Otherwise, the needed modifications in (27) require only the number of potential subscribers and the ratio of the number of library to

personal subscriptions.

III. Determining Best Price Adjustments from Current Data

There is considerable methodological difficulty in deriving from (26) and (27) insights that are relevant to current practices. of journal pricing. The variables (elasticities, circulations, and number of potential subscribers) to which the formulae relate p are all to be evaluated at the to-be-determined prices. This endogeneity, endemic to necessary first order conditions, means that the optimal prices can only be determined as the solutions to simultaneous equations whose global behavior is almost impossible to deduce from available local data. Further, intuitions that we may have concerning current values of the variables governing p cannot be logically utilized via such first order conditions as (26) and (27) to illumine the optimal, prices. We cannot use a comparison, for example, of (NS/NS)/(NL/NL) across journals to deduce from (28) a comparison of the corresponding optimal values of p. The relevant quantities to compare, holding other components of (27) equal, are the values of [NS/NS/NL/NL) at the different optima. But these, themselves, are

the objects of interest.

Fortunately, there is an analytic line of inquiry which

circumvents these conceptual difficulties. We can ask for the direction of change from the current prices which is best for social welfare while preserving the current level of profit. It can be shown 10 that

if the current p =

PL-C
Ps-c

is greater than the current value of

(defined

in (24)), then the best, profit constrained, direction of change required that PL be lowered and Ps be raised. Inversely, if, at current levels, p < 4, then p should be raised and ps lowered. It should be emphasized that these calculations do not necessarily indicate the relationships between the current and the optimal prices. Instead, they give the best local price adjustments that can be determined from strictly local information on the relevant functions.

From this point of view, y, calculated at current values of the variables, can indeed be meaningfully compared with the current ratio PL-C Ps-c

Since both (26) and (27) give expressions equal to y, they can serve as vehicles for the application of current data to the study of

present journal prices, yielding recommendations for the best direction of change. It now becomes meaningful to investigate the behavior of

with respect to its component variables. This is not the standard comparative statics technique which requires consideration of the feedback between the underlying parameters and the consequent optimum at which the equations are evaluated. Instead, we study the level of , always evaluated at current prices, as a function of the values its parameters could take on as they pertain to different journals. Here, these parameters need not be viewed as functions of prices, as they must in comparative statics (with prices endogeneous), because the prices are themselves parametrically fixed at their currently realized values.

We shall first utilize this novel and powerful technique to establish conditions under which it can be unambiguously asserted that welfare would increase (without affecting profits) by introducing a positive margin between currently equal library and personal subscription prices. This assertion can be made if the current value of for a particular journal, with PS PL, exceeds 1. For this journal, the current p is equal to 1, less than , indicating that PL should be raised and ps lowered.

=

PL, exceeds 1.

Using the representation of given by the right hand side of (27),

Thus, 1 is equivalent to (k-1) + Z(1-n) > 0. This condition will be met whenever the circulation ratio, n, is less than 1 and the ratio of the elasticities, k, is greater than 1. The meager empirical evidence suggests that k is significantly larger than 2, for all journals studied. 11 Further, the best available data indicates that n < 1 for a majority of technical journals. 12 Thus a finding that > 1 for a journal with ps = PL would not be surprising, and the policy recommendation to differentiate the subscription prices, PL PS, would be rigorously justified.

>

For journals already charging differentiated prices, the investigation of the best direction of price changes requires more current information. If k, n, and Z were known, then the test is just p. However, Z may be more difficult to estimate than are k or n. Nevertheless, we can use (28) to determine the minimum value of y, over all Z > 0, as a function of k and n. If for a particular journal it should be the case that p < min, then surely p < & and the recommendation to increase PL and decrease ps would follow.

Holding PL, PS, k, and n constant, (28) shows that is either monotone decreasing or increasing in Z as (PL/PS)nk is greater or less than one. In the latter case, min = (PL/PS)k. In the former case, we need an upper bound on Z to establish a Tower bound on .

Substituting this uppen bound for Z into (28) gives

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 < min, and the ratio of PL to Ps

Ps

should be increased.

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), Ps was 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. The marginal costs were calculated form the formula,14

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, nk > 1 for k > 2, and so we can

PL
Ps

presume16 that (30) applies. Column 8 lists the values of micolumn 9

computed from (30) with the underestimate of 2.0 used for k. 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.