Inefficient rationing with post-contractual information

We study a contractual design problem between a seller and a buyer where some information correlated with the buyer's valuation is publicly observed ex-post and the allocation, but not payments, can be made contingent on it. Our analysis shows that, to maximize her profit, the seller should offer one contract in which the good is transferred to the buyer only if the ex-post signal turns out to be bad; this generates inefficient rationing: some buyers with low valuation are assigned the good more often than others with higher valuation. We show that, in contrast with previous results, the optimal contract may decrease social welfare relative to the case in which no signal is available (or it is not used). We apply our model to interpret two real-world situations: internet plans with bandwidth caps for mobile phones and promotion schemes in organizations with exogenously fixed wages.