Note further that the expression given for min in (30) is an increasing function of k. Hence a perceived lower bound on k can be substituted into (30) to yield min as a function of the directly observable values of PL, Ps, and n. Moreover, by equating (30) to p, we can solve for the unique value of k, k*, for which p = min• It follows that if k > k*, and if the condition for the validity of PL (30), nk > 1, is satisfied, then p こ should be increased. < "min, and the ratio of PL to Ps We now apply these methods in a pilot study of the 1975 prices of five economics Journals: Quarterly Journal of Economics (QJE); American Economic Review, together with the Papers and Proceedings, and the Journal of Economic Literature (AER); Journal of Political Economy (JPE); Economic Inquiry (EI); and the Journal of Economic Theory (JET). The prices, taken from the public record, pertain to all issues published in 1975. For the association journals (AER and EI), taken to be the membership fee, and we ignore any benefits and costs of membership unrelated to the journal subscriptions. Circulation figures, NL and NS, were obtained directly from the editorial offices.13 The marginal costs were calculated form the formula,14 Ps was and then inflated by 25 percent.15 These data appear in columns 1-6 of Table 1. Column 7 holds p, the ratio of the deviations of the subscription prices from marginal cost, which is to be compared with v. For each of the five journals, PL nk > 1 for k ≥ 2, and so we can Ps > presume16 that (30) applies. Column 8 lists the values of computed from (30) with the underestimate of 2.0 used for k.miColumn 9 exhibits k*, the value of k which would make min = p. These calculations suggest that p is indeed well below for all the journals but JET. Both intuition and the evidence support the contention that the own price elasticity of personal subscriptions is more than twice that of library subscriptions. With k > 2, both columns 7 and 8 show that the values of p are below those of min. The policy conclusion 17 is that net consumer welfare can be increased, while the levels of publishers' profits are maintained, by simultaneously increasing PL and decreasing Ps, for QJE, AER, JPE, and EI. Includes Papers and Proceedings and the Journal of Economic Literature. 干 The value of k for which min p. PL Ps For JET, Table 1 shows that it is unlikely that p nk > 1, is decreasing in Z, and (28) yields max PL Since = 2, p < 4max for k > 1.5. Ps Thus, for reasonable values of k, 4min << "max, and we cannot reject the hypothesis that the subscription prices of JET satisfy the optimality conditions. In fact, rearrangement of (28) shows that if k and Z satisfy k = 1.5 + 6Z. It is certainly plausible, for example, that Z = .5 and k = 4.5. Thus far we have studied welfare maximization, and our concern with profits has been restricted to the constraint of nonsubsidized viability of the publisher. However, these very same tools can also be usefully applied to the study of profit maximization. The first order conditions for the choice of PL and PS which is optimal for profits can be expressed as This This matrix equation can be derived from (11) by letting λ → ∞. follows heuristically from observing that as grows large, the Am term dominates the W term in the Lagrangian underlying (11), and, in the limit, maximization of L is tantamount to the maximization of π. It is evident from (32) that a necessary condition for the current levels of p and Ps to be profit optimal is that p = . Thus the results displayed in Table 1 can be interpreted as evidence that all the journals but JET are neither successful profit maximizers nor constrained welfare optimizers. However, with the profit objective function, inequality between p and cannot be utilized to determine the best direction of price change without either further information or additional assumptions. Algebraic manipulation of (32) reveals that One interesting application of (33) concerns a publisher who is currently charging a profit optimal nondiscriminating price (Ps = P1 and p = 1). At these equal prices, + = 0. It follows then from (33) that дп дп aps ар if, at current values, > 1 N ρ, then > 0 and < 0. In such a aps case, increasing PL and decreasing Ps would definitely increase profits. Together, (32) and (11) show that prices which are profit optimal and prices which are profit constrained welfare optimal both satisfy the condition p = . However, it is also evident from the equations and from common intuition that the former prices will both be larger than the latter. Of course, this is a reflection of the well-known welfare loss due to profit maximizing monopoly behavior. IV. Profit and Welfare Optimal Choices of Provision Modes In the present context, new and significant questions arise: Is there an additional welfare loss caused by the monopolist choosing a socially suboptimal set of provision modes? Will the monopolist refuse to make the journal available to libraries or perhaps to personal subscribers? Might these also be the constrained welfare optimal choices of provision modes? In one sense, these structural questions can be viewed from the now familiar standpoint of pricing. Clearly, PL or Ps can be set high enough to drive to zero library or personal subscription demand. However, this view obscures the causal economic forces. Indeed, the very form and interpretation of the function changes with the provision modes generated by the changing levels of Ps and PL. There are several cases to consider. N's = = First, suppose P were set well above the willingness to pay of all library populations. Then, of course, N = 0 and N _NL = 0. It follows from (20) that here NS NS 0. Thus, in this case, the publisher effectively faces only the market for personal subscriptions and consequently, the public good aspect of the situation is absent. By lowering p, to the level of the maximum (over library populations) willingness to pay, the publisher gains that amount, less the marginal cost, while losing pec for each prospective subscriber in that library population. It is they who leave the personal subscription market in favor of utilizing the newly acquired library copy. The welfare effects are the gains, B - T, of each peruser who now has access to a library copy, the cost c of providing that copy, and the ambiguously signed T-c of each subscriber. The profit impact of opening the library market is also ambiguous. SIt As p, drops further, these processes continue with additional libraries acquiring the journal, N becoming negative and with N and L N becoming positive. This is the case in which both provision modes are fully operative and the formulas (11) and (33) govern the optimal prices. Only the library mode is operative when Ps is set above the reservation prices of all agents. In this case there are no personal subscribers and no potential subscribers using the libraries. The profit maximizing publisher sets the monopoly level for PL, viewing the libraries as the only effective market. As PS falls to the level of the largest B in the population, two different cases can occur. If the agent with the maximal B has T > B > c, then he will purchase a personal subscription, whereas previously, when Ps was higher, he was neither purchasing nor using the library. In this case, both profits and welfare unambiguously increase with the opening of the personal subscription market. At such a set of prices, the library and personal subscription markets are both operative, although decoupled from one another. This is, so because there are no potential subscribers, and hence, from (15), N = N = NE = 0. If, instead, the agent with the maximal B has BT, B > c, then the reduction in Ps to just below the level of his B does not induce him to switch from library use to a personal subscription. Yet, his willingness to pay for the library copy is diminished. This can cause the set of subscribing libraries to shrink, an unfortunate eventuality for both welfare and profits. However, as ps falls further, new personal subscribers appear and both the welfare and profit effects are ambiguous. Hence, little can be said at this level of generality about the welfare or profit preferability of the diverse market structures we have identified. To investigate the question of whether the welfare and profit rankings of the different market structures agree, and, further, to gain insight into the economic causes of such disagreement, we have resorted to a class of numerical examples. The mathematical model used in the simulations is a simplified version of the one employed in Sections I and II. Production cost is + cQ. We assume that, in the B,T space, agents are uniformly distributed over a parallelogram. Their benefits from reading lie between zero and Bmax. max is finite and greater than the constant marginal cost c of producing a journal copy. Agents with some particular value of B have inconvenience costs uniformly distributed between To + aB and T + aB. The parameter a, constrained to be between zero and one, reflects the dependence on B of the mean conditional inconvenience cost. If, for example, a were zero, the mean inconvenience cost would be independent of the value of B. The assumption that a does not exceed one is introduced so as to ensure that at least for some values of personal subscription prices there will be library readers. Figure 2 depicts the special assumptions made about |