Long-term contracting with time-inconsistent agents

We study contracts between naive present-biased consumers and risk-neutral firms. We show that the welfare loss from present bias vanishes as the contracting horizon grows. This is true both when bargaining power is on the consumers’ and on the firms’ side, when consumers cannot commit to long-term contracts, and when firms do not know the consumers’ naiveté. However, the welfare loss from present bias does not vanish when firms do not know the consumers’ present bias or when they cannot offer exclusive contracts.