Reduced Costs and Continued Cures Act This bill establishes and alters several programs and requirements relating to the prices of prescription drugs. For example, the bill establishes and alters several requirements under Medicare and Medicaid, including requiring drug manufacturers to issue rebates to the Centers for Medicare & Medicaid Services for covered drugs under Medicare that cost $100 or more and for which the average manufacturer price increases faster than inflation, capping annual out-of-pocket spending under the Medicare prescription drug benefit, and increasing the maximum rebate amount under the Medicaid Drug Rebate Program. The bill also makes changes relating to market exclusivities and manufacturer price concessions for prescription drugs, including authorizing the Federal Trade Commission to initiate proceedings against parties to settlements of patent infringement claims that have anticompetitive effects with respect to drugs or biologics, limiting in certain instances the number of patents that the manufacturer of a biologic can assert in a lawsuit against a company seeking to sell a biosimilar version, and nullifying regulations relating to the treatment of certain Medicare prescription drug benefit rebates from drug manufacturers for purposes of federal anti-kickback laws.