Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 145: The First-Best Sharing Rule in the Continuous-Time Principal-Agent Model with Exponential Utility

Holger M. Müller
Additional contact information
Holger M. Müller: Department of Economics, Postal: University of Mannheim, LS Hellwig, A5, Room A237, 68131 Mannheim, Germany

Abstract: The continuous-time principal-agent model with exponential utility developed by Holmström and Milgrom (1987) and generalized by Schättler and Sung (1993, 1996) and Sung (1995) admits a simple closed-form solution: The second-best sharing rule is linear in output. Unfortunately, the first-best sharing rule has never been derived. In this note, we show that the first-best sharing rule is also linear in output, which fits in nicely with an analogous result from static risk-sharing theory. In addition, we show that the slope is equal to the principal’s share of total absolute risk-aversion. This result is consistent with Borch’s (1962) fundamental theorem of Pareto-optimal risk-sharing.

Keywords: Moral hazard; continuous-time principal-agent problem

JEL-codes: D82

8 pages, December 1996

Note: Published in Journal of Economic Theory 79/2, 1998, 276-280

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