Cultural Capital and the Consumption of Cultural Services

Pethig, Rüdiger; Cheng, Sao-Wen Article Cultural Capital and the Consumption of Cultural Services Schmollers Jahrbuch – Zeitschrift für Wirtschafts- und Sozialwissenschaften. Journal of Applied Social Science Studies Provided in Cooperation with: Duncker & Humblot, Berlin Suggested Citation: Pethig, Rüdiger; Cheng, Sao-Wen (2002) : Cultural Capital and the Consumption of Cultural Services, Schmollers Jahrbuch – Zeitschrift für Wirtschafts- und Sozialwissenschaften. Journal of Applied Social Science Studies, ISSN 1865-5742, Duncker & Humblot, Berlin, Vol. 122, Iss. 3, pp. 445-468, https://doi.org/10.3790/schm.122.3.445 This Version is available at: https://hdl.handle.net/10419/292023 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Schmollers Jahrbuch 122 (2002), 445-468 Duncker & Humblot, Berlin Cultural Capital and the Consumption of Cultural Services* By Rudiger Pethig and Sao-Wen Cheng Abstract Cultural capital is assumed to benefit all members of society. It is built up by the aggregate consumption of cultural services and is diminished through depreciation. Cultural goods (e.g. cultural heritage, works of arts, literature and music) turn out to give rise to a flow of cultural services. In the no-policy market economy, consumers tend to ignore the beneficial external effects of their cultural service consumption on the other consumers (and on themselves) through augmenting cultural capital. Cultural Services will be less consumed and, as a result, cultural capital will be underprovided. The efficient allocation is shown to be restored by an appropriate subsidy on cultural services that stimulates the consumers demand for cultural services and thus promotes the accumulation of cultural capital. Zusammenfassung In diesem Papier wird angenommen, dass Kulturkapital allen Mitgliedern einer Gesellschaft nützt. Es wird durch Konsum von Kulturdienstleistungen akkumuliert and verringert sich durch Abschreibung. Der Bestand an Kulturgütern (z. B. Kulturerbe, Kunstwerke, Literatur und Musik) wird durch Bereitstellung von Kulturdienstleistungen genutzt. In einer Laissez-F&ire-Marktwirtschaft neigen die Konsumenten dazu, den durch Erhöhung des Kulturkapitals entstehenden positive externen Effekt ihres Konsums an Kulturdienstleistungen auf andere Mitbürger (und auf sich selbst) zu ignorieren. Der Konsum von Kulturdienstleistungen ist deshalb zu gering mit der Folge Unterversorgung an Kulturkapital. Es wird gezeigt, dass Allokationseffizienz durch eine geeignete Subventionierung von Kulturdienstleistungen wieder hergestellt werden kann, welche die Nachfrage nach Kulturdienstleistungen stimuliert und somit das Kulturkapital erhöht. JEL Classification: H 2, H 3, Z 1 * Helpful comments by Thomas Eichner, Marco Runkel, Andreas Wagener and by three anonymous referees are gratefully acknowledged. Remaining errors are the authors' sole responsibility. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 446 Rüdiger Pethig and Sao-Wen Cheng 1. Introduction Consumption of culture has a major social component. We share the widespread presumption or conviction that the consumption of culture yields positive effects for society: creativity will be further developed, tolerance for others (race and gender) will be enhanced, criminality will be reduced, people's sense of identity will be strengthened.1 Though economists have extensively discussed the concept of positive externality, they either claim an undersupply of culture without further specifying what the concrete link between culture and externality may be like, or they enumerate various externalities and invoke them to justify public support for culture. Those arguments are not stringent, and none is demonstrated analytically, to our knowledge. For example Robbins (1963, p. 58) argues that "... the positive effects of the fostering of art and learning and the preservation of culture are not restricted to those immediately prepared to pay cash but diffuse themselves to the benefit of much wider sections of the community in much the same way as the benefits of the apparatus of public hygiene or of a well-planned urban landscape". In their pioneering contribution to cultural economics Baumol and Bowen (1966, p. 382n.) pay much attention to four types of general benefit (national prestige, advantages cultural activity confer on business in its vicinity, benefit for future generations, contribution to education) which flow from the arts. They also point out that "... performing arts confer direct benefits on those who attend a performance but which also offer benefits to the community as a whole ...". Peacock (1969, p. 328n.) invokes also intertemporal spillovers of culture and argues that even "... those who do not understand and appreciate music and drama may be glad to contribute towards making available their fruits to those who do, and to those whose tastes are not yet formed. Present generations may derive positive satisfaction from preserving live performance safe in the knowledge that they do not risk being accused of narrowing the range of choice of cultural activities for future generations through allowing Arts to die". Netzer (1978, p. 22n) extends the list of external benefits by adding that the interdependence of art forms tends to support one another, and that inovation is fostered through artistic undertakings and business advantage through culture and arts. Fullerton (1992, p. 80) offers a new twist on the externality argument and justifies public support of the arts as follows: If there are enough persons (external beneficiaries) who want others to attend art events and hence "... are willing to pay to see subsidized arts, and if similar individuals can 'free ride' by enjoying others' donation, then none of them has sufficient in- i See e.g. "The First World Culture Report (1998) of UNESCO, Part one". Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 447 centive to give to the arts. It is possible for government, potentially, to make everybody better off by taxing those individuals who do value others' attendance, and then using the funds to subsidize the arts." While all these positive externality arguments have some appeal in the cultural context, they are not made precise in formal intertemporal analysis and they do not explicitly account for the distinctive characteristics of culture. The present paper aims at capturing the specificities of culture in a dynamic stock-flow model by distinguishing - and focusing on the relations - between cultural goods, cultural services and cultural capital. It then models the social component of the consumption of culture via a process of accumulation (and depreciation) of cultural capital which in turn affects the individuals' well-being. The notions of culture and related terms are applied in the literature in various often incompatible ways. We refrain from presenting a comprehensive survey and comparison of major concepts. Instead, we define how we will use the terms culture, cultural goods, services and capital in the present paper and content ourselves with a few remarks about other connotations and terms suggested in the literature. For the purpose of the present paper, it suffices to think of culture "... as being represented by the 'cultural sector' of the economy" (Throsby 1995, p. 202). Cultural goods2 are considered to be all items of cultural significance like heritage buildings, sites, locations, works of arts (e.g. paintings, sculptures), literature and music.3 There is a stock of cultural goods inherited from the past, and there is an ongoing process of creating new cultural goods which are then added to the stock. Although the production of new cultural goods is of great importance (Throsby (1999), Ulibarri (2000)), we restrict our subsequent analysis to the inherited, constant stock of cultural goods to avoid overloading our model with a complex analysis of the supply side. Following Throsby (1999, p. 7) we assume the cultural heritage to "... give rise to a flow of services that may be consumed as private and/or public goods entering final consumption immediately, and / or they may contribute to the production of future goods and services, including new cultural goods". Suppressing the role of these services as productive factors (see 2 The notion of cultural goods as introduced here is closely related to what is termed 'cultural capital' by Throsby (1999), except that we do not link cultural goods with Thorsby's 'cultural value'. The latter is considered by Throsby (1999, p. 6) as "... different from, though not unrelated to economic value", but Throsby does not specify how this value emerges. 3 Cultural goods are durable. They may be further differentiated according to whether they are tangible or intangible or whether they are private or public goods. These distinctions are not relevant in the context of our model and are hence omitted. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 448 Rüdiger Pethig and Sao-Wen Cheng above) we focus on consumptive cultural services, called cultural services, for short. These cultural services take many widely differing forms. Examples of (first-order) cultural services are (guided) tours to cultural sites, visits to museums, attendance of concerts or of opera and drama performances, reading books. Other cultural services (of second or higher order) are e.g. reading books about medieval paintings, about the Chinese terracotta army, or about the cultural treasures of Paris; watching broadcasted reports about these cultural goods, watching broadcasted opera performances or concerts; listening to broadcasted or recorded music; enjoying sculptures, replica paintings, or replica heritage buildings; watching a photo of the London parliament building in the show window of a travel agency, enjoying (own) photos or videos taken during tours to cultural sites. This rather selective list of cultural services strongly suggests that the meaning and importance of cultural heritage for society is closely linked to the amounts and kinds of cultural services flowing from the stock of cultural goods.4 The magnitude and the structure of those flows depends, in turn, to a large extent on costs to provide them and on income and relative prices to consume them. Public cultural policies, intervention and regulation may have a great impact on these economic determinants. Consequently, there is no automatism in the cultural heritage 'giving rise to a flow of cultural services'. Leaving the supply, demand and the pricing of cultural services to markets (laissez-faire) would be highly recommendable, if the consumption of cultural services were comparable to services like e.g. hair-cutting which do not appear to have a major social component. Our principal hypothesis is that the continuous consumption of cultural services over time leads to an accumulation of cultural capital which, in turn, is positively valued by all members of society Like Becker (1998, p. 12n.) we conceive of cultural capital as an intangible and depreciable asset that is a form of social capital in the sense of Coleman (1990) who argues (ibidem, p. 317) that "... social capital [and hence cultural capital, as presently defined; the authors] is an important resource for individuals and can greatly affect their ability to act and their perceived quality of life." He also maintains that "although it is a resource that has value in use, it cannot be easily exchanged. As an attribute of the social structure in which a person is embedded, social capital is not the private property of any of the persons who benefit from it" (ibidem, p. 315). According to Becker (1998) cultural changes over time may be 4 This is most clearly seen by considering the fictitious polar case in which not any cultural service flows from the cultural heritage. This would be a situation as if there exists no cultural heritage at all. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 449 slower than changes of other kinds of social capital but he rightly rejects the view "... that culture so dominates behavior that little room is left for choice" (ibidem, p. 16n.). Introducing cultural capital as outlined above in a dynamic setup implies that the more cultural services are consumed the more cultural capital is generated (after depreciation is accounted for) and the greater will be the external benefits provided for society. Though consumers may realize their own benefit from an increase in the stock of cultural capital brought about by their own consumption of cultural services, they tend to ignore the beneficial impact which their own contribution to the generation of cultural capital has on their fellow citizens. When the number of consumers is very large, they may even neglect that their own utility is enhanced through an increase in cultural capital induced by their own (negligibly small) consumption of cultural services. This myopic individual behavior gives rise to external cultural benefits. Related to the concept of cultural capital as perceived in the present paper is the theory of human capital inspired by Becker (1964) and elaborated over the last decades in the context of endogenous growth theory surveyed, e.g., by Aghion and Howitt (1998, chapter 10). Human capital is accumulated by and 'within' the individual consumer/worker either through education or through learning by doing. On an aggregate level, the stock of human capital enhances productivity and is therefore considered the driving force for economic growth. In the model to be analysed here, no individual consumer is supposed to build up her own 'stock of cultural capital' in analogy to human capital. Consumers rather contribute to the accumulation of cultural capital (which is not the private property of any of the persons who benefit from it, as observed above) and thus enjoy not only a secondary benefit from their own investment in cultural capital but also a purely external benefit from the other consumers' investment in cultural capital. The individual's investment in cultural capital is not at all or not primarily her intention when consuming cultural services. In contrast, when consuming education the individual's main objective is the accumulation of human capital to improve her own market value. Human capital formation through learningby-doing is closer, in spirit, to the process of cultural capital accumulation, but both are definitively different concepts. Society benefits from the stocks of human capital built up by all individuals through the enhancement of productivity. In this sense the presence of external benefits is common to both approaches. Consider now - as we will do below - all those (first order) cultural services that are price excludable and suppose that price exclusion is applied. Owing to the consumers' failure to internalize the external benefits of their Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 450 Rüdiger Pethig and Sao-Wen Cheng consumption of cultural services, cultural capital will be underprovided in the laissez-faire economy, even if the cultural services under consideration are private rather than public goods.5 As an immediate consequence this paper provides a justification for subsidies on cultural services that serve to internalize the external benefits of cultural service consumption. Although the basic argument has a strong common sense intuition, it has not yet been developed and demonstrated to our knowledge, in a dynamic theoretical framework modeling the distinctive characteristics of culture. Positive externalities of the consumption of cultural services are introduced in a dynamic setting and different regimes are studied and compared. As a benchmark, the efficient allocation is characterized (as e.g. implemented by a omniscient benevolent social planner). Then the focus is on the inefficiency of unfettered competitive markets providing a rationale for subsidies on cultural services. Section 2 develops the model of consumption of cultural services. Section 3 sets out the first-order conditions for welfare maximization under full consideration of its dynamics and characterizes the efficient intertemporal allocation. Section 4 presents the underprovision of cultural capital in the laissez-faire economy with two alternative assumptions about consumer behavior. Section 5 compares the results from sections 3 and 4. Section 6 discusses the options for restoring efficiency by appropriately designed tax/subsidy schemes. Section 7 concludes. 2. The Model Consider a simple economy in which two consumption goods X and Yare produced. Denote by Xf and Yts respectively, the quantities produced (and supplied) of these goods by means of the linear technologies (1) R? = CDDst , for D = X, Y and for t > 0 , where Rf is the input of a generic resource and where Cx,Cy are positive time-invariant input-output coefficients. Y is a standard (composite) good and X is a cultural service based on a given (inherited) stock of cultural goods. For example, Xs is the supply of visits to a museum or the supply of attendances of art performances, dramas, operas etc. The given stock of cultural goods is clearly the origin of these services 5 If the cultural service is a public consumption good, e.g. a television broadcast of an opera performance, another allocative distortion is added to that involved in cultural capital formation. In the present paper cultural services are treated as private goods to isolate the allocative displacement caused by cultural capital in the laissezfaire economy. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 451 (Shakespeare's Summer night Dream, Beethoven's 9th Symphony) but the total amount of cultural services supplied and demanded is not determined by that stock of capital goods, as e.g. in Ulibarri (2000). For all there is a constant number nt = n of identical consumers. Denoting by Xt and Yt the representative individual's consumption of the cultural service and of good Y, respectively, her utility is, at each point in time, (2) ut = U(Xt,Yt,Zt) , where UD > 0, UDD < 0 for D = X, Y, Z and Uxy = UYx > 0 . (The variable Z will be specified further below). To simplify the exposition and the analysis, we assume that the utility function (2) is additively separable and well-be- haved6 (20 U(XU YuZt) = Ul{Xu Yt) + U2(Zt) . The 'consumption good' Z from (2) is a non-excludable public good called cultural capital, which we motivated and discussed in the introduction.7 By hypothesis, cultural capital is created through all individuals' consumption of cultural services and it declines through depreciation. Following Becker (1998, especially footnote 2 on p. 12) we formalize this concept by assuming that the change in time of cultural capital is J ^ (3) Zt = nXt-aZt, where Zt: = -^,a6]0,1[, Zt > 0 for i>0. In (3) the aggregate consumption of cultural services represents the gross investment in cultural capital; a is the depreciation rate. The model is completed by specifying the supply conditions. nR is assumed to be the economy's aggregate resource endowment available at each 6 U is well-behaved in the sense that lim Up = oo for D = X, Y, Z. As an implica- D—>0 tion, consumption bundles (Xt, YtlZt) with Dt = 0 for D = X, Y, Z, t > 0, will be ruled out along the optimal path to be derived below. The additivity of C/7( ) and U2(-) is unnecessarily restrictive for some results. However, without the separability assumption it would be impossible to characterize the dynamics by means of phase diagrams in the subsequent sections. 7 The hypothesis in (2) is that "culture" enhances each consumer's utility not only by her consumption of cultural services, X, but also by the "prevailing" cultural capital, Z, irrespective of who contributed how much to its accumulation. This specification clearly distinguishes our model from the human capital cum endogenous growth approach where each individual only benefits from the human capital she accumulated herself. In addition, human capital is typically modeled as productivity improving while in the model of the present paper, cultural capital does not affect production technologies. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 452 Rüdiger Pethig and Sao-Wen Cheng point in time. Since Y is a private consumption good, the associated supply constraint is Yf > nYt. One can find relevant types of cultural services that are either private or public goods. More importantly, most public cultural services are excludable, and in the real world, price exclusion is often applied.8 Here we will restrict our attention to good X being a private cultural service, i.e. we assume Xs t > nXt. Considering the supply constraints Xs t > nXt and >nYt as equalities and invoking (1) yields the linear production possibility constraint (4) nR = CxnXt + CYnYt (for all t > 0) . The allocative problem to be solved is how consumption Xt and Yt develop (or should develop) over time and how the consumption of cultural services, Xu impacts on cultural capital, Zt. 3. Allocative Efficiency The social planner maximizes the present value of the consumers' aggregate utilities over an infinite time horizon and with a constant rate of time preference, 6: oo (5) max [ nU(Xt, Yu Zt)e~6tdt , 0 subject to (3) and (4). In this optimal control problem (3) - (5), Xt and Yt are the control variables and Zt is a state variable. This problem is solved by applying the current-value Hamiltonian (6) H = nU{Xt,Yt,Zt) + V(nXt - aZt) + W(nR - nCxXt - nCvYt) . The costate variable V is the shadow price of cultural capital measuring the value the social planner attaches to an increment of cultural capital. In other words, V measures the additional utility in the future which today's consumption Xt creates by raising the cultural capital. Hence it measures the value of the positive externality for future periods of today's consumption Xt. Wis the Lagrange multiplier attached to equation (4). The FOCs for a solution to (5) are: 8 Fullerton (1992, p. 73) observes correctly that "... art can be bought and sold, and admission to art events can be charged. The primary benefits of art and its viewing are excludable." Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 459 According to equation (16) each consumer's MRS between the cultural service and good Y equals the price ratio at each point in time along the equilibrium path. Denote by (XM, YM) the unique solution to (16) subject to R = PXXT - PYYT. Then we obviously have10 (Xt, YT) = (XM, YM) for all t. Since iit = 0 for all t by assumption (implying fit = 0 for all t) the steady state is now fully characterized by Z = 0. In terms of Figure 3 the entire Z = 0 locus collapses into the point ZM. Since each consumer chooses Xt = Xm for all t, Zm ' = hXm/a is clearly the steady state value of cultural capital. Hence the phase diagram of Figure 3 degenerates to changes in the stock of cultural capital along the abscissa (Z-axis). If the initial endowment of cultural capital happens to be Z0 > ZM, cultural capital Z will gradually shrink until ZM is eventually reached. Conversely, if Z0 < ZM cultural capital accumulates until the steady state ZM is attained. 5. Inefficiency of the Laissez-faire Market Economy We now compare the cultural capital formation for the regimes: E: Centralized economy with an omniscient benevolent social planner CN: Market economy with Cournot-Nash consumers M: Market economy with ignorant consumers Table I Steady states of different regimes Steady state values Characterization of steady state E Vjp, ZE, XE V = 0,Z = 0,X = 0;VE, ZE and XE satisfy VE = nK(ZE),V = G(ZE,n) and XE = aZE/n CN I^CN, ZcN, XcN FI = 0, Z = 0,X = 0; HCN,ZCN and XQN satisfy FJBCN = K(ZCNI M — G(ZCN,K) and XCN = aZcN/N M FIM = 0, ZM, XM ¡i = 0, Z = 0,X = 0; ZM and XM satisfy G(ZM, ri) = 0 and XM = OLZM!N The characteristics of the pertinent steady states are summarized in Table I in which the functions G and K are used as defined in the Appendix A. To see how the steady state values of the three regimes are related to each other, 10 The additive separability assumption on function U from (2') is unnecessarily strong for this result to hold. Weak separability of U between X and Yon the one hand and Z on the other hand would do the job. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 460 Rüdiger Pethig and Sao-Wen Cheng observe that the steady state capital stock associated to the regime j = E, CN, My respectively, is determined by the equation (17) mjK(Z) = G(Z,n) , if and only if THE = n > 2, MCN = 1 and THM = 0. Since K(Z) > 0 for all Z > 0, Kz < 0 and Gz > 0, it is straightforward that ZM < ZCN < ZE> Using the steady state condition X = nZ /a these inequalities yield immediately XM < XCN < XE, and (4) gives us YM > YCN > YE. We conclude, therefore, that in the steady state of the laissez-faire market economy both cultural services and cultural capital are underprovided and that the underprovision is greater in case of ignorant than in case of Cournot-Nash consumers. Table II The impact of the numbers of consumers on the steady state value of cultural capital E CN M dZ dn Gn-K(Z) Gn Gn Gz dZ dn Gz - nKz Gz — Kz Gn Gz To determine the impact of exogenous changes in the number of consumers, n, on the respective steady states we totally differentiate the steady state condition (17) and obtain the results listed in Table II. We find that the steady state value of cultural capital increases in all regimes as the number of consumers gets larger. Unfortunately, comparisons across regimes are not feasible, in general, since the partial derivatives in the terms listed in Table II are taken at different values of Z(ZM < ZCN < ZE). Suppose, however, the functions G and K happen to have constant partial derivatives (approximately, at least). The Table II implies (DN)E > (DN)CN> GOM In that case, the underprovision of cultural capital in the market economy would be the more pronounced the larger is the society under consideration, and the market economy with ignorant consumers fares worse than the economy with Cournot-Nash consumers. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 461 6. Pigouvian Subsidies on the Consumption of Cultural Services We showed in the previous section that in the absence of cultural policy the market economy provides cultural services and cultural capital at inefficiently low levels. It is therefore natural to think about subsidizing cultural services as a means to stimulate demand. In formal terms a subsidy turns the consumer's budget constraint (13) into (19) R > T + (PX - Sx)Xt + PY Yt . Where Sx is the subsidy rate and T is a lump-sum tax taken as given by the consumers and set by the government such as to finance the total subsidy on cultural services. In section 5 the extent of market failure was shown to depend on consumers behavior. Hence the rate of the corrective subsidy must take the consumers' actual behavior into account. It is therefore necessary to investigate the appropriate subsidies for each type of market economies starting with Cournot-Nash behavior of consumers. 6.1 Cournot-Nash consumers Taking (19) into account, the Hamiltonian (14) is modified to read (20) H = U(XuYuZt) + fx(Xt +X- aZt) + \[R - T - (Px - Sx)Xt - Py Yt] . The FOCs can be written as: (21) Ux = Px~Sx M [ J UY Py Uy ' Denote by S™ that particular subsidy rate that internalizes the cultural externality It is implicitly defined by setting equal (10) and (21): (22) Ux = Px-S$N _ Px V 1 } UY Py Uy PY Uy ' Solving (22) for S%N yields: (23) In view of (23) is essentially the difference between the social value of cultural capital, V, and its private value, fi, where Py/Uy is used to turn the Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 462 Rüdiger Pethig and Sao-Wen Cheng dimension 'utility' into the dimension 'money'. As shown in the Appendix (cf. (A2) and (B9)), equation (23) can be transformed into (24) PYUZ (n-1) Uy a+ö According to (24) the subsidy rate Sdepends on the number of consumers, n, the depreciation rate of cultural capital, a, the time preference, 6, and on the marginal willingness-to-pay for cultural capital, (Uz/UY). The greater is n, the higher is the efficient subsidy rate, ceteris paribus. The faster the cultural capital depreciates, the lower is the efficient subsidy rate. The higher the agents' preference for present consumption, the lower is the efficient subsidy rate. (24) has another interesting interpretation: Suppose through her consumption of the cultural service, consumer h increases the cultural capital at the margin. Since h is a Cournot-Nash consumer, she takes the beneficial effect of this change on her own well-being into account and evaluates that effect at ¡j, = Uz/(a +6). Owing to symmetry the same beneficial effect accrues to all other consumers. But since no market transaction is involved, h does not receive any remuneration for her contribution to the other consumers' well-being and therefore ignores these (external) benefits in her own utility maximization calculus. The subsidy rate S%N from (24) is designed to pay consumer h exactly the value of her (previously external) benefits to the (n-1) other consumers. Thus the cultural externality is internalized. 6.2 Ignorant consumers Using (19), the Hamiltonian from equation (15) is now: (25) H = U(Xt,Yt,Zt) + A [R-T- (Px - Sx)Xt - PYYt} The FOCs are: Ux Px - Sx (26) UY Py Denote by the efficient subsidy rate which is characterized, in view of (10), (24), and (26), as (<)rj\ o-m_PyV_PyUz n _ CN PYUZ Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 463 Comparing (27), and (24), turn out to be quite similar. Since the terms and ^ are the same in both cases, it follows that S% > S It is straightforward to interpret this observation: The ignorant consumer disregards the beneficial effect of an increase in cultural capital, induced by herself, on all other consumers. In this respect she behaves like the Cournot-Nash consumer, and to internalize that externality she needs to be subsidized by the rate S™. But in contrast to the Cournot-Nash consumer the ignorant consumer also ignores in her consumption plan the benefits she offers to herself through an increase in cultural capital induced by her own cultural service consumption. The value of this benefit is ¡J, = UZ/(A + <$), in terms of utility, or, PYUZ/[UY{OL + <5)], in terms of money This amount of money must be added to the subsidy rate S™ to achieve a complete internalization of the cultural externality in a market economy with ignorant consumers. A final remark is in order regarding the comparison of S^ and Swhen the number of consumers becomes very large. With increasing n, the difference Sx - S%N remains positive but tends to zero. The greater is n the smaller is the impact of each individual Cournot-Nash consumer on the formation of cultural capital and the less significant becomes the difference between Cournot-Nash behavior and ignorant behavior. In that sense ignorant behavior may be considered a fairly good approximation for Cournot-Nash behavior in sufficiently large societies. 7. Concluding Remarks The justifications for government support of cultural services discussed in the cultural economics literature are mostly confined to static analysis. The present paper demonstrated that the consideration of dynamic aspects of positive externalities associated to the consumption of cultural services makes a strong, and in our view, more convincing case for government subsidization. The preceding analysis builds on a simple game theoretic model and finds that, in the absence of government intervention, both cultural services and cultural capital are underprovided and that this allocative inefficiency can be eliminated by an appropriate subsidy on the consumption of cultural services. Essentially, this conclusion is driven by the basic hypothesis that the consumption of cultural services is not only beneficial for the individual consumer but contributes to form a "better" or a "more civilized" society which is enjoyed by all its members irrespective of (and in addition to) their own cultural service consumption. Therefore, the empirical relevance of that ap- Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 464 Rüdiger Pethig and Sao-Wen Cheng proach depends heavily on our concept of cultural capital and its measurability. Similar as with the related notion "social capital" or even "human capital", empirical measurement turns out to be difficult which, unfortunately, leaves us without clear-cut evidence for the hypothesis that citizens appreciate the accumulation of cultural capital. While this ambiguity is clearly unsatisfactory, it is not convincing to argue, on the other hand, that a concept is rendered elusive and (hence) useless whenever it is difficult to measure. Consider, as a case in point, the notion of merit goods that was introduced some fifty years ago and is heavily disputed since then. The present model may be interpreted as a rationalization of the issues involved in the allocation of a good which some people use to call a merit good. One could argue that our modeling of the cultural service as a merit good is as unsatisfactory as the ad hoc merit good approach because the "black box" merit good is merely substituted by a new "black box" called cultural capital. We maintain, however, that our model focuses on a well-defined externality issue and draws our attention on a specific hypothesis about cultural capital, its development and effects. In our view it offers better guidance in tackling merit-good type of problems than the traditional paternalistic merit-good approach. In concluding, recall that we did not incorporate into our model the process of creating new cultural goods. Conceptually, it is clear how the present model must be extended to accommodate for investments to augment the stock of goods. First, this stock would need to be explicitly introduced as a state variable in addition to cultural capital and, second we would need a production function for new cultural goods that are interpreted as investments in the stock of cultural goods. It is plausible that, among other inputs, cultural capital should enter that production function as a production factor creating a feedback effect that makes the dynamics of cultural growth or decline both more realistic and very complex. Tackling these additional aspects in a rigorous analysis is a highly relevant and rewarding item on the agenda for future research, since such an approach would promise to give new insights into an issue which was clearly beyond the scope of the model in the present paper: the rationale of supply-side subsidies to stimulate the production of new cultural goods. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 465 Appendix A Derivation of the Steady State In view of (2') we have XJz{X,Y,Z) =C/|(Z). Hence equation (9) reads (Al) V = (a + p)V - nlj\{Z) . For V = 0, equation (Al) yields (A2) v = T^^l=:nK(Z). OL+b Since Uzz < 0 by assumption, the V = 0 locus implied by equation (A2) is negatively sloped. Using equation (10), Vcan be rewritten as (A3) V = ^U]r(X,Y)-U1 x(X,Y) . Substituting Y= ^ - X from (4) into equation (A3) we get (A4) V = gi^lX, (A - gx)] - U&X, (A - gx)] =: F(X) . The derivative of function F is: (A5) FX = 2^UXY - ^ 2 Uyy - UXX . Owing to the assumptions on U introduced in equation (2), Fx is positive. For Z = 0, equation (3) yields X = We insert this equation in function F from (A4) to obtain the Z = 0 locus in the (V, Z) space. (A6) V = F^j=G(Z,n) Hence along the Z = 0 locus V is strictly increasing in Z. Note that the steady state value ZE is then obtained by solving the equations (A2) and (A6) simultaneously: nK(Z) = G(Z, n). Since Z7 is assumed well-behaved (cf. footnote 6) the solution ZE to this equation is unique and satisfies Ze > 0, because Gz > 0 and G(Z, n) > 0 for large values of Z and because Kz < 0 and Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 466 Rüdiger Pethig and Sao-Wen Cheng K(Z) > 0 for all Z > 0. As a consequence, VE = G(ZE,n) > 0 and Xe: = olZeIu> 0. We also conclude that Ye > 0 since F(X) is not defined for X = Xmax = R/Cx- Appendix B Derivation of the Cournot-Nash Equilibrium The optimal control problem (11) - (13) is solved by applying the currentvalue Hamiltonian: (14) H = U(Xt,Yt,Zt) + fi(Xt +X- aZt) + A(R - PxXt - Py Yt) . The FOCs for a solution to (11) are: 3H (Bl) Qx=Ux+ti-\Px = 0 , flTJ (B2) — Uy-APy, (B3) ^ = Sn-^=(a + S)n-Uz . Combining equations (Bl) and (B2) we obtain (B4) = K } UY Py Uy Similar as (10), equation (B4) shows that each consumer's MRS between X and Y must equal the price ratio minus the ratio of the shadow price of cultural capital and the marginal utility with respect to Y. Combining equations (B3) and (B4) and substituting ^ - ^ X from (13) // can be rewritten as (B5) „ = g*)] = :F(X) . Since all consumers are assumed to be identical, it is appropriate to restrict the equilibrium analysis to a symmetric Cournot-Nash equilibrium. Hence for every agent there exists an individually optimal time path Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 Cultural Capital and the Consumption of Cultural Services 467 {Xf}, {Yt}, {Zt} for any given X. The associated necessary equilibrium condition is then Xi = Xj = X for all i, j = 1,..., n. It follows that (B6) = 1)X. frh As before, the change in the stock of cultural capital is given by (B7) Z = nX — aZ . The equations (12), and (B7) are not contradictory since (12) is the individual consumer's perception whereas (B7) reflects the actual intertemporal changes of cultural capital under the (necessary) equilibrium condition Xj = Xh = X for all j, h = 1,..., n. We combine (B7) and (B5) to obtain the Z = 0 locus in the (/z, Z) space: (B8) » = F(X) = F^=:G(Z,n). For ¡1 = 0 equation (B3) yields (B9) ß = The Cournot-Nash equilibrium of cultural capital ZCN is then implicitly defined through the equation G(Z,n) = K(Z). We also know that ßCN' = G(ZCN) > 0 and hence the equilibrium dynamics are qualitatively the same as in case of the optimal time path discussed in section 3.2. References Aghion, O./Howitt, P., Endogenous Growth Theory, 1998, Cambridge. Becker, G., 1964, Human Capital, New York. - 1998, Accounting for Tastes, Cambridge. Coleman, J., 1990, Foundation of Social Theory, Cambridge. Feichtinger, G./Hartl, R. F., 1986, Optimale Kontrolle Ökonomischer Prozesse, Berlin. Fullerton, D., 1992, "On justifications for public support of the arts", Journal of Cultural Economics 16, 67-82. Netzer, D., 1978, The Subsidized Muse, Cambridge. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34 468 Rüdiger Pethig and Sao-Wen Cheng Peacock, A., 1969, "Welfare Economics and Public Subsidies to the Art", Manchester School of Economics and Social Studies. (Reprinted in Journal of Cultural Economics 18, 2, 1994, 151-161.) Robbins, L., 1963, "Art and the States", in Politics and Economics. New York. Throsby, D., 1995, "Culture, Economics and Sustainability", Journal of Cultural Economics 19, 199-206. - 1999, "Cultural capital", Journal of Cultural Economics 23, 3 -12. Ulibarri, C., 2000, "Rational Philanthropy and Cultural Capital", Journal of Cultural Economics 24, 135 -146. UNESCO, 1998, First World Culture Report, UNESCO, Paris. Schmollers Jahrbuch 122 (2002) 3 OPEN ACCESS | Licensed under CC BY 4.0 | https://creativecommons.org/about/cclicenses/ DOI https://doi.org/10.3790/schm.122.3.445 | Generated on 2023-04-04 12:30:34