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Detailed derivations for the case of normally (Appendix S1) and uniformly (Appendix S2) distributed uncertainties and derivation of marginal cost expressions (Appendix S3) and analysis of robustness to the linearity assumption (Appendix S4) are available online. The authors are solely responsible for the content and functionality of these materials. Queries (other than absence of the material) should be directed to the corresponding author.

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