Multi-agent contracts with positive externalities

I consider a model where a principal decides whether to produce one unit of an indivisible good (e.g. a private school) and which characteristics (emphasis on language or science) it will contain. Agents (parents) are differentiated along two dimensions: a vertical parameter that captures their privately known valuation for the good (demand for private education), and an horizontal parameter that captures their observable differences in preferences for the characteristics. I analyze the optimal mechanism offered by the principal to allocate the good under incomplete information about the valuation of agents and argue that it is similar to an auction with positive externalities. The main feature of the optimal contract is that, in order to reduce informational rents, the principal will produce a good with characteristics more on the lines of the preferences of the agent with the lowest valuation than under complete information. Furthermore, if the principal has also a private valuation for the good, he will bias the choice of the characteristics against his own preferences.