It is interesting to note that each library population would prefer to circumvent the positive a rule and to pay p1 solely out of the lump sum taxes characteristic of perfect purveyance. However, each library population benefits from the decreases in Ps and PL PS which results from collective adherence to the rule.

APPENDIX 2

Multidimensional Characterization of Library Populations

Throughout the paper, we have characterized library populations by the scalar m, and have assumed that the willingness to pay is increasing in m. This is an overly restrictive formulation which, however, finds frequent use in the literature. Here we show how the model can be considerably extended to allow for a multidimensional characterization of library populations, without at all affecting the power of the onedimensional approach.

Let each library population be characterized by the vector m = (m1, m2, ..., mn), where m; represents the number of agents in the population m of type i. Type i agents are themselves characterized by the density function g; (B,T). Thus, the histogram function of the population m is

All population specific structural functions have their analogues defined for each agent type. Thus, here, for example, we have an analogy to (3) the willingness to pay of a unit population of type i, wpi. Then,

Because WP (m) is increasing in each component, by (A8), a population purchases a library subscription if

Now, mt plays the

Here, we have arbitrarily chosen to normalize on m1. same central role as that played throughout the paper by m*. Thus, for example,

A specific analytic gain from this more general specification is the replacement throughout of the number of potential subscribers in the marginal library," PNS (m*), by "the average number of potential subscribers in the marginal libraries." To see this, calculate from (A10):

Thus, we have ǝN/ǝps//ǝPL = PNS (m*), the average number of prospective subscribers in the marginal libraries. When the basic model is specified this way, PNS (m*) replaces PNS (m*) throughout. The same applies to all the concepts specific to marginal libraries.

FOOTNOTES

1.

2.

3.

4.

This debate was stimulated by the celebrated case of Williams and Wilkins v. U.S. [13]. Summaries of various arguments and positions can be found in [12].

For example, the analysis of Y. Barzel [1] rested on the public goods properties of the information disseminated in journals, while it ignored the public nature of library journal collections.

It was Ramsey [9] who first studied welfare optimal prices under such a constraint. See [2] for a cogent survey.

See Willig [14], for the development of this general approach.

5. Thus, throughout, we ignore distributional effects.

9.

10.

11.

S. Berg's important study of journal demand [3], overlooked this effect.

See Willig [14].

See Berg [3]. Research in progress by Y. Braunstein et al. [6] seems to indicate values of k significantly above 2.

12. See Fry and White [7].

13.

These data for AER and EI 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.

14. This equation was estimated by Y. Braunstein [5], from a 1973 cross-section of 56 technical journals.

15. 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.