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elasticity formula identifies demand elasticities as being the focal points in the process of setting prices. Our analysis also uncovered additional variables which previously escaped the attention of the analysts. We find that in the model considered in the paper, the best (profit maximizing) prices are quite sensitive to the value of the variable which we term "the average number of potential subscribers". Roughly speaking, this variable measures the average number of additional private purchases that would be gained from those institutions that would discontinue their purchases in response to a small change in the institutional price of the commodity. To illustrate the concept, let us assume that an increase of one dollar in the institutional price induces six institutions to discontinue their purchases. This, in turn, induces two users from each institution to purchase the commodity. In this example, the average number of potential subscribers is two. If we were to change the hypothetical data somewhat and assume that there would be no new private buyers from four of those institutions, the value of the average number of potential subscribers would drop to two-thirds.

We have been able to show that if for a wide range of prices offered in the two markets the average number of potential subscribers exceeds one, the institutional price ought to exceed the private price irrespective of the elasticities of demand in the two markets. This result is of some interest because in some situations the values of the elasticities of demand in the private and institutional markets may not be known while the firm may have some information from its marketing surveys on the numbers of potential subscribers.

It must be admitted that sophisticated pricing rules like the one presented in this paper require significant amounts of information for their implementation. However, as we indicated earlier, the optimal price rules can be employed to test whether current prices can be improved upon yielding higher net income for the firm or higher net benefits for the product's users. For the purposes of this test much less detailed knowledge of market demands is required. The test is particularly simple for the firm which is not currently price discriminating between its institutional and individual customers. In this situation, it is very easy to show that in most circumstances price discrimination in favor of individual buyers would be desirable from the standpoint of profits and the welfare of the consumers as a whole. When the firm already has a two-tier price scheme, our tests enables the decision-maker to ascertain whether the current spread between the two sets of prices should be widened or narrowed.

There is no need to give here a detailed exposition of the price adjustment test since the test is described at great length in the paper. It is important, however, to reiterate that the procedure for price revisions developed in the paper relies wholly on the information that should be easily available to those responsible for price decisions. If such information is not currently available, it can be obtained from the existing data, using standard econometric techniques which we have discussed elsewhere.

It may be useful at this point to restate the motivation behind the analysis of Sections II and III of the paper. Our most abstract consideration was to extend the economic analysis of optimal pricing to those situations in which significant cross-market effects of pricing decisions are present. Although there are already some pricing rules which are applicable to that case, these rules are not easily interpretable even by a theorist. Furthermore, they are formulated in ways which are not particularly helpful to those who will in the end use them for actual pricing decisions. Hence, our second objective was to derive a set of guidelines to be followed by those who are responsible for deciding on prices for scientific and technical information. We strived to make a strong case for imaginative pricing and we argued that price discrimination between various classes of buyers is not only desirable for profits but perhaps paradoxically, also for the users of information as a whole.

Section II of the paper presents, we believe, a strong case for allowing the producers to employ sophisticated pricing policies and to have protection via copyright for their product. If the production of sceintific and technical information did not involve a fixed cost component, then economic theory would indicate prices closely to the incremental (marginal) production costs. When fixed costs are present, however, at prices equal to marginal costs, the firm cannot cover its total costs. Consequently, prices must deviate from incremental costs. In Sections II and III, we show what directions those deviations from marginal costs should take. It would be unfortunate if the producers and disseminators of information were to be prevented from employing those sophisticated pricing rules for the purposes of recovering their fixed costs.

Section V and Appendix I deal directly with the problem of whether user charges ought to be levied on those who use the institutionally owned excludable public good. This question is directly relevant to the discussion of copyright royalties. The first argument for user charges is entirely consistent with that encountered above. We argued earlier that the burden of defraying the fixed cost component of the total production costs should be allocated to the various classes of users according to well-defined principles (the inverse elasticity rule, for example). The question may be raised as to why the users of the institutionally-owned excludable public good should be exempted from sharing in that burden. The answer is, of course, that they should not. It is conceivable that those user charges should be "low". But our theory says that if those charges should be low, it is not necessarily because the cost to the society of an additional use of the institutionally owned excludable public good is also very small, perhaps even zero. Rather, the argument for no user charges ought to be based on the empirically verifiable proposition that the demand for institutional use is highly elastic with respect to user charges. (This demand should not be confused with the demand by institutions for the commodity in question. Undoubtedly, the two demands are related in some way.) When, a small increase in these charges above zero would discourage so many users

that the additional revenue gained from user charges would not be sufficient to justify the collection costs, user charges are not desirable. It is those who oppose the introduction of user charges, however, who must provide a positive showing that the collection costs are prohibitive, for otherwise the implications of economic analysis are quite clear: carefully structured user fees are a rational and desirable method of defraying at least some part of the fixed costs incurred in production and dissemination of scientific and technical information.

The second argument for user charges is less complex. An imposition of user charges would discourage some use of the units of the commodity owned by the institutions. Some of these discouraged users would enter the private market. By increasing private demand, they would stimulate production of the commodity, thus driving down its average cost. Some of those gains could then be passed on to the buyers in the form of lower prices, yielding concomitant improvement in the dissemination of the product.

The reader will have noted that in this summary of the paper, we have dealt with the class of excludable public goods. The discussion in the paper is couched specifically in terms of scientific and technical journals. We differentiated in the paper between personal and library subscriptions and argued strongly for the imposition of user charges on those who utilize the library copy by, for example, photocopying articles from a journal. We built our argument on a very general proposition which asserts that no group of consumers should be exempted from financing some part of production costs unless reasons of equity, costly collection, or significant positive externalities stop us from doing so. The formulae for prices presented in the paper apply when those objections to the use of prices as rationing devices are not present.)

Those formulas and the arguments behind them apply not only to journals. Instead of journals, we can imagine a system in which the publishers do not provide hard copy to the subscribers but rather video discs or tapes of journals. Those discs or tapes can then be read using minicomputers and/or display consoles. In such a hypothetical system, we would again have at least two-tier price structure: one

I see J.A. Ordover and R.D. Willig, "On the Role of Information in Designing Social Policy towards Externalities," Center for Applied Economics, Discussion Paper #76-03, New York University, for the discussion of the case in which there are external effects. Those effects exist whenever the societal benefit from a given activity exceeds the private benefit that accrues to the person who undertakes that particular activity. It may be argued that the users of scientific and technical information generate significant positive externalities. If so, then perhaps information should be made freely available to all users and not only to those who use it in the library.

price for individual subscribers and another for institutional subscribers including libraries. In addition, in accordance with our theoretical analysis, user charges will be levied as well. Indeed, in this modified system, user charges are even more desirable than in the presently extant system. This is so because the collection costs would be much lower if the information were transmitted through computer.

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APPENDIX C2

ON THE OPTIMAL PROVISION OF JOURNALS QUA

EXCLUDABLE PUBLIC GOODS

by

J. A. ORDOVER* AND R. D. WILLIG*

NEW YORK UNIVERSITY AND BELL LABORATORIES

*The views presented in this paper are solely those of the authors and do not necessarily represent those of New York University or Bell Laboratories. Authors' names are in alphabetical order.

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