A Model of the Danish Book Market

Journal of Cultural Economics 24: 27 43, 2000. 2000 Kluwer Academic Publishers. Printed in the Netherlands. 27 A Model of the Danish Book Market CHR. HJORTH-ANDERSEN Institute of Economics, University of Copenhagen, Studiestraede 6, 1455 Copenhagen K, Denmark Abstract. Traditionally, books have been a major factor in the cultural life of a nation, although little attention has been paid to the book market. In an attempt to redress this situation, a simple macro model of the (Danish) book market is presented where demand, conventions in the publishing industry, and technology interact. The results are dramatic as the book market has changed decisively in the past two decades, in effect forcing us to reconsider what it means to publish and to be an author. Key words: authors, books, market structure 1. Introduction Books are without any doubt a major factor in the cultural life of a nation; however, not very much attention has been devoted to the book market in cultural economics. One may indeed wonder why this is so. Historically, books have been the major means of communication of new thoughts in times where the majority of the people had little opportunity to go to the theatre and electronic entertainment was not yet invented. The influence of authors has certainly been recognized, frequently by kings and almost invariably by dictators trying to combat dangerous ideas. In cultural economics, there is an extensive literature on the theatre, but with the exception of official reports, not very much on the book market, although its economic importance, and arguably also cultural importance, would indicate otherwise. A major reason for this state of affairs is presumably that in most countries the book market has traditionally been a free market activity, while the theatre has been subsidized by the state. Subsequently, an extensive discussion of the justification of these subsidies has arisen, and a similar discussion could presumably be held with respect to the library system, especially with regard to the activities dealing with fiction literature. In this paper, I first intend to discuss the book market in general terms. It is important to form an overall idea of the operations of the book market as many public reports and many organizations take a very narrow and partisan view. Actually, aspects of the book market are often discussed by non-economists, such as representatives of authors associations, librarians, prominent authors, and professors of the sociology of literature, with very little idea of how the entire market works. It turns out that the eventual market consequences of a specific change in a parameter may very well be completely different from the immediate partial consequence. I

28 CHR. HJORTH-ANDERSEN Figure 1. The important sectors of the book market. shall therefore concentrate, not on some detailed aspect of the book market, but on the structure of the market. The model presented here is implicitly based upon the Danish book market, as is also some empirical evidence, but I believe most of the mechanisms will be found in other countries, although the emphasis and the specific circumstances would, of course, vary. This paper deals with the book market, fiction as well as non-fiction. It could be argued, of course, that only works of fiction should be included, as only they are of interest in cultural economics. There are, however, important reasons for including non-fiction. One reason is that available statistics, e.g. price indices, do not allow for the distinction fiction/non-fiction. Furthermore, non-fiction may be an integral part of the cultural atmosphere of a country. Thus, it could be argued that well-known history books are more important in shaping the minds and thoughts of people than many highly praised but little read poetry editions. Finally, from an economic point of view, the market of fiction and the market of non-fiction are interdependent. Many publishing companies have a major part of their turnover from non-fiction, e.g. school books, which enables them to publish a certain amount of not very profitable serious literature. 2. The Structure of the Book Market In Figure 1, an overall description of the book market is given for a specific economy. As always, the book market is determined by the forces of supply and

A MODEL OF THE DANISH BOOK MARKET 29 demand, and in each period a great many new books, or titles, are introduced, priced, and sold. Let us start with the supply side. In each period, the publishers will be offered a number of manuscripts from national authors. These manuscripts may come to the publishers exogenously or they may have been commissioned, but the origin of the manuscript, while very important to the individual author and for the individual contract, is probably not very important for the book market. Very little is solidly known about the number of manuscripts offered to the publishers, or how many manuscripts that are rejected and possibly reoffered to another publisher. 1 What we do know is that the publishers have the choice not to publish some national manuscript, but to translate and publish some foreign manuscript, be it a novel or a textbook. 2 The number of books appearing on the world market is in an order of magnitude larger than the number of books appearing in any national economy. Any individual publisher has an almost limitless number of manuscripts to choose from, especially if it is taken into consideration that translated works need not be chosen from the titles of the current period, but may be chosen from any previous period. In economics, attention is devoted to scarce resources. As the supply of manuscripts is not limited, the authors actually play a negligible role in the functioning of the book market! Of course, publishers often complain about the quality of offered manuscripts as they would prefer manuscripts guaranteed to turn into best-sellers, but the economic fact is that the book market is not limited by the amount of available manuscripts. The central agents in the book market are the publishers. Essentially, a publisher has to make two decisions. The first is to determine which titles to be introduced, and the second is to determine the prices. In the case of an expected best-seller, the decision to accept the book may be obvious, and the only problem is setting the price of the book. However, most books are not obvious best-sellers, and these two decisions will have to be solved in one step. The central decision in the publishing industry is the decision to publish new books. I use the term titles for new works, to distinguish titles from reprinted works, books in new editions or cover, and so on. The crucial feature is the very large stochastic component that is involved in the decision. In principle, each new title is a new commodity. The publisher does, of course, have previous experience from other titles, but the problem is from which of the previous titles an analogy is to be inferred. Will this manuscript resemble novel A with excellent sales or novel B with poor sales? It is important to understand the technology of the publishing business as it is heavily influenced by fixed costs. Essentially, there are two types of fixed costs. One is the ordinary fixed costs f of running a business, such as management salaries and rent. The other is the fixed cost f i of introducing a new title i such as evaluating the manuscript, preparing and editing the manuscript, and so on. These fixed costs are usually a very substantial portion of the total costs of publishing a new book. Consequently, books cannot be priced according to a marginal cost principle as the publishers would suffer a loss. Therefore, it has been a longstanding

30 CHR. HJORTH-ANDERSEN Figure 2. The pricing decision. practice in the printing business to calculate prices on the basis of some full cost concept. The publisher has an initial notion x about the sales of a particular title based on experience. 3 The fixed costs f and also the marginal costs c, assumed to be constant, are known. The publisher calculates an initial price p based on a full cost formula, so that the initial price p is a declining function of x, p = f(x ) with dp /dx < 0. He now has a situation depicted in Figure 2. If actual sales meet expectations, the publisher will get the expected profit. This description of the pricing process is usually frowned upon by economists as it does not seem to involve optimizing behaviour. In fact, there is nothing to prevent the publisher from formally starting with another and, for example, more pessimistic notion of initial sales, x, calculate the corresponding higher price p >p and see if expected profits would be higher corresponding to this set of values (x, p ). However, this is probably done only mentally by an experienced publisher choosing the initial value x. This description of the pricing process differs from the usual description of monopoly pricing, but so does the problem. In monopoly theory, the monopoly is already assumed to exist, and, knowing the strength of the demand, the producer only tries to optimize with respect to the elasticity of demand. The book publisher has to evaluate the strength where sales could be compared to x for a given price p as well as the elasticity, and the strength of demand is much more important in the long-run survival of the firm than finetuning with respect to the elasticity. A publishing company has to set prices for hundreds of books each year, and this process must necessarily be done on a more routine basis.

A MODEL OF THE DANISH BOOK MARKET 31 It is important to realize that the attention of the publisher quite naturally becomes concentrated on evaluating the expected number of copies sold. With independent firms, the publisher will not consider the effect of publishing a new title on the entire book market. 4 Thus, the sale of one book will to a large extent be at the expense of other publishers who will see reduced sales due to the substitution between the books described above. It should also be noted that the pricing decision is thought to be autonomous. Usually, there are no strategic interactions involved. A publisher may publish a novel or a textbook without fear of reprisal from other firms. There are exceptions, of course, where two books are likely to compete directly, as for example two Danish Romanian dictionaries. But usually, and especially within fiction, a book is thought to compete with a great many other books; so there will be no recognized interaction between the different books. The market is a prime example of Chamberlinian monopolistic competition, many substitutes but no close substitutes. The publishers sell their books to the retail sector or, as a recent phenomenon, via the Internet directly to the consumers. There is a long-standing tradition in economics to ignore the retail sector, and I shall essentially follow this tradition. In some European countries, including Denmark, books are sold under a resale price maintenance system so that publishers actually set two prices, one for sale to the bookshops and another for sale to the consumers. This system has been widely debated as it affects all the market agents and probably also to some extent the eventual outcome with respect to prices and composition of the books sold, but I shall not go into this debate. 5 While the interactions between the publishing sector and the retail sector are interesting in an industrial economics perspective, they are probably not important for an overall description of the book market. The publishers also sell books, directly or indirectly via the book shops, to public libraries. In some countries, including Denmark, there is a very extensive public library system where books, even quite new books, can be borrowed free of charge. It is an interesting question to what extent the library system influences the book market. It has, of course, the direct effect of buying some of the new books, and for certain books this can be an important factor in the marketing planning. No doubt, there is also an indirect crowding-out effect as private sales through book stores would have been higher had people not had the opportunity to go to the library. It should be noted that while Danish authors face foreign competition, Danish publishers do not. Books in Danish are not exported even to other Scandinavian countries, and while some Danish students are required to read textbooks in English, imports of books in foreign languages, mainly English, constitute only a small fraction of the total book market. This feature sets the Danish book market apart from, for example, the English or the French book market.

32 CHR. HJORTH-ANDERSEN 2.1. THE DEMAND SIDE As shown in Figure 1, it is probably useful to think about demand divided into the long-run inclination to read and the factors that will influence demand in the short run, that is the change in the yearly number of books sold. The long-run demand will give the level of the number of books that could be sold in the economy. It is dependent upon factors not likely to change very much from year to year, and in a regression these factors will show their influence in the constant and the trend factor. These long-run factors are presumed to be: 6 (a) Reading ability of the population. This is not the same thing as the official number of literates in a society. Quite a number of people can technically read, but they are not at ease with reading most books; (b) Education, which is correlated with reading ability. It is well documented that education is combined with actual reading. The higher the education, the more people read, be it fiction or non-fiction. However, it is not easy to characterize the educational level of a population. While a number of statistics, such as the number of people having a specific education, are readily available, the question remains that such an indicator may not say very much with respect to the present issue; (c) Leisure. Again, it is very difficult to characterize the amount of leisure available to a population. Furthermore, the amount of leisure is probably not very important for the inclination to read. In fact, quite a lot of people, the unemployed, retired people, and part-time workers, may have all the leisure they want, and yet even with free library facilities they do not read very much. Hardworking people usually have quite some hours free during the week, but prefer to spend their leisure on other activities; and (d) Alternative goods. These would be newspapers and magazines, directly related to the book market, and especially the electronic media, such as video and television. Undoubtedly, television is the major competitor. This can be seen from the budget studies of the time allocation of families that are conducted all over the world. Much has been written about the magic powers of the electronic media, but economists like to talk about the price mechanism; therefore, I should like to add that besides cable television watching an hour of television has a zero cost to the consumer, or at least a zero marginal cost. This institutional feature certainly sets the book market at a disadvantage compared to television. 7 These long-run factors are difficult to characterize, and they are unlikely to show any marked change from year to year. Therefore, it is not possible to measure their influence using econometric techniques. The short-run factors are supposed to be real book prices, real income, and the number of titles. Book prices are described by a book price index, but, in order to obtain real book prices, this index must be divided by some other index. I have

A MODEL OF THE DANISH BOOK MARKET 33 chosen the consumer price index with the implication that the choice of buying a book comes at the expense of ordinary consumer goods. This is an economic assumption about the way I believe the Danish book market works. In theory, there are other possibilities. If cable-tv were to become dominant, one might divide the book price index with an index of cable-tv prices. Alternatively, if books were considered to compete with newspaper and magazines, one could use an index of these prices. That real income should enter into the demand relation requires no explanation. But the introduction of new titles may need explaining. The idea is that there is certainly substitution between the individual books, but there need not be perfect substitution. No doubt there is substitution, so it makes sense to talk of one book market rather than a large number of individual book markets, one for each title. One unread crime novel may ex ante substitute another when planning for a vacation, and if one introductory textbook in economics is out of print, another will do. Books are often given as presents, and according to Danish practice one new book may be exchanged for another in the bookshop. However, there is not unlimited substitution. If you are planning a trip to Poland, a travel guide of Poland may be considered, while a travel guide of Bulgaria is not a substitute. If you are a John le Carré fan, you may be induced to buy his latest work but would not consider substitutes. One might, therefore, expect the total number of titles to influence demand. 8 3. A Skeleton of a Macro Model The basic fact of the book market is that its size is constrained by demand. As argued in the previous section, there is an abundance of manuscripts and there are usually no capacity limitations in the printing business; thus, there are no capacity constraints on supply. Nor is it possible for the publishers to limit the supply as there is free entry into the business. The core of a macro model of the book market must, therefore, be the demand relation. 3.1. THE DEMAND EQUATION Demand is modelled as X = f(p,y,t,t), (1) where X = number of books sold per year; P = the average price of books; Y = an expression for real disposable income; T = number of new titles per year; t = time. The basic structure of the demand relation is quite conventional. Demand depends upon price and income, titles as argued above, and a time trend to catch movements in the long-run inclination to read as well as the competition from the electronic media. It could be argued that the logic of the argument leading to

34 CHR. HJORTH-ANDERSEN the inclusion of titles in the demand function would lead to a formulation where demand would depend upon the total number of titles available and not the total number of titles issued in a given year. While this may indeed be so, sales are very strongly dominated by new books; so the simple formulation (1) is preferred. Data is supposed to be available for N consecutive periods. It should be noted that (1) denotes total demand for books. This is where the minimum model comes in. A desirable alternative would be to disaggregate the model according to demand categories. It could be outlet (Internet, book clubs, and retail) or it could be fiction and non-fiction. An interesting disaggregation would be to operate with three demand categories: Sales to libraries B; sales of school books and textbooks S; and sales to the private sector C defined residually, with X B + S + C. It would then be possible to have separate relations determining B, S, and C. Especially interesting would be to estimate the equation C=f(B...)which in principle would settle the question whether or to what extent the crowding-out effect is present. Another possibility would be to disaggregate the market into the market for hardbacks and paperbacks. Implicit in the present model is the assumption that the structure of the book market has not changed with respect to the composition of these two submarkets. 3.2. THE TITLE EQUATION Titles are modelled as T = g(f,y). (2) In the decision to publish a new title, the fixed costs f are an important factor. These are sunk costs and describe the maximum risk that the publishing firm takes. Y is an income measure. Using cross-section data, the dependence of T on Y has been estimated by Hjorth-Andersen (1996). A reasonable description was: ln T = 6.37 + 0.65 ln Y for a number of OECD countries for 1985 with both coefficients being strongly significant, and R 2 = 0.76. Similar results were obtained for 1987. The idea is simply that a larger economy will sustain more titles. 3.3. THE PRICE EQUATION In the model, price does not function as an equilibrating mechanism, but is determined separately: P = g(x/t,f,z), (3) where f denotes the fixed costs of publishing a new book and Z is a vector of exogenous variables. The traditional pricing formula implies that book prices will be lower the higher the number of copies is expected to be. The factor X/T denotes the average number

A MODEL OF THE DANISH BOOK MARKET 35 of copies sold, and price will thus be negatively related to the average number of copies sold. The factor f will, according to this description, obviously be positively related to P. Thus, if the fixed costs decrease, there will be two opposing effects. One is that price will decrease due to the pricing formula, while the other will be that according to the title Equation (2) the number of titles will increase, diminishing the average number of copies sold per title, which will in turn increase the price. It should be noted that during this discussion, it is implicitly assumed that prices set by the publishers are apart from a mark-up factor identical to the prices confronting the consumer. In other countries, interactions between the publishers and the retail sector may have to modelled explicitly. 3.4. THE TOTAL MODEL The model is now complete, consisting of Equations (1) (3). Consumers determine the total number of books to be bought. Publishers determine the number of titles to be introduced and the price of each title. 9 Retailers respond passively to the prices set by the publishers. If these decisions do not bring about equilibrium in the short run, something will have to adjust. The essential assumption in the model is that equilibrium occurs as the number of copies sold per title adjusts. This description of the adjustment process is certainly in accordance with the empirical facts. Sometimes sales of a new title are way ahead of expectations, and the publisher orders a new printing. This can be done in a matter of weeks. If sales do not meet expectations, the remaining copies may later be sold at sharply reduced prices or, more frequently, simply be silently destroyed. In the long run, with consistently disappointing sales, publishers will reduce their expectations with respect to the number of copies X/T sold per title. This will, ceteris paribus, be reflected in the pricing policy and the policy of introducing new titles. The model as described in Equations (1) (3) is a simultaneous model. In order to show as clearly as possible the essential working of the model, I shall use a simplified parameterized version excluding constants as well as the title factor in the demand equation as it turns out to be empirically unimportant: X = P α Y β α<0, β>0 (4) P = (X/T ) δ f ε δ<0, ε>0 (5) T = f γ Y κ γ<0, κ>0. (6) Solving these gives: ln X = γδα/(1 αδ)ln f + (β κδα)/(1 αδ)ln Y (7)

36 CHR. HJORTH-ANDERSEN ln P = (ε γδ)/(1 αδ)ln f + (βδ κδ)/(1 αδ)ln Y. (8) In this version, the average price P and the number of books sold X are functions of two exogenous factors, the fixed costs f of printing a book and national income. A decrease in fixed costs will have two effects. One will be the immediate (and obvious) reaction, symbolized by the parameter ε, that fixed costs, ceteris paribus, will decrease the price. There is, however, another, not quite so obvious factor. A decrease in fixed costs will also lead to more titles, and thus decrease the average number of copies sold. As can be seen from the expressions above, the sign of the coefficient of f is indeterminate. In particular, the sign of the factor (1 αδ) cannot be deduced by a priori reasoning. If the average price is very responsive to X/T, that is if δ is large, and if the price elasticity α is also large, a decrease in fixed costs will lead to higher prices and lower sales. A similar effect will be found in an expanding economy. Increasing Y will lead to expanding sales X, but it will also lead to more titles to be introduced. More titles will tend to decrease the average number of copies per title and thus increase the price, and so it will depend upon the particular elasticities what the net effect will be. 4. Some Facts from the Danish Book Market Unfortunately, it is not possible to estimate the model (1) (3) due to a lack of data, in particular with respect to the development in the technology. There are no published figures on the fixed costs in the publishing industry and, as they are assumed to be important for the pricing process, neither the price equation nor for that matter the title equation can be estimated. Nevertheless, some facts may be deduced and it is possible to estimate the demand equation. In Table I, some of the most important figures for the book market are presented for the period 1973 1993. For the period 1973 1993, we can see one of the major tendencies in the book market, namely a marked increase in new titles. The number rose by more than 75 per cent in this period, and it is with a very good reason that the macro model includes a title equation. This time series is based upon official reports and can be assumed to be quite reliable. 10 Nor is the increase in new titles a Danish phenomenon. For example, in the U.K., the number of titles increased from 55,000 in 1987 to 95,000 in 1995. 11 The real book price is defined as an index of book prices divided by the consumer price index. The book price index describes the development in the price of new books, disregarding books eventually sold at reduced prices. As may be seen in Table I, there was a marked tendency for book prices to increase more than average consumer prices, in fact by about one third. This is certainly quite surprising, considering the fact that prices are based upon a full cost formula and the fixed

A MODEL OF THE DANISH BOOK MARKET 37 Table I. Important time series for the Danish book market Year Number of Index of Real turnover titles real book in millions of published price 1973 Krone 1973 6500 100 696 1974 6822 93 740 1975 7068 92 765 1976 6836 99 719 1977 8021 93 817 1978 8642 93 828 1979 9415 99 738 1980 9256 98 658 1981 8563 93 675 1982 10189 100 632 1983 9460 104 579 1984 10660 108 565 1985 9554 110 560 1986 10957 116 515 1987 11129 118 486 1988 10584 120 483 1989 10762 122 475 1990 11082 123 479 1991 10198 128 488 1992 11761 131 475 1993 11492 129 466 Source: Hjorth-Andersen (1996) and Danish Statistical Yearbook. costs of introducing a book declined markedly during the period. There has been a massive technological development as manuscripts are no longer delivered to the publisher as a stack of papers, but on a disk. The clue to this mystery is given in the next column. Real turnover is defined as sales of books in current prices divided by the book price index. It gives a rough indication of the number of books sold. Real turnover has shown a declining tendency from the beginning of the 80 s. With real turnover declining and the number of titles increasing, one would expect the average number of copies sold per title to have fallen, which is exactly what we observe. We do have some estimates, not from official statistics but from informed guesses in the publishing industry. They indicate that the average number of copies sold per title in the middle of the 70 s declined from about 6,500 to about 2,300 in the beginning of the 90 s, a remarkable development. Hence, a reasonable interpretation of the data would indicate that while the decrease in fixed costs has tended to lower the

38 CHR. HJORTH-ANDERSEN prices, it has also via the title equation introduced so many new books that X/T has declined rapidly, leading to an increase in the book price. 4.1. THE DEMAND FOR BOOKS As noted above, it is possible to estimate Equation (1). In a logarithmic version chosen for its simplicity, we have ln X = α + β ln P + γ ln Y + δ ln T = εt, t = 1973...93. (9) Price is measured as the real book price in Table I. Income can be measured in different ways, but here real disposable income is preferred. The time series for titles is presented in Table I. The inclusion of a trend is meant to describe the longrun competition from other media, but there is of course no guarantee that this factor can indeed be captured by a trend. It would certainly have been preferable to have a specific indicator of the competition from other media rather than subsuming everything into a trend. The result of this estimation, called the basic specification, is presented in (10) with standard errors in parenthesis. It is estimated with ordinary least squares, ignoring the fact that P is not a truly exogenous variable due to the price equation. ln X = 2.21 1.44 lnp + 1.97 lny + 0.003 lnt 0.0263t (0.346) (0.178) (0.265) (0.102) (0.00588) (10) N = 21, R 2 = 0.9817, s= 0.0305, DW= 1.70. The result of this estimation would seem to be quite encouraging. All coefficients have the correct sign; the coefficients to the price variable, the income variable, and the trend are all strongly significant. The model explains the data quite well and there seems to be little or no problem with autocorrelation. However, in order to test the relation, a number of experiments have to be carried out. 4.1.1. Experiment a The first experiment consisted of estimating (13) without one or several explanatory variables. It gave consistently poorer results as measured by R 2 and DW. 4.1.2. Experiment b The second experiment was to estimate (13) in differences, denoted with D: D ln X = 0.0207 1.34 D ln P + 1.31 D ln Y + 0.010 D ln T (0.010) (0.231) (0.453) (0.101) (11) N = 20, R 2 = 0.679, s= 0.0372, DW= 1.94.

A MODEL OF THE DANISH BOOK MARKET 39 A possible autocorrelation in the basic specification has completely disappeared by estimating the relation in differences. The coefficients remain significant and have the same magnitude, although the income elasticity declines somewhat. 4.1.3. Experiment c Implicit in the basic specification is an assumption of immediate adjustment (within the year). As the expenditure on a book is rather modest, it seems quite plausible that it should be current income that determines the consumption of books. Empirically, it can be shown that poorer results will be obtained using lagged values of the income variable. However, it would not be surprising if there was a lag in the price variable. The reason is that the book price index gives information on the price of a new book. However, a book will keep its price for several years, and as some books, especially textbooks, are sold for several years after their first appearance on the market, it could be argued that not only the current but also lagged values of P should be included. Empirically, this does not seem to be the case as poorer results were obtained using lagged values of P, presumably because the major part of the turnover in the book market comes from new titles. 4.2. INTERPRETATION With these experiments in mind, we shall base our conclusions on the basic specification. I do not wish to exaggerate these results. With the available data, they describe the specific circumstances of the book market in Denmark for a given historical period. There is no presumption that these elasticities could be assumed to be universally valid or even cover other periods in Denmark. 12 With these reservations, it is worth noting that the fit between the actual observations and the basic specification is in fact quite close. There are three basic forces that determine demand and thereby the book market: Price; income; and the time trend as a proxy for competition from other media. The coefficient of titles is positive, but not statistically significant. The introduction of new titles does not expand demand very much, if at all. So, in effect when a publisher introduces a new title it will be at the expense of other publishers, a fact not appreciated by publishers. The price elasticity is not only, as required, significantly negative, but it is also significantly less than minus one. The demand for books seems to be price-elastic. Rising book prices will therefore lessen the total turnover of the book market. The income elasticity is estimated to be 1.97, which is significantly higher than not only zero but also one. It may be that the estimate is too high, as the estimate in Equation (11) may indicate. But, it is quite possible that books at the aggregate level are, in fact, luxury goods. Considering the plausibility of the income elasticity, the public library system has to be taken into account. Books in Denmark are, apart from certain school books et cetera, a convenience good. If you do not think you can afford a book, you can always go to the library. One explanation for the slow

40 CHR. HJORTH-ANDERSEN performance of the book market in this period is the slow rise in real incomes in Denmark during the 80 s. The income elasticity should be interpreted with caution. It gives an estimate of γ, the immediate effect on the total number of book sales, but, if income rises, it will have an indirect effect as well, as described in the previous section. Due to the title equation, an increased income will mean more titles, decreased average number of copies sold, and thus higher prices. 13 The time trend indicates that book sales diminished by 2.6 per cent per year. It may be, but is by no means certain, that the competition from the electronic media was particularly felt in this historical period and that the impact will not continue to diminish the book market. If some readers think this is a rather superficial description of the process, I entirely agree; much more research into the interactions of the various cultural goods is needed. Publishers sometimes proudly point out that, despite all the electronic media, the book still exists. The fact remains, however, that without the electronic media, the book market in Denmark would have been about twice as large as it is now. 5. A Concluding Remark The book market in Denmark, and presumably other countries, has undergone a dramatic change. The impact from the electronic media has diminished the market, but I shall not dwell upon this as it has been widely commented upon by others. At the same time, another change but less publicly known has occurred. Technology has been introduced into the printing and publishing industries and the results have been remarkable. The costs of introducing a new book have decreased substantially and the publishing industry has responded by publishing an avalanche of new books. Consumers have been offered a greater supply of titles, but this development comes at a price as it has had the unintended effect of increasing book prices. This is, in fact, the standard welfare implication of monopolistic competition, higher variety, and higher prices. For the individual consumer, this may be a mixed blessing. A greater choice of titles may give the consumer exactly the kind of book he or she is interested in, but it will also increase the difficulties of surveying the market. Thus, while the book you are interested in is actually available, in practice you may not know of its existence. In my view, the force of technology will eventually change the very concept of being an author. It has become much easier for an author to have his or her work published, but much more difficult to have someone reading the work! Sometimes, Danish publishers are willing to print only 200 300 copies of a new title. If the publishers are not willing to introduce a new title with expectations of very small sales, quite often authors themselves pay to have their work published. The interesting thing is that it is publication that counts for the renown of an author. It is important for an author, be it of a poetry collection or a work of science, to have the work published. Whether it is actually read by anyone is not that important. In

A MODEL OF THE DANISH BOOK MARKET 41 fact, we have probably not seen the end of this development. As of now, quite a few scientists publish their work on the Internet. This work may or may not be read by anyone, but it has been published. There have also been initial newspaper reports about poets doing the same thing. If a poet cannot sell his poems to a publisher, he or she can at least publish them on the Internet. The very concept of being an author may thus have to change. So far, being an author has been connected with supply. An author is someone who has published a book with an ISBN number, which is sold to the general public. But if (almost) everyone can publish something, be it on the Internet or through a publishing company, we may have to think about an author as someone who has not only published by some means, but who is also being read by someone. Demand will enter into the concept. Possibly, one could use a distinction between formal and real authors. Formal authors would be authors who publish, but are not read by more than a handful of people; real authors publish and are read by more than just a few people. Notes This paper is based on research originally supported by the Danish Social Research Council which resulted in a book (in Danish) on the Danish book market. I am much indebted to comments from my friend Kurt Pedersen as well as the able assistance from Nicolai Tillisch. A number of seminar participants at the Tenth Biennial Conference of the Association for Cultural Economics International, Barcelona, 14 17 June 1998, Danish econometricians meeting at Sandbjerg, the editor Ruth Towse, and two anonymous referees have also given valuable comments. 1. There are a number of interesting aspects in the relation between the publisher and the author. Book publishing is a risky business, so not only profits but also risk must be allocated between the two parties. In economic terms, the contractual arrangements may differ from one extreme where an author pays the publisher to publish the work, a phenomenon that actually happens quite frequently, to the other polar case where a famous author arranges a (common value) auction thus receiving (most of) the profit and avoiding the risk. The idea of differential contracts is not new. Krieg (1953) tells the amusing story about Wolfgang v. Goethe who was offered 60 70,000 Thaler from his usual publisher when considering to publish his collected works, a formidable sum in Germany in 1825. However, being not only a man of letters, but also a statesman distrustful of publishers ( Die Buchhändler sind alle des Teufels für sie muss es eine eigene Hölle geben ), he contacted other publishers searching for better offers. Eventually, Goethe settled on a contract with his usual publisher giving him 60,000 Thaler and 60,000 Thaler more, should more than 40,000 copies be sold. 2. The propensity to translate and publish foreign manuscripts has been discussed in detail in a companion paper, see Hjorth-Andersen (1996). 3. There is very extensive marketing literature on the introduction of new products. Most of these techniques are, however, either irrelevant to the book market or simply unprofitable. With a few obvious exceptions, it is simply too costly to conduct a consumer survey for each new title considered for publication. Many other commodities are, prior to their introduction, submitted to extensive experimentation in order to reduce the risk of introduction. This is not possible in the publishing business and may be one of the reasons why publishing is considered a risky business. 4. The publisher will, of course, take the effect of introducing a new title on his own books into account. It is well known, see e.g. Tirole (1988), that a monopolist selling many mutually sub-

42 CHR. HJORTH-ANDERSEN stitutable products will charge a higher price for each individual product in order to compensate for lost sales for the other products. Presumably, the publisher will deal with such problems by not publishing manuscripts supposed to be in direct competition with his previous books, and so the concentration among publishers as described with respect to the American book market by Szenberg and Lee (1994) will matter in the long run for the outcome. 5. The effect of book clubs also deserves serious attention. Presumably, book clubs enjoy advantages as prices can be reduced due to large sales, and risk is reduced. Consumers benefit from lower prices and maybe also from having experts suggesting the best of the new literature, thus lowering the search costs in a very large and complicated market. Nevertheless, these benefits to the consumers come at a price as they must accept the lower range of choice. To my knowledge, these phenomena have not been investigated. 6. I am ignoring structural changes. This could be expansion of the library system or an increase in the availability of books in the retail channel distribution. During the period under consideration, these factors have not changed markedly. It should be noted that this paper is concerned with a macro model of the book market. A number of interesting phenomena, and very much to the interest of the publishers, are simply not important for a description of the entire book market. It is, for example, of crucial importance to a large publishing firm to get some of the real bestsellers, but even the best-selling book of the year presents only a small fraction of the book market and is not important for the development of the market. 7. Actually, there have been commercial book clubs in Denmark where you paid a membership fee, while the marginal costs of borrowing a new book were zero. These clubs have disappeared, however, due to the competition from libraries and administrative costs bringing the book to and from the consumer. 8. Estimating the demand for tickets to the Royal Theatre in Copenhagen, Trine Bille Hansen obtained significant coefficients, statistically and materially, introducing as a variable the number of new productions in each season, see Bille Hansen (1996). 9. This was before the world saw book discounting by Internet companies. 10. The other statistics on the book market are probably not of the same quality. The book market is quite unimportant from a macroeconomic point of view. The book market is a private market. There is not much public interest in producing good statistics and, accordingly, it has a low priority in the statistical bureau. This is contrary to the public library sector where the statistics are very good. The figures and the conclusions should be interpreted with that in mind. 11. See Selwood (1994). I thank Ruth Towse for this reference. 12. In fact, with the preliminary figures available, it would seem that the model tends to underestimate the book sales in 1994, but this may be due to the data as much as to the model. 13. If one assumes that the development in f could be described by a trend, the reduced Equations (7) and (8) would give ln X and lnp as linear functions of Y. However, these relations give a quite poor fit. References Bille Hansen, Trine (1996) Danskernes værdisætning af Det Kgl. Teater. Ph.D. Dissertation, Copenhagen. Hjorth-Andersen, Chr. (1996) A Model of the Transmission of Culture. Paper presented to the Ninth Biennial Conference of the Association for Cultural Economics International, Boston, MA. Hjorth-Andersen, Chr. (1996) Bogmarkedet i Danmark. Jurist- og økonomforbundets Forlag, Copenhagen. Krieg, Walter (1953) Materialien zu einer Entwicklungsgeschichte der Bücherpreis und des Autoren- Honorars vom 15.bis zum 19. Jahrhundert. Herbert Stubenrauch Verlag, Wien/Zurich.

A MODEL OF THE DANISH BOOK MARKET 43 Selwood, Sara (ed.) (1994) Cultural Trends: 24, Policy Studies Institute, London. Szenberg, Michael and Youngkoo Lee, Eric (1994) The Structure of the American Book Publishing Industry. Journal of Cultural Economics 18: 313 322. Tirole, Jean (1988) The Theory of Industrial Organization. MIT Press, Boston, MA.