Ps For JET, Table 1 shows that it is unlikely that p < min• Since nk > 1, is decreasing in Z, and (28) yields max Since PL Ps PL = 2, P < 4 for k > 1.5. Thus, for reasonable values of k, max "min << 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 (P = PL and p = 1). = 0. It follows then from (33) that эп Эп At these equal prices, + aps PL Эп if, at current values, >1 = ρ, then > 0 and PL 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 Is In the present context, new and significant questions arise: 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. First, suppose PL were set well above the willingness to pay of all library populations. Then, of course, NL = 0 and N = 0. It follows from (20) that here N = N = 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 p1 to the level of the maximum (over library populations) willingness to pay, the publisher gains that amount, less the marginal cost, while losing PST The library population. It is they who leave the personal subscription As p1 drops further, these processes continue with additional PL libraries acquiring the journal, N becoming negative and with N and NS 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 Ps 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 = 0. = If, instead, the agent with the maximal B has B > T, 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. вmax 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 T1 + 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 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 N = 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, P 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 opened, the constrained welfare-optimal personal subscription price, ps, is the smallest psc which allows the resulting profits, including p,, to be nonnegative. The welfareoptimal mode of provision of the journal is then obtained by comparing the level of total welfare at PS PS 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. A 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 Bmax, To, T1, a, c and $. 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 PL 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-T to PS - T. The counter-balancing profit increase arises from the high B, high T agents whose new contribution to profit as a personal subscriber, Ps - 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. It Numberical simulations confirm our expectations that different provision modes may emerge from profit and welfare maximization. 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. |