Score contribution per author:
α: calibrated so average coauthorship-adjusted count equals average raw count
Many services provide outputs that depend partially on the customers as inputs; the presence of other customers often contributes to the output experienced by each purchaser. Higher education is the premier example; others are legion. The authors provide a simple model that addresses the questions of competitive pricing and allocative efficiency for these types of services. Prices that charge customers for what they get on net (output minus input) from the firm both are competitive and support efficient allocations; these prices internalize the apparent external effects of customers on each other. Few examples of such prices exist in the real world. Copyright 1995 by University of Chicago Press.