simulation model for journal subscription by libraries

Simulation Model for Journal Subscription by Libraries

Richard E. Quandt Department of Economics, Princeton University, Princeton, NJ 08544- 7 02 1. E-mail: [email protected]

In the context of empirical work on the determinants of journal prices by several authors, the present article con- siders a simulation model of the evolution of library subscriptions when some costs increase for exogenous reasons. Journal costs are thought to consist of “first-copy costs” and “additional copy costs”; when costs rise, subscription prices are increased by publishers and some libraries, being faced with fixed budgets, cancel some subscriptions. Publishers then find that the price charged is not correct and increase subscription prices again. This iterative process ultimately terminates in a new equilibrium that is characterized by significant erosion of total subscriptions. In one variant of the model, publishers may own more than one journal, and if they do, they realize economies of scope.

The effect of various parameters on the final equilibrium is considered. The percentage of costs accounted for by first-copy costs has no significant influence, but the profit made by publishers does: The higher the profit that publishers attempt to maintain, the lower is the erosion of subscriptions. A key element in the process is the algorithm employed by libraries to decide which journal subscriptions to cancel; when they cancel on the basis of the cost of the journal or the importance of the journal, many more journals go entirely out of business than when cancellation is essentially random. The final conclusion is that while the precise outcome depends on the parameters of the model, the erosion in subscriptions can be extremely severe.

Introduction

It is well known that research libraries have faced serious problems in the 1970s and 1980s at least in part because of the dramatic increases in the subscription prices of scholarly journals. The economic and technological history of university research libraries since the 1950s has been documented in detail in a recent report by The Andrew W. Mellon Foundation (Cummings, Witte, Bowen, Lazarus, and Ekman, 1992). For nearly 20 years, from the early 1950s until about 1970, the number of volumes added annually at research libraries grew sub- stantially, although after 1970 the annual additions re-

Received November 14, 1994: revised April 12. 1995: accepted July 3. 1995.

C 1996 John Wiley&Sons, Inc.

mained largely constant, or even declined somewhat. While aggregate library expenditures increased substan- tially, as a percentage of instructional and departmental expense they stabilized in the early 1970s and declined thereafter. Noteworthy is the fact that expenditures on serials, as a percentage of total expenditures on materials, have been increasing sharply.

A significant factor in this latter change has been the increase in serials subscription prices to libraries. Thus, for example, periodical subscriptions in Chemistry and Physics have increased between 1970 and 1982 by 432%, and between 1982 and 1990 by 13 1.9%, with similar increases reported for other sciences. The situation is only slightly better in the social sciences, and in the humani- ties, which have generally exhibited the smallest increases during the two subperiods, but the increases from 1970 to 1982, for example, are still typically over 200%. The number of subscriptions has declined as prices have risen and some institutions have drastically reduced their serials acquisitions budgets and some have canceled journal subscriptions worth several hundred thousand dollars (Thatcher, 1992 ) .

Several explanations have been advanced for the price increases (No11 and Steinmueller ( 1992), Chressanthis and Chressanthis ( 1993, 1994a, 1994b), Petersen ( 1992)). Chressanthis and Chressanthis, as well as Pet- ersen. regress journal prices on a variety of independent variables. They find that there are statistical reasons to believe that higher costs, as signalled by the presence of more pages and of illustrations in journals, contribute to higher prices. European journals tend to cost more, partly perhaps because of the higher cost of distributing them in the U.S., partly because of the rise over the last decade of foreign exchange rates relative to the dollar and the ever-present foreign-exchange risk, and partly because a limited number of European publishers have a dominant position in journal publication, and are thus better able to price-discriminate between individuals and libraries. Accordingly. there is some evidence that at least some journal publishers may behave as monopolists. It is also the case that journals published by commercial publishers tend to cost more than those published by

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not-for-profit organizations. Chressanthis and Chres- santhis ( 1994a) also find that circulation reduces journals’ library prices significantly, but only modestly: Cir- culation has to increase by 1,000 copies in order to reduce the price by $2. Exploiting the effect of the circulation variable, a straightforward economic expla- nation is offered by a model made popular by No11 and Steinmueller ( 1992). According to this model, the chief culprits are academics who are constantly seeking new outlets for their article production. Publishers respond to this pressure by creating more and more specialized journals, because it is easier for a journal to become pres- tigious in a narrow field. But by virtue of the fact that their circulation is necessarily limited, first-copy costs ’ become a greater fraction of the average total cost per copy, which leads to a higher subscription price. Focus- ing on the Noll-Steinmueller distinction between first- copy and additional-copy costs, we can now imagine an initial period of (temporary) equilibrium, in which libraries spend their serials budgets on exactly those journals that they would like to have, followed by an exogenous cost increase for publishers. They will have to raise subscription prices; but then some libraries’ budgets would be insufficient for the journals that they previously used to subscribe to; libraries then drop some subscriptions, which has to generate another price increase, and so on.

No11 and Steinmueller’s empirical findings do not consider variables other than circulation and they may be partly driven by the correlation between circulation and some of the other variables considered by Chres- santhis and Chressanthis, and Petersen. But even if we abstract from the other variables, it is not clear a priori how significant the role of first-copy costs is in the process described in the previous paragraph. How far will this process go? What will its impact be on the total number of subscriptions? We shall attempt to provide sche- matic answers through a very simple simulation model.

The Model

The equilibrium that gets established in the market consisting of libraries and publishers is one of monopo- listic competition and bears some similarities to the case of viewers (who are analogous to libraries subscribing to journals) and television programs (which are analogous to journals produced); see, for example, Spence and Owen ( 1977 ). Under these conditions we encounter the usual result that the product will be priced above mar-

’ According to No11 and Steinmueller ( 1992), first-copy cost “. includes all activity associated with producing the basic information that the product contains. For publications, the first-copy costs include the editorial contents. the composition of the journal, and the prepara- tion of the basic inputs for the printing process.” Cummings et al. (1992) define first-copy costs as “the costs incurred in producing the first copy of the title-editorial work, typesetting, and so on.”

ginal cost, which involves a loss of efficiency, and it is possible that a journal would make a positive contribu- tion to total (social) surplus if it were published, but is not, because it would yield a negative profit for its publisher. The analysis of the equilibrium is made more complicated by the presence of individual subscribers, who tend to have a more elastic demand for subscriptions than libraries, because, among other reasons, of the possibility of photocopying library copies of the journal. Since libraries can count on revenues from permitting photocopying, they are able to pay higher subscription prices than they could otherwise, and publishers, by charging higher prices to libraries, can in effect indirectly exact payment from individuals for the use of their intel- lectual property (Liebowitz, 1985 ). Kingma and Eppard ( 1992) suggest that social welfare would improve if libraries raised their charges for photocopying, since the demand for individual subscriptions would become more inelastic as a result, publishers would set individual subscription rates above marginal cost as well, and the profits from doing so might lead publishers to reduce library subscription rates.

The model in the present article ignores the existence of individual subscribers and concentrates entirely on the behavior of libraries. The operation of the model can be decomposed into two logical stages. In the first stage, the initial values of the model variables are set, which implies choosing values for the journal prices and publishers’ first-copy costs, and measures of the relative importance of the various journals to each library, as well as their journal budgets, from which the serials’ subscriptions of the libraries, and publishers’ profits are determined. Given upper and lower bounds for certain parameters, random numbers are used to assign values to the key parameters of the problem. After the initial stage, which may be thought to represent an initial equilibrium and which fixes library budgets for the simulation, publishing costs are perturbed by a specified percentage. In the second stage of the model, libraries have to drop some subscriptions, because at the new prices subscription costs exceed their budget. Then journal publishers realize that they are selling fewer copies than before and have to raise prices to be able to make the same (absolute or percentage) profit as before. This leads to further subscription cancellations. The iterative process continues in this fashion, until a new equilibrium is attained in the sense that no further subscriptions are dropped.2 It is

* It should be clear that the present article discusses only a partial equilibrium model, since it ignores supplementary methods by which libraries may attempt to contain costs. One such obvious method is the development of document delivery services in a consortium of libraries or employing commercial document delivery services, on both of which there is an extensive literature. See, for example, Miller and Tegler (1988), Dickson and Boucher (1989), Simpson (1990), Getz ( 199 1 ), and many others. Document delivery has two costs associated with it: The dollar cost of, and the time delay in, effecting delivery. The lower these are, the easier it is for libraries to cancel subscriptions. In fact, neither of them is trivial. Miller and Tegler report median delays

JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE-August 1996 611

clear that this is a model of myopic behavior on the part of the publishers. If they were to behave non-myopically, they would realize that the aggregate demand for journals by libraries has unit elasticity in the model (except for the minor discrepancy that the number of journal subscriptions is, by definition, discrete, and thus cannot be varied continuously). But even if they knew the elasticity of aggregate demand, publishers would still have to face the problem of not knowing the elasticity of demand for their own product because they might not know how libraries decide, when there is a shortfall in library budgets, which of many potential journal subscriptions to cancel. Under these circumstances even rational, non- myopic publishers might behave as indicated above. In fact, it might be quite reasonable to argue that profes- sional societies that publish journals simply aim at covering the budget and that commercial publishers wish to maximize subscriptions, subject to a minimum profit constraint. Both of these objectives are compatible with the mechanism described in the present model.

There are, of course, other things that publishers might do when facing declining circulation, that the present model does not take into account at all; i.e., they might cut costs by revising downward their views about the desirable quality of their journal or they might change their minds about the discount rate applicable for making investment decisions and computerize their operations earlier than had originally been intended.3

Normally, the initial stage would be determined by confronting the demand functions of libraries (derived by solving some appropriate optimization problem) with the cost structures of publishers. The libraries’ optimization problem might, for example, be cast in a discrete choice framework as in Anderson, de Palma, and Thisse ( 1988 ). They derive the utility function of a representative consumer (“library”), who chooses among discrete alternatives (“subscriptions to journal titles”) employing logit choice probabilities. One could posit for each library a utility function of the general form determined by Anderson, de Palma, and Thisse, and differing among each other only in terms of the parameters of the function; these could then be used to simulate libraries’ de- mands for subscriptions. The problem with this ap- proach is that the resulting solutions will permit nonin-

of as much as 28 days and median costs as high as $14.10 per transac- tion. Since at least the delays, if not the costs, are likely to grow as more and more libraries attempt to take advantage of certain types of document delivery, it may well become a less suitable substitute for subscribing to a journal, which would retard the rate at which subscriptions are canceled.

3 An additional factor worth considering briefly is the effect of cancellations on advertising revenue, which some journals do receive. If circulation declines, advertising in the journal may become less attrac- tive. and advertising revenue would tend to decline with fixed page charges for advertising. The net impact would then depend on the ex- tent to which publishers compete with one another in setting advertising rates and on the elasticity of demand for advertising.

teger-valued numbers of subscriptions; but since the subscription problem is essentially an integer problem, fractional subscriptions do not make sense.4

We also note that a library’s problem of deciding what journals to subscribe to is essentially the knapsack problem of integer programming. Assuming that each journal’s importance5 is measured by Y;, its subscription price by pi, and the number of subscriptions to journal i purchased by x, , the problem is

” maximize 2 r,x,

1=l

subject to

i pix, 5 B, Xi = integer and Sk, ,=I

where B denotes the budget and where k, is the maxi- mum number of copies of journal i that the library will ever purchase. A heuristic (but generally not optimal) solution to this problem would consist of purchasing journals in the order of u, /p, , starting with the highest6

The Initial Phase

The model assumes that there are n journals and m libraries, where the user of the model may specify the values of these parameters. Each journal has a unique name given by the value of the index j = 1, . . . , II and each library has a unique name given by the index i = 1, . . . , m. The user also has to provide an initial specification of the smallest and largest number of subscriptions that any one library may have; these parameters are denoted by n, and nh; obviously we must have 0 < n/ < nh 5 ~1. The number ofjournals that each library will subscribe to ini- tially, nj, is computed as (the rounded value of) nj = nl + (Q, - nl) tl, where u is a random variable uniformly distributed on the (0, 1) interval.

The computation of which n, (out of n possible) journals will comprise the jth library’s subscription list is determined as follows. First of all, each journal is assigned randomly an “importance factor” measured by a random number between 0 and 1. These importance factors are identical from every library’s point of view and thus measure, in some sense, the importance of journals irre-

4 It is well known that computing the noninteger solution ofa problem and then rounding the solution to the nearest integer does not, in general. provide a solution to the properly formulated and solved integer problem.

5 We have to assume that it is possible to construct a cardinal measure of importance on the basis of considerations such as the impact factors ofthe various journals.

’ If a library subscribes to many journals, the “integer” problem might not be too serious and the new solution based on the r,/p, crite- rion may be close to optimal.

612 JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE-August 1996

spective of the libraries’ field interests-they indicate in a sense the “intrinsic importance” of journals. Next, the “names” of the journals are thought of as arrayed in a circle, with journal Number 1 at 12 o’clock, Number 2 a small distance from Number 1 in clockwise direction, and so on. Each library starts picking subscriptions by selecting a random point along the circle. This is intended to account for the variation in libraries’ field interests, i.e., since libraries typically subscribe to fewer journals than the population of journals, if they start picking journals at different points along the circle, they will, in effect, choose from overlapping but not identical subpopulations of journals.’ Then, proceeding in clockwise direction from the starting point, the importance factor of each journal encountered is compared with a new random number generated; if the importance factor exceeds the new random number, that journal is selected; otherwise it is not and then next journal in the clockwise direction is examined. This process continues until n, journals have been selected for the jth library.

Next, a set of subscription prices for the various journals is generated after the user specifies lower and upper bounds for the annual subscription prices; if these are pI and ph, the price for the jth journal is generated asp, = pl + (ph - p,)u, where u is another uniformly distributed variable on (0, 1). If Ji is the set of indices for the journals that have been assigned to library i, the library’s budget is given by default as8

Bi = C P,.

By examining each library’s list of journals, we can determine how many copies each publisher is selling and what each publisher’s total revenue is. We denote the number of copies sold by the jth publisher by s, and his total revenue L, = PjSj. The next step is to determine each publisher’s profit margin and first-copy cost. In order to determine each publisher’s profit margin, we need to generate for each publisher-j a fraction Cj, such that his aggregate costs C, are a fraction Cj of his total revenue. In order to allow these fractions to vary among publishers, the user has to specify a lower and an upper bound for the fraction of total revenue that is needed to cover costs (the rest being profit).’ Once these lower and upper bounds uI and ah, where 0 < al < Cj < ah 5 1, are specified, we generate CjS by Cj = al + (ah - a,) U, where u is another uniform random variate on (0, 1). The total costs of the jlh then is

’ It could be argued that each library might make its choices from a differently arranged “circle.” We ignore this generalization here.

’ But note that in reality some journals might be obtained free of charge.

9 In the present version of the model, no publisher is making losses. This feature is easily altered.

Next, we need to decide what fraction bj of total costs C, is accounted for by first copy costs. Again in order to permit variation in this for different publishers, the user specifies a lower and an upper bound b1 and bh for the fraction of the total cost accounted for by first-copy costs, which allows the computation of this fraction for the jth journal as b, = b1 + ( bh - b,) u, where u is another uniform random variable on (0, 1). First-copy costs& are then determined by calculating4 = bjCj and additional- COPY costs gj are then gj = (C, - J)/Sj. Finally, profit is determined by x, = Lj - Cj, and initial parameters are set in such a manner that all profits are nonnegative.” Once these startup values are determined, revenues are the customary price X (number of copies sold) and costs are the customary (first-copy cost) + (additional-copy cost) X (number of copies sold).

The basic model that we are about to outline has a number of restrictive assumption, although all of these could be relaxed. Among these restrictive assumptions are the following: ( 1) All random variables, wherever they occur in the model, are independently distributed from one another; (2) in the model, each journal is assigned an “importance factor”; these importance factors are identical across libraries; (3) each “publisher” publishes only one journal, and hence no scope economies in first-copy costs are realizable; (4) the initial exogenous cost increase affects first-copy and additional-copy costs equally; (5) the libraries’ aggregate demand for journals has unit elasticity; (6) the simulation model examines only the effect of a cost shock and does not deal with the potential consequences of a new publisher entering the market. However, assumptions ( 3) and ( 5) are subse- quently relaxed and the effects of relaxing these assumptions are discussed in the next section.

The iterative Stage

At the conclusion of the initial stage, an exogenous cost increase takes place by a percentage amount specified by the user.” Libraries now realize that their journal subscription cost has suddenly exceeded their budget and that they must drop some subscriptions. The model permits this to occur in one of three ways. According to the first method, subscriptions are canceled arbitrarily;

” To generate the initial state, we randomize numbers of journals subscribed to, journal prices. journal costs, and the division ofjournal costs into first-copy and additional-copy costs. All random numbers generated come from the uniform distribution and are drawn independently of one another. There is no intrinsic reason other distributions could not be used or the independence assumption could not be relaxed. It is also the case that one could require some publishers to break- even or even make permanent losses (covered by perpetual subsidies).

” In the current version, this cost increase affects first-copy costs and additional-copy costs identically. This is by no means necessary. and one might specify the exogenous cost increase to affect only first- copy costs or only additional-copy costs, or both of them, but une- qually.


TABLE I. Effects ofparameter variation journal cancellation by importance.

Parameter values

c-range b-range Percent decline No subscriptions

0.4-0.6 0.2-0.3 35 2,869 0.4-0.6 0.8-0.9 35 2,90 I 0.4-0.6 0.2-0.9 35 2,887 0.2-0.8 0.5-0.6 35 2,882 0.2-0.4 0.5-0.6 24 2,400 0.4-0.6 0.5-0.6 35 2,889 0.6-0.8 0.5-0.6 43 3,215

each library starts canceling subscriptions in the order in which they were first selected and cancels as many journals as is necessary for its outlays to be once again within the budget. According to the second way, libraries cancel journal in reverse order of their importance factors. Ac- cording to the third method, libraries cancel the most expensive journals first.” As soon as all libraries have reacted to the price increases, some publishers realize that they can no longer sell as many copies as before and that they are no longer making the required profit. They then have to adjust prices.

After the exogenous cost increase, given as a fraction y, first-copy and additional-copy costs increase, so that their new values become I3

If absolute profit is to remain the same, on the assumption that subscriptions will not change, the new total cost becomes

c-7 = “f,* + g,*s,

and the new prices are given by

However, libraries cannot subscribe to all the journals they subscribed to in the previous period and have to drop some. After they have dropped some journal subscriptions, publishers realize that they have not received the revenue that they expected, and hence they have to adjust prices again, in order to make the same profit. To- tal revenue at the tth iteration of this process now is

I2 The most reasonable assumption would, ofcourse. be that libraries cancel journals on the basis of some weighting of both importance factors and cost.

r3 Clearly, one could also model cost increases as additive rather than multiplicative.

Lf-’ =f,* + g,*sj-’ + 7rj

and the price becomes

The timing thus is the following: Prices rise at the begin- ning of each period; hence sales and revenues are down in that same period; hence prices are adjusted at the be- ginning of the new period so as to restore the original revenue on the assumption that no further sales declines will occur. This process is allowed to continue for as many “periods” as it takes to reach equilibrium, i.e., a state in which no further subscriptions are dropped.14

Some Simulation Results

In the case we examine, the number of journals, n, is assumed to be 5,000, the number of libraries, m, is assumed to be 1.500, the initial journal prices range from $20 to $400 and the number of journals that libraries subscribe to range from 200 to 1,500. Since all the random variables are generated from the uniform density, the mean number of journals subscribed to by libraries is 850.

We experiment with a variety of c and b parameters and focus particularly on two of the methods for deciding what journal subscriptions to cancel, namely the methods based on the journals’ importance factors and on their costs. In all cases, the exogenous cost shift repre- sents a doubling of costs.

Tables 1 and 2 display the ranges of c and b values,

TABLE 2. Effects of parameter variation journal cancellation by cost.

Parameter values

c-range b-range Percent decline No subscriptions

0.4-0.6 0.2-0.3 20 974 0.4-0.6 0.8-0.9 20 989 0.4-0.6 0.2-0.9 20 981 0.2-0.8 0.5-0.6 19 932 0.2-0.4 0.5-0.6 13 659 0.4-0.6 0.5-0.6 20 984 0.6-0.8 0.5-0.6 25 1.226

I4 The model described above yields formally a difference equation in price. and hence equilibrium may be approached only asymptoti- cally. However. because of the integer property of journal subscriptions, the actual expenditures oflibraries may fall strictly below budget, in which case further price increases need not cause further contrac- tions in subscriptions and equilibrium may then be actually attained in finite time. This occurs in every one ofthe simulations reported below, since after a small number of iterations, no further change takes place in prices and numbersofsubscriptions(except in the case when journal cancellations are random, in which case convergence is slow).


percentage decline in aggregate subscriptions from the start to the point at which equilibrium is reestablished, and the number ofjournals with zero subscriptions at the final equilibrium, with Table 1 covering the cases where subscription cancellation is on the basis of importance factors, and Table 2 covering those based on cost considerations.

We should note that for each simulation run, we have reused the original set of random numbers, so that each simulation starts with exactly the same number of aggregate subscriptions, namely 1,27 1,8 18. This corresponds to a mean subscription list for libraries of 847.9 and a mean subscription volume for journals of 254.4; at the be- ginning, nine journals have sold no subscriptions at all.

We first examine Table 1, Note that low c values indicate high profits and low b values indicate low first-copy costs. When c is near the middle of the range of possible values, variations in b have essentially no effect on the reduction in journal subscriptions or on the number of journals that end up having no sales. In particular, neither the change in the mean value of b (rows 1 and 2), nor in the standard deviation of b (row 3) has any effect. While this does not contradict the empirical finding of No11 and Steinmueller ( 1992) that low circulation journals tend to be expensive ones, it does say that in a cu- mulative shrinkage process induced by exogenous cost increases, high first-copy costs will not have a significant further effect. Conversely, when b is held constant at an intermediate set of values, low c values cause a smaller decline in subscriptions and a smaller number of journals have no subscriptions than in the case when c is high. Overall, the decline in subscriptions is about 35% and more than half the journals “go out of business” by having no sales.15

When journal cancellation is on the basis of cost considerations only, variations in b again have no effect. When b is held at intermediate values and the range of cs increases, we note the same phenomenon as in Table 1, namely that the subscription decline also increases. The average decline in subscriptions is much smaller in Table 2 than in Table 1. This is to be expected, since in Table 2 libraries cancel the most expensive journals first; hence fewer subscriptions need to be canceled to achieve a given volume of savings.

Tables 1 and 2 are based on the assumption of unit elasticity of demand on the part of libraries. We now consider the possibility of constant-elasticity demand functions with elasticities other than - 1. Since the elasticity of expenditures with respect to price is 1 + {demand elasticity } , if we were to set demand elasticity at, say, - 1.1, a 1% increase in price would be accompanied by

I5 Paul Kantor pointed out the following intuitive interpretation of the simulated contraction of subscriptions. If subscription prices were to increase proportionately from p to p( 1 + c), the level of subscriptions would change from s to s/( 1 + c). Taking the midpoints ofthe c- ranges in Table 1 as c yields results very close to those in the table.

a 0.1% decrease in expenditures (assuming continuous adjustment of quantity demanded, which is only an ap- proximation here). Thus, at each iteration, when publishers recalculate prices, we compute for each library the new average price that it has to pay and adjust its budget downward by the appropriate fraction. Thus, for example, when journal cancellations are in reverse importance order, with c in the range of 0.4-0.6 and b in the range of 0.2-0.9 (compare with line 3 of Table 1 ), a demand elasticity of - 1.1 leads to a 42% and an elasticity of - 1.2 to a 49% decline in total subscriptions. When the most expensive journals are dropped first (compare with line 3 of Table 2 ), the corresponding percentages are 24 and 29, respectively.

We consider four additional examples. In the first one, journal subscriptions are canceled arbitrarily or randomly; that is to say, in the order in which the subscription lists of the various libraries were built before the exogenous cost increase. For the case in which c ranges between 0.4 and 0.6 and b between 0.5 and 0.6, subscriptions decrease by 96%, although the number of journals with zero subscriptions is only a relatively mod- est 855.16 The reason for this is not difficult to un- derstand. Whether subscription cancellations are by importance factors or cost factors, and even though there is variation among libraries as to which journals they subscribe to, there is a strong tendency for the same group of journals to be canceled (i.e., the least important ones or the most expensive ones). Hence, there is a relatively high chance that successive cancellations will lead to a number of journals having no subscriptions at all. In the case of cancellations that are essentially random, the cancellations are distributed over all 5,000 potential journals, more or less evenly, with the result that many inex- pensive journals are also canceled; hence, on the average, many more subscriptions need to be canceled for equilibrium to be reestablished. However, since these cancellations do not single out a particular subset of journals, relatively few end up with no copies sold.

In the second case, cancellation occurs in reverse order of expense. This case tends to simulate a situation in which the less expensive journals are deemed to be the less important ones. ” (In this case the original importance factors would have to be interpreted as simply a randomizing device for generating the initial subscription lists.) In this case there is a fairly massive collapse of subscriptions: With c in the 0.4-0.6 range and b in the 0.5-0.6 range, subscriptions decrease by 62%, and the number ofjournals with zero sales becomes 2,667. Since this case again singles out a particular subgroup of journals for cancellation, the brunt of the cancellations again falls on a subset of journals, which explains the large

I6 It is also noteworthy that in this case it requires 60 iterations for convergence to occur, while in other cases convergence is achieved typically in less than 10 iterations.

” We are not making the argument that this is a plausible scenario.


number with no sales at the end. Since these are the in- expensive journals, the total cancellations must be large.

Thirdly, we reconsider the case in which cancellation occurs for the most expensive journals first, but assume that Cj = 1 for all journals; i.e., all journals operate on a nonprofit basis. In this case, subscriptions decline by 32% and 1,540 journals have zero subscriptions at the end. This figures compare with an average of about 20% for subscription decline and an average of slightly over 1,000 for journals without subscriptions in Table 2.

In addition, mindful of the observation that the libraries’ problem is really the knapsack problem of integer programming, one reasonable algorithm for cutting out subscriptions would be to eliminate first the journals that have the lowest rj/pi ratio. With a unit elasticity of demand, c in the 0.4-0.6 and b in the 0.2-0.9 range, the decline in subscriptions is 24%, a result intermediate between the corresponding results in Tables 1 and 2.‘*

Finally, we have to consider what happens when we relax the assumption that each publisher publishes only a single journal. We assume (arbitrarily) that there are 100 publishers who own more than one journal and generate the number of journals owned by each by taking 100 draws from the Pareto distribution, according to which

Pr( number ofjournals owned) 5 z = 1 - 0

i 0

where we fixed k = 2 and CK = 0.97.‘” The resulting draws are rounded to integers: denoting these by z*, i = 1, . . . , 100. the total number of journals owned by publishers who own more than one journals is C :=, z, and the number of journals that are the sole journal published by a publisher is 5000 - C :=, z, . A consequence of the Pareto distribution is that the generated numbers contain a few very large ones (one “publisher” ends up owning over a thousand journals, with another owning several hundred-reminiscent in the sciences of Elsevier and Springer Verlag, respectively) with many more owning only in the dozens. We then recognize that publishers with more than one journal may benefit from economies of scope: Having an organization that produces many journals may reduce both first-copy costs as well as additional-copy costs. This leads to an attenuation of the publisher’s costs and we model the attenuation factor m, for publisher i as

” All conclusions continue to hold as other variables, e.g., the number ofjournals subscribed to or the price range ofjournals, is varied.

” In the Pareto distribution, k is the lower bound of the random variable and setting it at 2 expresses the fact that 2 is the lowest number of journals that can be owned by a publisher with multiple journals. The parameter 01 was set at 0.97. because we wished to generate data from a fat-tailed distribution, and for a < 1 no moments exist for the Pareto distribution.

m, = 1 - $(e? - ~-~~=l)~

where Y was at 0.01 and $, an artificial parameter that merely permits the number of journals owned systemat- ically to affect cost attenuation, was alternately set at 0.6 and 0.2. Total costs for the ifh publisher are Cim, . Thus, if a publisher owns only one journal (z, = 1 ), no attenuation occurs; the more journals a publisher owns, the more costs become attenuated, but at a decreasing rate. The consequence of the values chosen is that publishers with very many journals have costs that are approxi- mately 80% ofthose of publishers with only a single journal for II/ = 0.2 and 40% for fi = 0.6.

In all cases we consider a c-range of 0.4 to 0.6 and a b- range of 0.2 to 0.9, and examine the journal-cancellation methods of canceling the most expensive first, or the least important first. The following interrelated observa- tions can be made. ( 1) The scope economies enjoyed by “large” publishers lead in the aggregate to fewer surviving subscriptions than cases without scope economies. (2) The greater the cost advantage of the large publishers, the smaller is the number of surviving subscriptions. Thus, for example, when journal cancellation is by the importance factor, the decline in the number ofjournals ranges from 0.38 to 0.41, depending on the size of the coefficient 1c/, compared to 0.35 in the case when no scope economies are present. (3) The greater the cost advantage of large publishers, the smaller is the number of publishers publishing a single journal. (4) Scope economies lead to an increase in the inequality of journal-distribution as measured by the Gini coefficient.20 We conclude that in the presence of multiple journal ownership with scope economies, the decay in journal subscriptions tends to become even more serious, with the burden affecting the publishers with single journals dispropor- tionately.

Conclusions

The results of the simulation experiments are to be considered as illustrative and suggestive, rather than rep- resenting any particular reality. We do not have a clear statistical view of the criteria employed to cancel subscriptions when budgets are about to be exceeded, and we do not attribute particular significance to the specific assumptions of the model, such as the independence of the various random variables or the fact that the model does not accomodate publishers with more than one journal. But it is instructive to note that in the presence of myopic behavior (a) the decline in subscriptions can be quite appreciable, ranging from 13 to 96% depending

” The Gini coefficient is defined as twice the area between the Lo- rentz curve and the 45 degree line and is thus 0.0 for a completely equal distribution and is 1 .O for a completely unequal distribution. The Gini coefficient is 0.498 at the start of the simulations and in every case examined is near 0.6 at the end.


on the precise assumptions, (b) profit making publishers who aim at maintaining the absolute level of profits cause a smaller decline in subscriptions than publishers with zero profits, (c) the fraction of first-copy costs in total costs has essentially no effect on subscription cancellations, (d) multiple journal ownership by publishers with scope economies tends to lead to larger subscription erosion than would otherwise be the case.

Acknowledgments

I am indebted to William J. Baumol, Avinash Dixit, Peter Cziffra, Paul Kantor, Stephen M. Stigler, and some anonymous referees for helpful comments. Responsibil- ity for errors is, of course, mine alone.

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simulation model for journal subscription by libraries

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