Optimal contracts to a principal-agent model with a diffusion coefficient affected by firm size

Xuemei Luo; Bing Liu

doi:10.3934/jimo.2023020

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2023, Volume 19, Issue 10: 7795-7810. Doi: 10.3934/jimo.2023020

This issue Previous Article A revised sequential quadratic semidefinite programming method for nonlinear semidefinite optimization Next Article

Optimal contracts to a principal-agent model with a diffusion coefficient affected by firm size

Xuemei Luo and
Bing Liu^,

School of Economics and Management, Southwest University of Science and Technology, Mianyang 621010, China

^*Corresponding author: Bing Liu
^*Corresponding author: Bing Liu

Received: July 2022

Revised: January 2023

Early access: February 2023

Published: October 2023

This work is supported by Doctoral Research Foundation of Southwest University of Science and Technology [22sx7108, 22sx7109].

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Abstract

We study a principal-agent model with its diffusion coefficient affected by firm size. Under the assumptions of linear production technology and exponential preferences, we obtain the explicit solutions of optimal contract of full information in a continuous-time environment. Applying martingale method, we characterize the incentive compatibility condition which is used to deal with the agent's problem. In the case of full information, the amount of optimal effort is a constant and the agent's consumption and principal's dividend are related to firm size. Through dynamic programming principle, the implementable contract in hidden actions is constructed by solving the principal's problem. When the firm size goes to zero, the effort of agent in hidden action case approaches the first-best effort level. In the hidden action case, the impact of firm size on dynamic incentives is shown and the moral hazard results in a reduction on effort.

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Mathematics Subject Classification: Primary: 91B41, 91B43, 90C39; Secondary: 90C47, 90C15.

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