How to apply penalties to avoid delays in projects

A planner wants to carry out a project involving several firms. In many cases the planner, for instance the Spanish Administration, includes in the contract a penalty clause that imposes a payment per day if the firms do not complete their activities or the project on time. We discuss two ways of including such penalty clauses in contracts. In the first the penalty applies only when the whole project is delayed. In the second the penalty applies to each firm that incurs a delay even if the project is completed on time. We compare the two penalty systems and find that the optimal penalty (for the planner) is larger in the second method, the utility of the planner is always at least as large or larger in the second case and the utility of the firms is always at least as large or larger in the first. Surprisingly, the final delay in the project is unrelated to which penalty system is chosen.