  In this paper we consider a principal agent problem where the agent is
allowed to quit, by incurring a cost. When the current agent quits the job, the
principal will hire a new one, possibly with a different type. We characterize
the principal's dynamic value function, which could be discontinuous at the
boundary, as the (unique) minimal solution of an infinite dimensional system of
HJB equations, parametrized by the agent's type. This dynamic problem is time
consistent in certain sense.
  Some interesting findings are worth mentioning. First, self-enforcing
contracts are typically suboptimal. The principal would rather let the agent
quit and hire a new one. Next, the standard contract for a committed agent may
also be suboptimal, due to the presence of different types of agents in our
model. The principal may prefer no commitment from the agent, then she can hire
a cheaper one from the market at a later time by designing the contract to
induce the current agent to quit. Moreover, due to the cost incurring to the
agent, the principal will see only finitely many quittings.
