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 P, 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 P 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, Pu, into our model. With a library available, an agent will purchase a personal subscription if B > Ps and Ps T + Pu. He will be a prospective subscriber (and library reader) if B Ps and T+ Pu Ps. The other library readers, the perusers, are those with B <ps and T + Pu< B. Figure 3 pictures these regions of B, T space.

<

PS

The willingness to pay of the library population m is now, given that we exclude the trivial case of Pu

Ps

(Ps-T-P1)h(B,T,m)dTdB

Its derivative with respect to p,, is minus the number of library readers. This is the function of På and Pụ 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 Pu given implicitly by

and

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

Here, LRT is the total number of library readers,

(43)

PS

Profit now includes the revenue from the usage fees:

We are now equipped to study the welfare and profit effects of the introduction of a positive usage fee. These are reflected in the behaviors of the V and functions at Pu = 0. Consider the introduction of a small P accompanied by a decrease in P, which exactly compensates the users of the marginal library. Together, these price movements leave the set of subscribing libraries unchanged. The ratio of such price changes is computed from (38) as:

The resulting rate of change of profit can be calculated from (43) and (38) to be

This just says that the number of journal readers in the marginal library is less than the average number of journal readers in the subscribing libraries.

The effect of the compensated change in Pu on net welfare is

Equation (46) shows that this is positive if ps > c and if there are any potential subscribers with T = ps. These agents are indifferent between library use and subscription purchase at Pu= 0. When Pu is increased, they are induced to buy personal subscriptions, with no welfare loss. However, these new purchases increase profit by A. Thus, given that A > 0, net welfare can be strictly increased by implementing a positive usage fee. Moreover, given the likely condition (47), the same set of price changes will also increase the publisher's profits.