Persuasion against self-control problems

I derive a social planner's optimal information design in an environment with quasi-hyperbolic discounting consumers without commitment. Consumption induces instantaneous utility, but unknown delayed cost. Consumers may or may not acquire additional costless information on the cost parameter. The planner's optimal signal can be interpreted as an incentive compatible consumption recommendation whenever the cost parameter is below some cut-off. Welfare strictly exceeds the one under full information. I characterize distributional conditions under which welfare attains first best.