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The First-Best Sharing Rule in the Continuous-Time Principal-Agent Model with Exponential Utility

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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.

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  • Müller, Holger M., 1996. "The First-Best Sharing Rule in the Continuous-Time Principal-Agent Model with Exponential Utility," SSE/EFI Working Paper Series in Economics and Finance 145, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0145
    Note: Published in Journal of Economic Theory 79/2, 1998, 276-280
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    1. Schattler Heinz & Sung Jaeyoung, 1993. "The First-Order Approach to the Continuous-Time Principal-Agent Problem with Exponential Utility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 331-371, December.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
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    More about this item

    Keywords

    Moral hazard; continuous-time principal-agent problem;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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