Many tax systems and private contractual arrangements require payments by means of fixed fees (lump sum taxes), percentages of gross revenues (royalties or ad valorem taxes), or percentages of net income (profit-sharing or income taxes). Even where payments due under such instruments have the same expected value, their risk-spreading implications for the parties involved may differ. For equal expected levies, profit-sharing is often ranked as the most effective means of risk-sharing, followed by royalty payments, and, finally, by fixed fees, which supposedly fail completely in spreading risk. We demonstrate that this common assessment does not hold in general. Using both mean-variance and expected utility frameworks, we derive necessary and sufficient conditions for a welfare ranking of these traditional financial instruments.
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