A Two-Factor Uncertainty Model to Determine the Optimal Contractual Penalty for a Build-Own-Transfer Project

Public-Private Partnerships (PPP) became one of the most common types of public procurement arrangements and Build-Own-Transfer (BOT) projects, awarded through adequate bidding competitions, have been increasingly promoted by governments. The theoretical model herein proposed is based on a contractual framework where the government grants leeway to the private entity regarding the timing for project implementation. However, the government is aware that delaying the beginning of operations will lead to the emergence of social costs, i.e., the costs that result from the corresponding loss of social welfare. This fact should motivate the government to include a contractual penalty in case the private firm does not implement the project immediately. The government also recognizes that the private entity is more efficient in constructing the project facility. The model’s outcome is the optimal value for the legal penalty the government should include in the contract form. A two-factor uncertainty approach is adopted and Adkins and Paxson (2011) quasi-analytical solution is applied since homogeneity of degree one can not be invoked in all of the model’s boundary conditions. Sensitivity analysis reveals that variations in the correlation coefficients have a strong impact on the optimal contractual penalty and also that there is a level for the comparative efficiency factor above which there is no need to impose a contractual penalty, for a given level of social costs. Finally, the effects of including a non-optimal penalty value in the contract form, which derives from overestimating or underestimating the selected bidder’s real comparative efficiency are examined, using a numerical example. Results demonstrate that overestimating (underestimating) the selected bidder’s real comparative efficiency leads to the inclusion of a below-optimal (above-optimal) value for the legal penalty in the contract and produces effects that the government would prefer to prevent. JEL Classification Codes: G31; D81.