Properties are derived for the profit-maximizing price schedule in a market where the firm can observe the size of any given purchase, but cannot directly observe the number of purchases made by any given consumer. In such a market, A consumer may make multiple purchases to minimize the amount paid for a given quantity of the good. It is shown that when purchase numbers are unobservable the schedule may entail quantity premia and may be strikingly different from the schedule that obtains when the numbers of purchases are observable. In particular, some individuals may consume more under the profit-maximizing outcome than under the first-best outcome.

A monopolist may earn greater profits by setting a nonuniform price schedule (one in which the price varies with the quantity purchased) than by charging a uniform price. In general, the profit maximizing non-uniform price schedule and the welfare maximizing schedule do not coincide. Thus, there may be scope for improving market performance through regulation. The paper considers a regulator who has limited information and authority. The issues addressed centre around the question of whether the level of total market output can be taken as a measure of market performance. Conditions under which welfare is a monotonic function of the level of total output are derived. 1.