The social value of public information with convex costs of information acquisition

In a beauty contest framework, welfare can decrease with public information if the precision of private information is exogenous, whereas welfare necessarily increases with public information if the precision is endogenous with linear costs of information acquisition. The purpose of this paper is to reconcile these results by considering nonlinear costs of information acquisition. The main result of this paper is a necessary and sufficient condition for welfare to increase with public information. Using it, we show that costs of information acquisition are linear if and only if welfare necessarily increases with public information. Thus, welfare can decrease with public information for any strictly convex costs. This is because convex costs mitigate the so-called crowding-out effect of public information on private information, thereby making the social value of public information with endogenous precision closer to that with exogenous precision.