A risk neutral principal hires a risk neutral agent to work on a project. The project can either yield high output h or low output l. The probability of h depends on the agent’s unobservable effort e. With probability 1 − e the output is low. The agent is protected by limited liability, so his compensation can never go below zero. Let t(h) and t(l) be the agent’s compensation as a function of the output. The agent’s outside option is zero and the cost of effort function is c(e) = e2/2. The principal offers to the agent a contract that maximizes the principal’s expected profit subject to the incentive compatibility, limited liability and participation constraints.

Find the optimal contract