Risk, limited liability and firm scope

This paper provides a new explanation for the relationship between firm scope, agent's effort and corporate risk. I set up a moral hazard in teams model with multiple agents and departments under the assumption that both the principal and the agents are protected by limited liability. Each agent exerts effort to reduce the probability of loss of his department. The two-sided limited liability assumption creates an externality between agents, since the bad performance of an agent could reduce the firm’s expected profit, and decrease the expected payoff of a good performing agent within the same firm. This would lower the incentive for other agents to exert effort, which causes 'Contagious shirking'. I prove for the optimal contract and derive conditions for effort to increase or decrease with scope, and explain why ‘contagious effect’ could better answer this question than diversification when firm scope is large. 1 Department of Mathematical Sciences and School of Economics and Management, Tsinghua University, Beijing, China. The author is indebted to (in alphabetic order) Chong-En Bai, Li Chen, Ming Gao, Ping He, Jaimie Lien, Hong Ma and Qing Liu for their comments, instructions and discussions. The author also benefited a lot from the discussions with Yuliy Sannikov, Lemin Wu and many others. 2 'Nothing can be so unjust as for a few persons abounding in wealth to offer a portion of their excess for the information of a company, to play with that excess, to lend the importance of their whole name and credit to the society, and then should the funds prove insufficient to answer all demands, to retire into the security of their unhazarded fortune, and leave the bait to be devoured by the poor deceived fish.' ---The Times of London, 1824.5.25