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i where we have used the fact that pn , the number of prospective
aps subscribers in a unit population of type 1. Substituting (A9) into the above gives am: (m2....mn
į, mypno 181
Thus, we have an-/aps/an/aPL = PN®(m*), the average number of prospective subscribers in the marginal libraries. When the basic model is specified this way, PN(m*) replaces PNS (m*) throughout. The same prospectived this whers is applies to all the concepts specific to marginal libraries.
This debate was stimulated by the celebrated case of Williams and Wilkins v. U.S. . Summaries of various arguments and positions can be found in .
For example, the analysis of Y. Barzel  rested on the public goods properties of the information disseminated in journals, while it ignored the public nature of library journal collections.
3. It was Ramsey  who first studied welfare optimal prices under
such a constraint. See  for a cogent survey.
4. See Willig , for the development of this general approach.
5. Thus, throughout, we ignore distributional effects.
9. S. Berg's important study of journal demand , overlooked this
10. See Willig (14].
See Berg . Research in progress by Y. Braunstein et al.  seems to indicate values of k significantly above 2.
13. These data for AER and El are annually released publicly. The
editorial offices of JPE and JET specified NS + NL precisely, and offered estimates of NL/NS. While Wiley, the new publisher of QJE, refused to give any, information, the editorial office offered estimates of 1975 NS + NL and NL/NS.
This equation was estimated by Y. Braunstein , from a 1973
We assume here that the prices of all costly factors of journal production rose by 25 percent between 1973 and 1975. Both the Wholesale Price Index of book paper and the BLS index of printing trades wages did increase by approximately 25 percent between those dates.
16. See footnote 11.
Of course, the conclusions rest upon the empirically untested model, and upon the numbers presented in Table 1. We regard this as a pilot study, hopefully pointing the way towards a full blown empirical treatment of both the model and the relevant parameters. Note that (20) and (22) can be utilized to generate several testable implications of the model.
 Y. Barzel, "The Market for a Semipublic Good: The Case of the
American Economic Review, American Economic Review, September 1971, 61, 665-74.
W. J. Baumol and D. F. Bradford, "Optimal Departures from Marginal
 S. Berg, "An Economic Analysis of the Demand for Scientific
Journals," Journal of the American Society for Information Science,
 M. Boiteux, "Sur la gestion des Monopoles Publics astreints
à l'équilibre budgétaire," Econometrica, January 1956, 24, 22-40.  Y. Braunstein, "Cost Data for Publication of Journals - Preliminary
Analysis," Discussion Paper No. 76-02, Center for Applied Economics,
New York University, 1976.  Y. Braunstein, "Economics of Journal Provision," (in progress),
New York University.
 B. Fry and H. White, Economics and Interaction of Publisher-Library
Relationship in the Production and Use of Scholarly and Research
 D. W. Katzner, Static Demand Theory. Macmillan:
New York 1970.
 F. P. Ramsey, "A Contribution to the Theory of Taxation,"
Economic Journal, March 1927, 37, 47-61.
 P. A. Samuelson, "The Pure Theory of Public Expenditure," Review
of Economics and Statistics, November 1954, 36, 381-89.
 1. W. Sandberg, "Two Theorems on a Justification of the Multiservice
Regulated Company," Bell Journal of Economics, Spring 1975, 6,
 United States Senate, Committee on the Judiciary, 93rd Congress,
Copyright Law Revision, Hearings on s. 1361, July 3T and
 The Williams and Wilkins Co. V. The United States, 172 USPQ 670;
478 F. 2d 1345 (180 USPQ 49).
 R. D. Willig, "The Economic Gradient Method," unpublished