Optimal nonlinear deployment subsidies : theory and application to the German solar program

Deployment subsidies for nascent technologies have moved to the forefront of climate action, industrial policy, and geoeconomics. To limit the substantial fiscal costs of such programs, policymakers routinely employ subsidy schedules that are nonlinear in the quantity agents deploy. However, nonlinearities can threaten a program's deployment goals because agents may respond to them at the intensive margin by reducing deployed quantity and at the extensive margin by ceasing participation. This paper characterizes optimal nonlinear subsidy schemes in which a principal trades off the benefits from deployment with its budgetary costs. Theoretically, it shows that nonlinearities are optimal only if adopters' participation responses are heterogeneous along the subsidy schedule. Yet, early-stage technologies typically exhibit limited heterogeneity in this dimension. As a consequence, the optimal subsidy rate is close to constant over a wide range of the schedule. In contrast to the celebrated Sadka-Seade "no-distortion-at-the-top" result, "no-distortion-atthe-bottom" emerges as an actionable policy prescription in this context. The insights generalize to screening problems broadly, and in particular to multidimensional screening à la Rochet and Choné (1998) and optimal nonlinear monopoly pricing. A quantitative analysis of the canonical German rooftop-solar program demonstrates the theoretical findings.