Abstract
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.
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