This paper studies the incentives of the private provider, but also of the public authority, under various contractual forms of Public Private Partnerships (PPPs). A critical aspect of any PPP contract is the allocation of demand risk between the public authority and the private provider. I show that contracts in which the private provider bears demand risk motivate more the public authority from responding to customer needs. This is due to the fact that consumers are empowered when the private provider bears demand risk, i.e. they have the possibility to oust the private provider in case of non-satisfaction with the service provision, which provides procuring authorities with more credibility in side-trading and then more incentives to be responsive. However, contracts in which the private provider does not bear demand risk motivate more the private provider from investing in cost-reducing efforts. I highlight then a tradeoff in the allocation of demand risk between productive and allocative efficiency. The striking policy implication of this paper would be that the current trend towards a greater resort to contracts where private providers bear little or no demand risk may not be optimal. I apply these results to understanding three famous case studies.