A principal provides budgets to agents (e.g., divisions of a firm or the principal’s children) whose expenditures provide her benefits, either materially or because of altruism. Only agents know their potential to generate benefits. We prove that if the more “productive” agents are also more risk-tolerant (as holds in the sample of individuals we surveyed), the principal can screen agents and bolster target efficiency by offering a choice between a nonrandom budget and a two-outcome risky budget. When, at very low allocations, the ratio of the more risk-averse type’s marginal utility to that of the other type is unbounded above (e.g., as with CRRA), the first-best is approached. A biblical opening enlivens the analysis.
Miller, Nolan, Alexander F. Wagner, and Richard J. Zeckhauser. "Solomonic Separation: Risk Decisions as Productivity Indicators." Journal of Risk and Uncertainty 46.3 (June 2013): 265-297.