Contract Design and Self-Control with Asymmetric Information

We study optimal contracting by a monopolistic seller of an investment good to a time-inconsistent consumer and, in doing so, introduce asymmetric information to the model of DellaVigna and Malmendier (2004). We find: (1) the below-marginal-cost-pricing rule may fail for a low-value consumer; (2) the firm's profit is no longer unaffected by the consumer's short-run impatience, as the latter is sophisticated. We find that there is an important threshold value of short-run patience. When the consumer's short-term patience is below this level, then, as the patience increases, the firm suffers. When the consumer's short-run patience is above this threshold, then, as it increases, the firm benefits. Finally, we show that unlike under monopoly, the first-best outcome is achieved under perfect competition