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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 i at Pu = 0, 01/aps Эт/әр
= 0. (45) shows that
If with A > O and (47) satisfied, an/aPL = 0, implies that am/pu > 0. LR
a TT dp
> 0. dp > 0, then di =
Also, ap ,
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 This yields d[v+)* .
where L is the Lagrangian of
the program, evaluated at Pu = 0 and at the optimal PS, PL, and . 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 = 0 and it will continue to be so
do* for small increases in Puo
ap . With
= 0, recalling (46),
Multiplying (50) by LR (m*) and subtracting from (49) does not affect the value of
Then, (38) yields
This is strictly positive, given (47), since we showed in Section II that with Pu = 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 Pu = 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.
The Ramsey Suboptimality of Perfect Purveyance
of Excludable Public Goods
In Section V we showed that full Ramsey optimality requires a positive usage fee. This is not too surprising since we are accustomed to Ramsey optimal prices being above the corresponding marginal costs, and here the marginal cost of an additional library reader is zero. The usual reason for this result is that with increasing returns to scale in production, prices must generally be above marginal costs for revenues to cover total costs.
Here, we show that perfect purveyance of excludable public goods is Ramsey suboptimal for a new and different reason. We consider a rule that each library must finance the proportion a of the subscription price PL by means of a use fee whose size then varies over libraries:
Under this regime, with a > 0, the library does not perfectly purvey the noncongested journal copy, and the use payments do not contribute directly to cover the publisher's total costs. Yet, we shall see that the Ramsey optimal value of a is positive. The sole effect of the introduction of a positive a is to raise profit by the mark-up on the personal subscription sales to the former marginal potential subscribers. Because the profit constraint is binding, this profit increment enables Ps and p, to be lowered, bringing profit back down to its previous level, and increasing consumer welfare.
To establish this result, we note first that given (Al), m* is implicitly defined by
As before, əWP/apu LR, and, from (Al), at a = 0, apu/da = PL/LR. Substituting these facts into (A3) gives, at a = 0,
The derivatives of consumer welfare, V, with respect to a, at a = 0, can be calculated from (39), recognizing that now Pu
is the function of both a and m given by (A1).
Profit is now simply a = PSMS + PLNL - CONS+NL),
and nh given by (42) and (5), again remembering that (Al) and (A2) give new interpretations to P, and m*. Here, in view of the critical (A4), calculation shows that at a = 0,
Applying the envelope theorem, as in Section V, dV* aL av
+ (1+2) = 0. This inequality is strict whenever there aa are any marginal prospective subscribers in any of the subscribing libraries. In this case, Ramsey optimized net or consumer welfare is strictly increased by the imposition of a positive a.