increase and on the time frame over which it occurs. Short-run analyses focus on the cost-effectiveness of incremental increases in solar capacity, holding the rest of the power system fixed. Solar's variability adds value if its power occurs at highdemand times and displaces relatively carbon-intensive generation. Medium-run analyses consider the implications of nonincremental changes in solar capacity. The cost of each installation may fall through experience effects, but the cost of grid integration increases when solar requires ancillary services and fails to displace investment in other types of generation. Long-run analyses consider the role of solar in reaching twenty-first-century carbon targets. Solar's contribution depends on the representation of grid integration costs, on the availability of other low-carbon technologies, and on the potential for technological advances. By surveying analyses for different time horizons, this article begins to connect and integrate a fairly disjointed literature on the economics of solar energy.

Greenhouse gas emissions can trigger irreversible regime shifts in the climate system, known as tipping points. Multiple tipping points affect each other's probability of occurrence, potentially causing a "domino effect". We analyze climate policy in the presence of a potential domino effect. We incorporate three different tipping points occurring at unknown thresholds into an integrated climate-economy model. The optimal emission policy considers all possible thresholds and the resulting interactions between tipping points, economic activity, and policy responses into the indefinite future. We quantify the cost of delaying optimal emission controls in the presence of uncertain tipping points and also the benefit of detecting when individual tipping points have been triggered. We show that the presence of these tipping points nearly doubles today's optimal carbon tax and reduces peak warming along the optimal path by approximately 1 degree Celsius. The presence of these tipping points increases the cost of delaying optimal policy until mid-century by nearly 150%.The threat of climate tipping points plays a major role in calls for aggressive emission reductions to limit warming to 2 degrees Celsius 3-6 . The scientific literature is particularly concerned with the possibility of a "domino effect" from multiple interacting tipping points [7][8][9][10][11][12] . For instance, reducing the effectiveness of carbon sinks amplifies future warming, which in turn makes further tipping points more likely. Nearly all of the preceding quantitative economic studies analyze opti-

Common views hold that the efficient way to limit warming to a chosen level is to price carbon emissions at a rate that increases exponentially. We show that this Hotelling tax on carbon emissions is actually inefficient. The least-cost policy path takes advantage of the climate system's inertia to delay reducing emissions and allow greater cumulative emissions. The efficient carbon tax follows an inverse-U-shaped path and grows more slowly than the Hotelling tax. Economic models that assume exponentially increasing carbon taxes are overestimating the cost of limiting warming, overestimating the efficient near-term carbon tax, and overvaluing technologies that mature sooner. (JEL H23, Q54, Q58)

We model optimal policy when the probability of a tipping point, the welfare change due to a tipping point, and knowledge about a tipping point's trigger all depend on the policy path. Analytic results demonstrate how optimal policy depends on the ability to affect both the probability of a tipping point and also welfare in a post-threshold world. Simulations with a numerical climate-economy model show that possible tipping points in the climate system increase the optimal near-term carbon tax by up to 45% in base case specifications. The resulting policy paths lower peak warming by up to 0.5• C compared to a model without possible tipping points. Different types of tipping points have qualitatively different effects on policy, demonstrating the importance of explicitly modeling tipping points' effects on system dynamics. Aversion to ambiguity in the threshold's distribution can amplify or dampen the effect of tipping points on optimal policy, but in our numerical model, ambiguity aversion increases the optimal carbon tax.JEL Codes: Q54, D90, D81