All-unit discounts and the problem of surplus division

All-unit discounts (AUD) are non-linear pricing schemes whereby buyers who reach a specific quantity threshold get rebates also retroactively for all units bought before. This sets high incentives for buyers to meet the quantity threshold, and may also have foreclosure effects on potential entrants. In a model where an incumbent faces second-period competition by entrants, we show that AUD can indeed be abused to shift rents from entrants. In contrast to exclusive dealing which is usually seen as very similar to AUD, inefficient quantity distortions may arise even with perfect information if and only if there is sufficiently intense competition among potential entrants.