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Here, LRT is the total number of library readers,
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 Pu accompanied by a decrease in PL 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 P = 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.
Here, the potential increase in net welfare from the introduction of Pu > 0 is driven by the increase in profit. However, if society grants the right to levy a usage fee to a profit maximizing publisher, then there are accompanying decreases in Ps and PL which will result in improvements in both profit and consumer welfare. With both ps and PL set to maximize ʼn at P1 = 0, /==/ р, 21 ап/арг = 0. (45) shows that with A > 0 and (47) satisfied, ǝ/PL = 0 implies that ǝ/ǝPu
Thus, there exist finite changes in Pu and Ps which increase both and V. Similarly, it can be seen that there is a decrease in PL which makes both the publisher and the consumers prefer a positive usage fee.
Nevertheless, it is problematic whether the profit maximizing publisher would find it in his own interest to effect these requisite price reductions if he were to be granted the right to collect a usage fee. In response to the increase in demand for personal subscriptions resulting from the newly positive pu, the publisher may well find it profit optimal to raise ps. He may be willing to allow m* to increase instead of lowering PL to keep the number of library subscriptions constant. In short, Consumer welfare may be lowered by allowing a profit minded publisher to charge a usage fee, even if its level is governmentally set.
In contrast, consumer welfare is improved by the introduction of a usage fee when ps and PL are chosen optimally for net welfare subject to the nonnegative profit constraint. To show this we view Pu as a parameter in the Ramsey maximization, and use the envelope theorem to calculate the derivative of optimized net welfare with respect to Pu
the program, evaluated at Pu= 0 and at the optimal pS, PL, and λ. λ is necessarily positive, since, otherwise, ps and PL would be set equal to marginal cost and the nonnegative profit constraint would be violated. Thus, the constraint is binding at Pu and it will continue to be so
for small increases in P. It follows that
With p1 = 0, recalling
O and dp
Multiplying (50) by LR (m*) and subtracting from (49) does not affect
This is strictly positive, given (47), since we showed in Section II that with p,, = 0, the Ramsey optimal ps is greated than c, and this suffices for A 0. Hence, comsumer welfare is strictly improved by vesting publishers with the right to levy usage fees, under the proviso that library and personal subscription prices are set to maximize net welfare subject to a profit constraint.
Let us review the insights for public policy gained in this section. Overall, we find that a positive copyright usage fee is an instrument which is desirable for net social welfare when properly employed. In particular, net welfare can be increased by the extension of copyright protection to the use of journals in libraries if the library subscription price is simultaneously reduced so as to maintain the set of subscribing libraries. These same price changes also raise publisher profit if the number of readers in the marginal library is less than the average number of library readers. This gain in profit is caused by the shift of marginal prospective subscribers into personal subscriptions which are priced above marginal cost. There are also counter-balancing (around P1 = 0) effects on consumer welfare and profit due to the usage fee payments.
Further, we have shown that a usage fee is a beneficial instrument in the hands of a welfare minded price setter. Specifically, consumer welfare is increased by the introduction of copyright protection to library journals when the subscription prices are chosen optimally for net welfare, subject to a breakeven profit constraint. It can be conceivably argued that nonprofit journal publishers do, in fact, seek to set prices in this way. Then, for this major category of publishers, our results may be interpreted to recommend library usage charges.
For profit maximizing publishers, moreover, the introduction of a copyright fee can increase both consumer welfare and the level of profits. However, this improvement in consumer welfare is predicated upon the implementation of concomitant reductions in the library and/or personal subscription prices. Such price reductions will not, in general, be profit optimal, although, accompanied by the new usage fee, they will result in higher profits than were previously attainable. The challenge for public policy is to develop an institution which will tie the consumer beneficial price reductions to the profit improving copyright protection. The present analysis shows the existence of such a compromise pricing package which will benefit both publishers and readers.