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the distribution of benefits and inconvenience costs. One shortcoming of the uniform distribution is that with it we cannot, generate the interesting case of market decoupling in which both NL and NS are positive but Nf = N = 0.
In order to simplify calculations even further we assume that all libraries are identical, characterized by the same histogram function h(B,T). As a consequence of this homogeneity, we cannot use the formulae derived from (11) to calculate the profit-constrained welfareoptimal personal and library subscription prices. Given Ps, the willingness to pay and, hence, PL are uniquely determined. Thus, it is no longer possible to simultaneously satisfy the first-order conditions and the profit constraint. However, in the mixed case, when both subscription markets are qpened, the constrained welfare-optimal personal subscription price, pg, is the smallest psc which allows the resulting profits, including PL, to be nonnegative. The welfareoptimal mode of provision of the journal is then obtained by comparing the level of total welfare at Ps = pŝ and PL = WP with that attained when Ps is set at the average cost and no library copies are provided. In all the calculations, social welfare is measured as the difference between the total gross benefits accruing to readers and the total production costs.
In the simulations we use as a benchmark the case in which provision of both personal and library subscriptions is optimal for profit maximizing publishers as well as for welfare maximizing publishers. À profit maximizng publisher will be in this mixed provision mode if and only if at least some agents with the maximum value of B have inconvenience costs higher than this B. The mixed mode is welfare optimal if the total willingness to pay (for the library copy) of agents with T <C< Ps exceeds the sum of the marginal cost of the copy, c, and the fixed cost, $.
Working from the benchmark situation in which the mixed mode is preferred by both types of publishers, we investigate whether other configurations of rankings of the market structures can be generated by suitable changes in the values of the parameters omax, To, Ty, a, c
The striking result is that, for some parameter values, the welfare and profit rankings of provision modes are diametrically opposed. Profit maximizing publishers would sell only to libraries, while constrained welfare maximization requires that only personal subscriptions be sold.
This extreme scenario is caused by two fundamental properties of the distribution of agents. The first is the small willingness to pay of those who would patronize the library when ps is set at c (or as close to c as possible) by the welfare optimizing publisher. This can be the result of only a small number of agents having T <c, or of
a tight positive association between B and T (B = T so that B-T : 0) of those with T < c. In such cases, welfare is served by foregoing library provision of the journal.
The second critical property is the lack of a strong positive association between the B's and T's of the high B agents. With many agents having a large B - T, the aggregate willingness to pay is large, in the absence of a personal subscription alternative. The publisher is able to appropriate all of this surplus via the pi collected from the perfectly purveying library. If, however, personal subscriptions were to be offered, then the willingness to pay of the high B, low T, now potential subscribers would be diminished from B - I to ps. - T.
c, is larger than the old willingness to pay, max(B-T, 0). The profit losses outweigh the gains, and the profit maximizing mode is library subscriptions only, if there are more high B-low T than high B-high T agents.
These two properties of the distribution of agents can be generated in our simple model by setting to close to c, a small, and Bmax large relative to T1. Less delicacy is required to generate the case in which welfare prefers both modes while profit maximization excludes private subscriptions. It is also possible to generate the case in which, due to a strong positive correlation between B and T, profits are maximized by the exclusion of library sales.
Numberical simulations confirm our expectations that different provision modes may emerge from profit and welfare maximization. It is therefore important to know whether the loss in social welfare from the presence of monopoly can be significantly diminished by constraining the monopolistic publisher to the socially optimal mode.
Governmental intervention into the structure of provision modes is desirable whenever the mixed mode is socially preferred, while the profit-maximizing provision is restricted solely to individual subscribers. In this case, there can be a significant gain in welfare resulting from the establishment of proper provision modes, even though the profit-maximizing firm will not charge the welfare optimal personal and library subscription prices. Simulations show that without libraries, at profit optimal personal subscription prices, social welfare is approximately one-third of the maximum welfare attainable under the mixed mode. If the monopolist is constrained to operate within the mixed mode, social welfare increases, often up to 70 percent of the maximum attainable level. The reduction in profits that results from the constraint imposed on the profit-making publishers is, in most cases, substantially less than the improvement in consumer welfare.
Unfortunately, however, regulation of the provision mode offered will be ineffectual in the most intuitively plausible case of profit maximization excluding personal subscriptions while welfare optimization requires both provision modes. Here, to satisfy a mixed mode constraint, the profit oriented publisher need only set Ps low enough to attract a few personal subscribers. The welfare effect of opening such an unattractive market would be minimal.
Curiously, simulations reveal the possibility of perverse effects of mode regulation. If a profit maximizing firm which desires to exclude personal subscriptions is forced into the welfare optimal mode of excluding library sales, it may then set its profit optimal Ps so high that all welfare gains from proper structure are thereby nullified. Thus, the partial correction of a market distortion through regulation of the provision structure may worsen, rather than improve welfare.
V. Welfare and Profit Effects of Library Usage Fees
In this section we study the economic impact of the imposition of a fee for the use of library journals. We maintain our underlying assumption that the journal is an excludable public good, so that the marginal cost of usage in a library is zero. Nonetheless, it is conceivable that a positive usage fee (greater than the associated marginal cost) is both welfare and profit desirable. This is so because such a fee would discourage library use, and, in the previous section we uncovered instances in which the very existence of library subscriptions was baneful to profits and welfare.
When the usage fee is paid to the journal publisher, it can be interpreted as a royalty payment to the owner of the copyright. Thus we feel that our analysis can illumine the current debate over the appropriate extent to which copyright law should apply to library use. We find that, under weak and plausible conditions, a positive usage fee is indeed optimal when welfare is maximized subject to the profit constraint. Further, under these conditions, without a profit constraint, the introduction of a usage fee, accompanied by an appropriate change in ple will increase both profits and net welfare. Moreover, if a profit maximizing publisher is given the right to charge a small use fee, then there exist accompanying reductions in Pi and ps under which both profits and consumer welfare increase. However, it must be recognized that such adjustments in PL and Ps are not necessarily in the interest of the publisher.
It is straightforward to incorporate a usage fee, Puy into our model. With a library available, an agent will purchase a personal subscription if B.? Ps and ps !+ Pu: He will be a prospective subscriber (and library reader) if B > Ps and T +
, . Pus Ps.
The other library readers, the perusers, are those with B < Ps and
The willingness to pay of the library population m is now, given that we exclude the trivial case of Pu Ps
Its derivative with respect to P. is minus the number of library readers. This is the function of ps and Pu given by
The derivative of the willingness to pay with respect to Ps is still the number of prospective subscribers, now given as
The marginal library, m*, is now the function of Ps, PL, and Pu given implicitly by
The first three terms capture the net benefits respectively of the prospective subscribers, the perusers, and personal subscribers in populations with libraries. The fourth term is the total payments for library subscriptions, and the last is the net benefits to personal subscribers in nonlibrary groups. Differentiation shows