infonet-economy

We study a continuous-time principal–agent model in which a risk-neutral agent withlimited liability must exert unobservable effort to reduce the likelihood of large but rel- atively infrequent losses. Firm size can be decreased at no cost or increased subject to adjustment costs. In the optimal contract, investment takes place only if a long enough period of time elapses with no losses occurring. Then, if good performance continues, the agent is paid. As soon as a loss occurs, payments to the agent are suspended, and so is investment if further losses occur. Accumulated bad performance leads to downsiz- ing. We derive explicit formulae for the dynamics of firm size and its asymptotic growth rate, and we provide conditions under which firm size eventually goes to zero or grows without bounds.KEYWORDS: Principal–agent model, limited liability, continuous time, Poisson risk, downsizing, investment, firm size dynamics.