# American Institute of Mathematical Sciences

October  2017, 13(4): 1815-1840. doi: 10.3934/jimo.2017020

## An uncertain wage contract model for risk-averse worker under bilateral moral hazard

 Institute of Systems Engineering, Tianjin University, Tianjin 300072, China

* Corresponding author: Yanfei Lan, Email: lanyf@tju.edu.cn

Received  February 2016 Revised  October 2016 Published  December 2016

This paper investigates a wage mechanism design problem faced by a risk neutral firm (he) who employs a risk averse worker (she) to sell products for him. The effort levels of both the firm and the worker are unobservable to each other, which results in bilateral moral hazard. The firm offers a wage contract menu to the worker with the objective of maximizing his expected profit. The results show that the firm will provide the same wage contract to the worker when the worker's effort is observable regardless of the market condition being full or private information. The optimal wage contract is related to the worker's risk averse level when the bilateral moral hazard exists. The information values of the worker's effort and the market condition are studied, respectively. The results show that the firm benefits from the worker's observable effort under full information and only when the sales uncertainty is sufficiently low, can the firm profit from that under private information. Moreover, only if the cost coefficient of the firm's effort is sufficiently high, the firm can benefit from full information in the scenario when the worker's effort is unobservable.

Citation: Xiulan Wang, Yanfei Lan, Wansheng Tang. An uncertain wage contract model for risk-averse worker under bilateral moral hazard. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1815-1840. doi: 10.3934/jimo.2017020
##### References:

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##### References:
Optimal bonus coefficient of the wage
Optimal effort of the firm
Optimal effort of the worker
Impact of the worker's risk adverse level on VE1 and VE2
Impact of the worker's risk adverse level on VM1 and VM2
The four information cases
 $X$ known $X$ unknown The worker's observable effort Case $\rm{OF}$ Case $\rm{OP}$ The worker's unobservable effort Case $\rm{UF}$ Case $\rm{UP}$
 $X$ known $X$ unknown The worker's observable effort Case $\rm{OF}$ Case $\rm{OP}$ The worker's unobservable effort Case $\rm{UF}$ Case $\rm{UP}$
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