Renewable electricity, particularly solar PV and wind, creates external benefits of learningby-doing that drive down costs and reduce CO 2 emissions. The Global Apollo Programme called for collective action to develop renewable energy. This paper sets out a method for assessing whether a trajectory of investment that involves initial subsidies is justified by the subsequent learning-by-doing spillovers and if so, computes the maximum justifiable additional subsidy to provide, taking account of the special features of renewable electricitygeographically dispersed and variable quality resource base and local saturation. Given current costs and learning rates, accelerating the current rate of investment appears globally socially beneficial for solar PV in most but not all cases, less so for onshore wind. The optimal trajectory appears to involve a gradually decreasing rate of growth of installed capacity. 1 The case for supporting renewables The Global Apollo Programme called for collective action with "one aim only-to develop renewable energy supplies that are cheaper than those from fossil fuels.. .. These price trends help to create a prima facie case in favour of focussing heavily on solar energy." (King et al., 2015, p15). The case for support is primarily to compensate for the otherwise unremunerated learning spill-overs arising from cumulative production. Each additional installation adds to the cumulative production, which figure 1 1 persuasively suggests is the prime driver of cost reductions * This paper was prompted by Neuhoff (2008), who was pessimistic about the social profitability of PV when its cost was much higher, but noted that increasing current investment might relax constraints on future investment rates, which conferred an additional and potentially large extra benefit. I am indebted to insightful comments from Rutger-Jan Lange, and very careful checking of the paper and formulae to Linden Ralph and Bowei Guo, as well as to very helpful reviewers. 1 Source: Delphi234-Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=33955173. The straight green line predicts that modules decrease in price by 20% for every doubling of cumulative shipped modules. The other line (with squares) shows worldwide module shipments vs. average module price. The data 1 of solar modules (Fraunhofer, 2016; Rubin et al., 2015a). Renewable electricity technologies, particularly wind and solar PV (hereafter just PV), have been heavily subsidized for many years. Both PV and wind are finally at the point of becoming commercially viable without subsidies in some locations, but new installations continue to enjoy significant, if now much lower, support in many jurisdictions. This paper asks whether past and continued support for such technologies is justified, and, more fundamentally, how to determine the appropriate level of support now and in the future for emerging low-carbon technologies with learning spillovers. While it is easy to present qualitative arguments for such support, the practical question is to qua...