clearer and more relevant to current policy issues, we cast our discussion in terms of journals. Nonetheless, our results apply to any excludable public good.

We work with the simplest model rich enough to reflect these issues. Each agent is characterized by his benefit from consuming the good via the private and public modes, B and B - T respectively. Thus T is the money-scaled subjective cost of patronizing the public mode over and above that of the private mode. For example, T might measure the inconvenience of library use.

The set of all agents is exogeneously partitioned into heterogeneous groups, each served by at most one public facility (library). The joint distribution of B and T in the group with characteristics vector m is given by h(B,T,m), while the distribution of m over all groups is f(m).

We assume that the production technology of the good exhibits increasing returns to scale. Thus, with C(Q) denoting the cost of producing Q units, C(Q) > QC' (Q); the revenue from marginal cost pricing cannot cover production cost. This assumption reflects the setup costs significant for public policy towards the publishing industry. We abstract, however, from costs of library operation and construction and from the concomitant overhead allocation problem. Thus, we assume that every group of agents has access to one and only one already established and noncongested library facility, and we focus on the potential acquisitions by the libraries of a particular journal.

Section II studies the personal and institutional subscription prices that are optimal for profits and that are optimal for welfare under the Ramsey nonnegative profit constraint.3 Here we assume that libraries are perfect (Samuelsonian [10]) purveyors of the public good to their user populations. That is, they levy no use fee and they finance their acquisitions through lump sum contributions. Further, a library subscribes to the journal if and only if the total willingness to pay of its population exceeds the institutional subscription price. This model gives special structure to the market demand elasticities which are crucial for the determination of the optimal prices.

We see that the ratio of the optimal deviations of the prices from marginal cost depends on the ratio of the own price elasticities of library and personal subscription demand, the ratio of library to personal subscriptions, and, the newly identified variable, the average number of potential personal subscribers who are users of the marginal libraries. However, the application of this Ramsey rule requires global information on the behavior of these critical functions of the prices. Unfortunately such data are unavailable.

Therefore, in Section III, we study the use of current values of the variables for the determination of the local price adjustments

which are best for welfare, while leaving profit unchanged." The same expression for the ratio of the deviations of Ramsey optimal prices from marginal cost can, when evaluated at current prices, be meaningfully compared with the ratio of current deviations. In particular, for reasonable and representative values of the current parameters, a journal currently setting equal personal and library subscription prices should move to a higher relative library price. Using analogous tools, it is shown that such a move would also be of benefit to a profit oriented publisher.

We apply these methods in a pilot study of the 1975 prices of five economics journals. We find that for four of them, welfare can be improved without loss of publisher profit by simultaneously increasing the library subscription price and decreasing the personal subscription price. Further, the hypothesis of profit maximization can be rejected for these journals.

In Section IV we investigate the profit and welfare optimal distribution structures. Numerical simulations show, for example, that profit maximization can lead to total exclusion of private subscriptions when break-even constrained welfare maximization implies the complete exclusion of library subscriptions. We identify some of the qualitative factors that generate such divergences between the profit and welfare optimal distribution structures. The total welfare loss from monopoly provision can be decomposed into the components which are attributable to incorrect prices and to incorrect structure. In the aforementioned example, it is the latter which are most significant. Generally, however, the welfare effect of constraining a profit maximizing publisher to provide the welfare optimal distribution modes can be negligible, or worse, perverse.

In Section V we study the economic impact of the introduction of a library usage fee, paid to the publisher, perhaps as a copyright royalty. We show that under weak and plausible conditions, net welfare, consumer welfare, and profits can all be increased by the implementation of such a fee, when accompanied by appropriate decreases in the subscription prices. Thus, we identify the difficult policy problem of how to tie such price decreases to the extension of copyright protection to library usage.

Appendix 1 shows the Ramsey suboptimality of the libraries behaving as perfect purveyors of their public good journal copies. While each population prefers to finance library subscriptions with lump-sum taxes, they all benefit from collective adherence to a rule specifying that usage fees partially finance library acquisitions.

Throughout the paper, the analysis is performed with library Populations indexed by a scalar, m, over which the relevant functions are assumed to be monotone. Appendix 2 shows how this model can be considerably extended to allow for a multidimensional characterization of library populations, without any loss of the analytic power of the

one dimensional representation. We feel that the analytic techniques presented in Appendix 2 can be used to gainfully enrich diverse one dimensional models found in the literature.

II. Optimal Subscription Prices

In this section we determine the rules that characterize the profit and constrained welfare optimal personal and institutional prices under the assumption that the institutions are perfect purveyors of the excludable public good to their populations. We build up from a detailed model of individual behavior.

Each agent is described by three characteristics: the unique library population to which he belongs, his benefit, B, measured in money units, from the use of a library copy of a journal, B T. Thus T can be interpreted as the money value of all psychic and pecuniary costs of using the library, exclusive of any user fees. B and B - T are income independent and, as such, are also independent of any money expended for personal subscription, use fees, or lump-sum library taxes. (That is, utility functions are linear in money.)

Each agent faces a personal subscription price, Ps. If he belongs to a group whose library does not own the journal, he will subscribe himself if and only if B > Ps. If, however, he does have access to a library copy, then his chosen mode will be the one yielding the highest net benefit. He will buy a personal subscription if B > Ps and T > Ps (B-Ps B-T). He will be a library reader if B - T > 0 and T ≤ Ps. Otherwise, he will choose not to read the journal.

It will be useful to dichotomize the library readers into the potential subscribers, for whom B Ps and T < Ps, and the perusers, for whom B< Ps and T < B. The latter group, unlike the former, would not buy personal subscriptions at ps, were the library to discontinue its subscription. Figure 1 depicts the aforementioned groups as regions in B, T space.

The library indexed by the parameter m serves a group of agents characterized by the histogram function h(B,T,m). The library, acting as a perfect purveyor, will subscribe if the aggregate willingness to pay, WP, of its population covers the institutional subscription price PL. WP can be expressed as the difference between the population's aggregate net benefits with (V) and without (V) the library subscription exclusive of the lump sum payments which sum to PL.

Reading left to right, the integrals measure the net benefits of the personal subscribers, the potential subscribers, and the perusers, respectively.

Here, without a library subscription, the only readers are those with personal subscriptions. Finally,

Thus, the personal subscribers contribute nothing to WP, and the perusers are willing to pay their full benefit, net of inconvenience, B-T. However, the potential subscribers add only the difference Ps - T between their evaluations of the library inconvenience and the money cost of a personal subscription.

Using the willingness to pay concept, we can identify the libraries which are just indifferent to acquiring the journal. Such marginal libraries will be denoted by the index m*, with

For convenience, we take m to be a scalar index defined so that the WP function is increasing in m. (In Appendix 2 we show how to arrive.

at our results with a mathematically more satisfying representation of multidimensionally differentiated libraries.) Letting f(m) be the number of population groups with characteristic m,

is the total number of subscribing libraries.

Denoting by NS the total number of personal subscribers, publisher

Total social welfare generated by the journal in question, given by the sum of producer's surplus and consumers' surplus,5 is denoted by W = V + π, where

Now, we can turn to the choice of Ps and PL which maximizes W subPS ject to the constraint that > 0. Forming the Lagrangian,

L = W + Xπ = V + (x+1)π, we investigate the necessary first order conditions for positive optimal prices: