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Media Mergers with Preference Externalities and Their Implications for Content Diversity, Consumer Welfare, and Policy

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Abstract

One of the primary concerns regarding media mergers involves their potential adverse effect on content/viewpoint diversity. This paper presents a formal treatment of the influence that within-group consumer preference externalities over media content have on a media outlet’s incentive to engage in product repositioning both before and after merging with another media outlet. We first present a model of consumer behavior under preference externalities and derive aggregate consumer expenditure functions for media output. It is shown that even assuming the merged entity sets a uniform price and content mix across market areas, the relative access to some minority (majority) group subscribers will increase (decrease) post-merger (and vice versa). We derive sufficient conditions under which the merged entity will in fact have an incentive to homogenize its post-merger price/content mix. And while the post-merger repositioning effects arguably suggest the consumer welfare implications of such mergers are ambiguous a priori, it is posited that the observed idiosyncratic preferences for media content among demographic groups may translate into significant losses to consumer welfare in some instances and may also adversely affect some individuals’ participation in civil affairs, such as voting. Finally, the relation of the model to previous empirical work on media mergers and diversity, and the potential for non-traditional policy interventions to offset the competitive harms of such transactions, are also discussed.

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Notes

  1. See, e.g., Bush (2002) and Waldfogel (2002).

  2. See Shelanski (2006) for further discussion of the history and controversy surrounding the FCC’s 2003 Order.

  3. Prometheus Radio Project vs. FCC, 373 F.3d 372,382 (3d Cir. 2004).

  4. See <http://www.fcc.gov/ownership/>. In November, 2006, the FCC again commissioned a series of economic studies as part of the review of its media ownership rules. See <http://hraunfoss.fcc.gov/edocs_public/attachmatch/DOC-268606A1.pdf>. In addition, in reviewing recent mergers within the media industry the FCC has explicitly considered their potential impact on the diversity of content (among other factors). See, e.g., FCC (2006b).

  5. See, inter alia, Dertouzos and Trautman (1990); Rogers and Woodbury (1996); Berry and Waldfogel (2001); and DiCola (2006).

  6. See, e.g., Siegelman and Waldfogel (2001); George and Waldfogel (2003); and Waldfogel (2003, 2004).

  7. This effect may occur by way of new product introduction or the repositioning of existing products (George and Waldfogel 2003).

  8. Bush (1994) models interdependent preferences within the context of Veblen (1899) effects and motivates the construct of a status utility function that is defined over own consumption and expectations of expenditures on goods by individuals in the next highest “social class” (where income levels are used as a proxy of class determination). (See also Charles et al. (“Conspicuous consumption and race,” unpublished manuscript, 2008) and Bagwell and Bernheim (1996) for formal treatments of utility maximization with Veblen effects.) The model presented here modifies Bush’s status utility function by abstracting from Veblen effects but accounting for the presence of within-group preference externalities. Bush shows that under certain conditions the status-maximization model will correspond to the neoclassical utility-maximization framework of consumer behavior.

  9. In this model it is assumed that each firm supplies only a single good.

  10. Appendix 1 contains the derivation of Eq. 4 for the case of one composite good.

  11. Note that Eq. 12 is similar to Stone’s (1954) Linear Expenditure System (“LES”) with a consumer expenditure function that allows for habit formation. With regard to Eq. 11, terms for quality/diversity and preference externalities enter in a similar fashion. Habits are, however, incorporated into the LES on an ad hoc basis. In the Stone-Geary utility function there is no term for habits. It is only after the LES is derived that a habit term is added. Again, under specific conditions the status-maximization model of Bush (1994) will reduce to the neoclassical framework of consumer behavior. As such, the bundling of content by a given media outlet can be viewed as a habit that consumers desire “less” (i.e., since the bundle will contain some fraction of content that is not preferred by either the majority or minority subscribers).

  12. This assumption obviates the need to explicitly model the outlet’s advertising price decision and allows us to focus more directly on the outlet’s decisions regarding price and content to the ultimate subscribers of the media, which is the fundamental goal of the analysis.

  13. We will abuse notation somewhat by allowing j to index both the geographic area and the (representative) media outlet supplying it.

  14. Equation 14 implicitly subsumes that a given media outlet cannot price discriminate between minority- and majority-type subscribers. This is not an unrealistic notion given that many types of media cannot easily observe the characteristics of the customers purchasing their output (e.g., a large-circulation local newspaper firm cannot determine what kind of consumers are purchasing its output at a news stand without incurring the potentially high cost of monitoring). In addition, the output produced by some media outlets (e.g., cable systems) may be price-regulated by state/local licensing bodies, which also prevents the firms from charging different prices to different customers.

  15. Thus, one may think of firm j purchasing all of its content from a representative firm in the upstream content market.

  16. For example, in the newspaper industry the marginal costs of distribution/transmission would include those involved with home delivery services. In other media industries, such as cable, these costs are likely to be very small.

  17. The complete proof is shown in Appendix 2.

  18. The result may be approximate due to the specific form of media outlet considered and rounding. For example, with respect to the cable industry, upstream content providers may “share” channels so, e.g., there might be 40.5 channels of majority-oriented programming.

  19. Several empirical studies on preference externalities have argued that minority-oriented programming tends to be “undersupplied” (Berry and Waldfogel 2001; Waldfogel 2003; Wang and Waterman “Market size, preference externalities, and the availability of foreign language radio programming in the U.S.,” unpublished manuscript, 2008). In particular, Wang and Waterman provide evidence that the fraction of minority-oriented programming is less than the proportion of minorities in the population. The results of Proposition 2, on the other hand, suggest that minority- or majority-oriented programming will be provisioned in exact proportion to the relevant subscriber population. There a number of possible explanations for this discrepancy. For instance, it is almost certainly the case that some minority consumers do in fact choose to consume what may otherwise considered “majority” programming. If so, then it may appear that minority-oriented programming is undersupplied in the context considered by Wang and Waterman, even though some (if not many) are still obtaining access to their “preferred” (minority) content. But both the extant empirical work on the model considered herein both abstract from the notion of “overlapping” preferences for content. Furthermore, the model effectively assumes that there is a perfectly elastic supply of either minority- or majority-oriented programming that the media outlet may purchase from upstream content providers. However, there may be a difference in the amount of minority-oriented programming that the media outlet may wish to make available and the amount that it is actually able to purchase. For example, the amount of minority-oriented programming that maximizes the profits of the upstream content provider that it makes available may not match the quantity that would satisfy the profit-maximization problem of the media outlet in accordance with Proposition 2 (which is determined by its local population mix). As such, the local media operator may effectively face a capacity constraint on the amount of minority-oriented programming it is able to acquire. Finally, it might be the case that data on minority population shares do not perfectly correspond to minority subscribership shares (“take rates”). The model implicitly assumes that all area-specific population members are consumers/purchasers of media output; however, it may be the case that, say, minority consumers, due to binding income constraints, consume media output less extensively relative to majority consumers (or are targeted less frequently by advertisers in a broadcast framework). If so, then the share of minority-oriented programming offered in a given area would tend to be lower than the minority group’s population share in the area.

  20. For example, the firms may be newspaper outlets operating in different cities, or they may be cable companies operating in adjacent franchise areas. This assumption is made only for the sake of conceptual ease and does not qualitatively affect the results.

  21. See, e.g., FCC (2002) at paragraphs 177–178, 180.

  22. See <http://stateofthemedia.org/2007/narrative_radio_ownership.asp?cat = 4&media = 9> (emphasis added).

  23. Clearly, if the merged firm continued to treat each market area “separately,” then one would not expect any change in the pre- and post-merger content shares or prices set in each area given the assumption of no marginal cost efficiencies. Of course, this latter outcome is unlikely to raise any anticompetitive concerns and, therefore, be of no inherent interest from an academic or policy perspective. Thus, the approach taken here is to assume upfront that the merged firm possesses an incentive to homogenize its output (which, again, is one of the key concerns regarding media transactions) and then explore the implications for the relative access to preferred content across groups given the presence of within-group preference externalities. In any event, the sufficient conditions under which the merged entity will possess the incentive to homogenize its output are derived below, which suggests that such post-merger behavior has some theoretical foundation.

  24. That is, homogenization of price/content will not necessarily occur in our model, but will so long as the sufficient conditions laid out after Remark 1 are satisfied. Again, the goal here is to analyze the welfare implications of media mergers with preferences externalities under the “worse case scenario,” i.e., “complete” homogenization (as it pertains to both price and content) in the post-merger. At the same time, we recognize that there are a range of other (non-homogenization) strategies that the merged firm may adopt under other conditions, some of which may closely resemble the pre-merger environment.

  25. A related study is George (2007), which documents a positive relation between the extent of ownership concentration in local newspaper markets and the extent of product differentiation and variety as based upon the allocation of reporters to various news topics. The points raised herein with regard to the Berry and Waldfogel (2001) study also generally apply to George’s study.

  26. See Berry and Waldfogel (2001, p. 1014) (“Our measure of programming variety is the number of different programming formats broadcast in a market.”).

  27. For example, post-merger there may have been an increase in the number of formats geared to listeners in the “majority” group (e.g., white listeners), which might include formats such as “country,” “big band,” and “oldies.” At the same time, there may have been a decrease in the number of formats preferred by the “minority” group (e.g., blacks), which might include “gospel,” “jazz,” and “black talk” radio stations. (See Waldfogel (2003) for empirical evidence of these demographic-specific preferences in radio formats). If the increase in majority-oriented stations post-merger was significantly greater than the decrease in minority-oriented stations, then there could still be an absolute or relative increase in the number or formats (or diversity as considered by Berry and Waldfogel) even though the minority-group would clearly have less access to its preferred content.

  28. The same can also be said of the finding regarding the greater propensity for local versus non-local siblings to broadcast in different formats, although at the same time this finding appears somewhat more in-line with our model’s predictions. However, it is worth noting that Berry and Waldfogel attribute this effect to strategic product positioning motives to preempt entry into a particular format (i.e., as opposed to the influence of preference externalities), an effect that is not considered in our model.

  29. See Marc Fisher, Washington’s Loss: XM Empties Out, available at <http://voices.washingtonpost.com/rawfisher/2008/10/washingtons_loss_xm_empties_ou.html?hpid = news-col-blogs>, from which the ensuing discussion is also drawn.

  30. According to Fisher, supra note 29, XM was perceived by many satellite radio subscribers as offering more “creative” programming compared to Sirius.

  31. See Heyer (2006) for a discussion and critique of various welfare standards used in the antitrust assessment of mergers. Note also that review of many media mergers in the U.S. falls under the jurisdiction of both the antitrust enforcement agencies and the FCC, the latter of which uses a broader “public interest” standard to evaluate transactions. This standard may include consideration of content diversity and the deployment of services based on economic status, race, and ethnicity (among other factors) in addition to traditional antitrust concerns. See, e.g., FCC (2006b, paragraphs 4 and 192).

  32. We do not provide a complete formal analysis of welfare effects since doing so would also require explicit consideration of the price and access effects of media mergers on advertisers as well as consumers (Berry and Waldfogel 2001). It is almost certainly the case, however, that the ambiguous (subscriber) welfare effects discussed herein would also pertain to advertisers, and as such, not provide any further illumination of effects on overall welfare.

  33. The welfare ambiguity is not necessarily obviated in the case where the post-merger (uniform) price rises relative to its pre-merger levels. While subscribers with less access to preferred content would be worse off, those subscribers who received greater access would effectively be receiving a product that they perceive has having higher quality (and thus would potentially be willing to pay some “premium” for).

  34. Indeed, this sentiment is eloquently expressed by Howard Shelanski (2006, p. 381):

    [A] merger among telephone companies might lead to slightly higher prices or poorer customer service. Such harms are important but are largely limited to pecuniary considerations and periodic inconveniences. Consolidation among major media providers, in contrast, implicates more than economic concerns. Ownership changes that threaten or that people perceive to threaten the availability of diverse news and information sources … strike at the heart of civic governance and political debate...

  35. See also George and Waldfogel (“Does the New York Times spread ignorance and apathy?,” unpublished manuscript, 2002).

  36. See <http://www.usdoj.gov/atr/cases/mcclatchy.htm>.

  37. See, e.g., Owen (“The FCC “further report” on the retail marketing of video programming services: An economic review,” unpublished manuscript, 2006) for a critique of FCC (2006a) and a discussion of the various potential harms associated with requiring MVPDs to completely unbundle their programming content. Some commenters have argued that MVPD channel unbundling in itself may diminish the extent of diversity. For example, unbundling may affect the extent to which small niche program networks can remain economically viable if offered outside of a diverse tier of channels (Owen 2006, p. 14). Unbundling may also diminish the ability of MVPD subscribers to “surf” across various program channels, which might expose them to alternative media and viewpoints (Owen 2006, p. 15). To some extent, the remedy considered here may lessen some of these concerns since all subscribers would still have access to a “range” of programming channels post-merger, but at the same time would be allowed to purchase those preferred channels that were “removed” from their tier post-merger (and/or to obtain the new channels geared toward their group’s preferences that are offered to the area that realizes an increase in the preferred programming post-merger). We leave investigation of these issues to future research while noting Uri’s (2005, p. 108) observation that:

    [T]here are too many unknown factors to equivocally conclude whether subscribers will be better off under a la carte pricing. These include how cable systems would price their services under an a la carte system, the distribution of subscribers’ purchasing patterns, and whether niche networks would cease to exist and, if so, how many would exit the industry.

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Author information

Authors and Affiliations

  1. Office of Inspector General, U.S. Federal Communications Commission, 445 12th Street, SW, Washington, DC, 20554, USA

    C. Anthony Bush

  2. Bureau of Economics, Antitrust I, U.S. Federal Trade Commission, 601 New Jersey Avenue NW, Rm. 8103, Washington, DC, 20580, USA

    Paul R. Zimmerman

Authors
  1. C. Anthony Bush
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  2. Paul R. Zimmerman
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Corresponding author

Correspondence to Paul R. Zimmerman.

Additional information

The views expressed in this paper are those of the authors and not necessarily those of the FCC, FTC, or their respective Commissioners and other staff members. The authors thank an anonymous referee for valuable comments and participants at the 2009 Workshop on Competition Policy and Regulation in Media Markets at Tilburg University for useful discussions. The usual caveat applies.

Appendices

Appendix 1

In this appendix we derive the media expenditure function for a given subscriber type. We assume that there is a single composite good with a price p 2. Subscriber z’s optimization problem is

$$ \mathop {\max }\limits_{\left\{ {v_j^{(z)},v_2^{(z)}} \right\}} {V^{(z)}} = {\left( {v_j^{(z)} - {\gamma_j}g\left( {p_j} \right) - {\alpha_z}{\Omega_j}} \right)^{{\beta_j}}}{\left( {v_2^{(z)} - {\gamma_2}{p_2}} \right)^{{\beta_2}}} $$

subject to \( v_j^{(z)} + v_2^{(z)} = {I^{(z)}} \) where β j  > 0 and β 2 > 0, i = 1,...,n. We assume that \( {\beta_j} + {\beta_2} = 1 \) and α z  > 0, γ j  > 0, γ 2 > 0.

Substituting the budget constraint into the objective function gives

$$ {V^{(z)}} = {\left( {v_j^{(z)} - {\gamma_j}g\left( {p_j} \right) - {\alpha_z}{\Omega_j}} \right)^{{\beta_j}}}{\left( {{I^{(z)}} - v_j^{(z)} - {\gamma_2}{p_2}} \right)^{{\beta_2}}}. $$

The first-order condition associated with the above problem is given by

$$ \begin{array}{*{20}{c}} {\frac{{d{V^{(z)}}}}{{dv_j^{(z)}}} = {\beta_j}{{\left( {v_j^{(z)} - {\gamma_j}g\left( {p_j} \right) - {\alpha_z}{\Omega_j}} \right)}^{{\beta_j} - 1}}{{\left( {{I^{(z)}} - v_j^{(z)} - {\gamma_2}{p_2}} \right)}^{{\beta_2}}}} \hfill \\ { + {\beta_2}{{\left( {v_j^{(z)} - {\gamma_j}g\left( {p_j} \right) - {\alpha_z}{\Omega_j}} \right)}^{{\beta_j}}}{{\left( {{I^{(z)}} - v_j^{(z)} - {\gamma_2}{p_2}} \right)}^{{\beta_2} - 1}}\left( { - 1} \right) = 0.} \hfill \end{array} $$

Rearranging the above expression gives:

$$ \begin{array}{*{20}{c}} { \Rightarrow {\beta_j}\left( {{I^{(z)}} - v_j^{(z)} - {\gamma_2}{p_2}} \right) + {\beta_2}\left( {v_j^{(z)} - {\gamma_j}g\left( {p_j} \right) - {\alpha_z}{\Omega_j}} \right)\left( { - 1} \right) = 0} \hfill \\ { \Rightarrow {\beta_j}{I^{(z)}} - {\beta_j}v_j^{(z)} - {\beta_j}{\gamma_2}{p_2} - {\beta_2}v_j^{(z)} + {\beta_2}{\gamma_j}g\left( {p_j} \right) + {\beta_2}{\alpha_z}{\Omega_j} = 0} \hfill \\ { \Rightarrow {\beta_j}{I^{(z)}} - {\beta_j}v_j^{(z)} - {\beta_j}{\gamma_2}{p_2} - \left( {1 - {\beta_j}} \right)v_j^{(z)} + \left( {1 - {\beta_j}} \right){\gamma_j}g\left( {p_j} \right) + \left( {1 - {\beta_j}} \right){\alpha_z}{\Omega_j} = 0} \hfill \\ { \Rightarrow {\beta_j}{I^{(z)}} - \left( {{\beta_j} + {\beta_2}} \right)v_j^{(z)} - {\beta_j}{\gamma_2}{p_2} + \left( {1 - {\beta_j}} \right){\gamma_j}g\left( {p_j} \right) + \left( {1 - {\beta_j}} \right){\alpha_z}{\Omega_j} = 0} \hfill \\ { \Rightarrow {\beta_j}{I^{(z)}} - v_j^{(z)} - {\beta_j}{\gamma_2}{p_2} + \left( {1 - {\beta_j}} \right){\gamma_j}g\left( {p_j} \right) + \left( {1 - {\beta_j}} \right){\alpha_z}{\Omega_j} = 0} \hfill \\ { \Rightarrow v_j^{(z)} = \left( {1 - {\beta_j}} \right){\gamma_j}g\left( {p_j} \right) - {\beta_j}{\gamma_2}{p_2} + \left( {1 - {\beta_j}} \right){\alpha_z}{\Omega_j} + {\beta_j}{I^{(z)}}} \hfill \\ { \Rightarrow v_j^{(z)} = \left( {1 - {\beta_j}} \right){\gamma_j}g\left( {p_j} \right) - {\beta_j}{\gamma_2}{p_2} + \left( {1 - {\beta_j}} \right){\alpha_z}\left[ {{\tau_z}\tilde S_j^z + \eta \left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln {S_{j,M}}} \right)} \right] + {\beta_j}{I^{(z)}}} \hfill \\ { \Rightarrow v_j^{(z)} = ag\left( {p_j} \right) + {a_{j2}}{p_2} + {{\tilde {\text T}}_z} + {{\tilde \alpha }_z}\left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln {S_{j,M}}} \right) + {\beta_j}{I^{(z)}}} \hfill \end{array} $$

where \( a = \left( {1 - {\beta_j}} \right){\gamma_j} \), \( {a_{j2}} = - {\beta_j} \times {\gamma_2} \), \( {\tilde {\text T}_z} = \left( {1 - {\beta_j}} \right){\alpha_z}{\tau_z}\tilde S_j^z \), and \( {\tilde \alpha_z} = \left( {1 - {\beta_j}} \right){\alpha_z}\eta \). The above expression is analogous to Eq. 4 in the text.

Appendix 2

In this appendix we prove Parts (i), (ii), and (iii) of Proposition 1. The media outlet maximizes its expected profits:

$$ \begin{array}{*{20}{c}} {E\left\{ {{\Pi_j}} \right\} = {G_j}\left( {p_j} \right) + \beta \left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln \left( {1 - {S_{j,m}}} \right)} \right. - c\frac{{\left\{ {{G_j}\left( {p_j} \right) + \beta \left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln \left( {1 - {S_{j,M}}} \right)} \right)} \right\}}}{p_j}} \hfill \\ { - {f_{j,CONT}} - {f_{j,NET}}.} \hfill \end{array} $$

The first-order condition is given by:

$$ \frac{{\partial E\left\{ {{\Pi_j}} \right\}}}{{\partial {p_j}}} = \frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}} - c\left[ {\frac{{\left( { - 1} \right)}}{p_j^2}\left\{ {{G_j}\left( {p_j} \right) + \beta \left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln (1 - {S_{j,m}})} \right.} \right\} + \frac{1}{p_j}\frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}}} \right] = 0. $$

Rewriting the above expression gives

$$ \begin{array}{*{20}{c}} { \Rightarrow {p_j}\frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}} - c\left[ {\frac{{\left( { - 1} \right)}}{p_j}\left\{ {{G_j}\left( {p_j} \right) + \beta \left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln \left( {1 - {S_{j,m}}} \right)} \right.} \right\} + \frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}}} \right] = 0} \hfill \\ { \Rightarrow \frac{p_j}{{{G_j}\left( {p_j} \right)}}\frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}} - c\left[ {\frac{{\left( { - 1} \right)}}{p_j}\left\{ {\frac{{{G_j}\left( {p_j} \right) + \beta \left( {{N_{j,m}}\ln {S_{j,m}} + {N_{j,M}}\ln \left( {1 - {S_{j,m}}} \right)} \right.}}{{{G_j}\left( {p_j} \right)}}} \right\} + \frac{1}{{{G_j}\left( {p_j} \right)}}\frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}}} \right] = 0} \hfill \\ { \Rightarrow \frac{p_j}{{{G_j}\left( {p_j} \right)}}\frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}} - \frac{c}{p_j} \times \left[ {\frac{{\left( { - 1} \right)}}{{{\omega_j}}} + \frac{p_j}{{{G_j}\left( {p_j} \right)}}\frac{{\partial {G_j}\left( {p_j} \right)}}{{\partial {p_j}}}} \right] = 0} \hfill \\ { \Rightarrow {\gamma_j} - \frac{c}{p_j} \times \left[ {\frac{{\left( { - 1} \right)}}{{{\omega_j}}} + {\gamma_j}} \right] = 0} \hfill \\ { \Rightarrow {p_j} - c \times \left[ {\frac{{\left( { - 1} \right)}}{{{\gamma_j}{\omega_j}}} + 1} \right] = 0 \Rightarrow {p_j} = c \times \left[ {\frac{- 1}{{{\gamma_j}{\omega_j}}} + 1} \right]} \hfill \\ { \Rightarrow {p_j} = c \times \left[ {\frac{{{\gamma_j}{\omega_j}}}{{{\gamma_j}{\omega_j}}} + \frac{- 1}{{{\gamma_j}{\omega_j}}}} \right] = c \times \left[ {\frac{{ - 1 + {\gamma_j}{\omega_j}}}{{{\gamma_j}{\omega_j}}}} \right] = c \times \left[ {\frac{1}{{\frac{{{\gamma_j}{\omega_j}}}{{ - 1 + {\gamma_j}{\omega_j}}}}}} \right] = c \times \left[ {\frac{1}{{\frac{{ - 1 + {\gamma_j}{\omega_j} + 1}}{{ - 1 + {\gamma_j}{\omega_j}}}}}} \right]} \hfill \\ { \Rightarrow {p_j} = c \times \left[ {\frac{1}{{\frac{{ - 1 + {\gamma_j}{\omega_j} + 1}}{{ - 1 + {\gamma_j}{\omega_j}}}}}} \right] = c \times \left[ {\frac{1}{{\frac{{ - 1 + {\gamma_j}{\omega_j}}}{{ - 1 + {\gamma_j}{\omega_j}}} + \frac{1}{{ - 1 + {\gamma_j}{\omega_j}}}}}} \right] = c \times \left[ {\frac{1}{{1 + \frac{1}{{ - 1 + {\gamma_j}{\omega_j}}}}}} \right].} \hfill \\ { \Rightarrow {p_j} = c \times \left[ {\frac{1}{{1 + \frac{1}{{ - 1 + {\gamma_j}{\omega_j}}}}}} \right] = c \times \left[ {\frac{1}{{1 + \frac{1}{{{\varepsilon_j}}}}}} \right].} \hfill \end{array} $$

The optimal shares of minority- and majority-oriented programming are derived as follows.

$$ \begin{array}{*{20}{c}} {\frac{{\partial E\left\{ {{\Pi_j}} \right\}}}{{\partial {S_{j,m}}}} = \beta \left( {\frac{{{N_{j,m}}}}{{{S_{j,m}}}} + \frac{{{N_{j,M}}}}{{\left( {1 - {S_{j,m}}} \right)}} \times \left( { - 1} \right)} \right) - \beta \times \frac{c}{p_j}\left( {\frac{{{N_{j,m}}}}{{{S_{j,m}}}} + \frac{{{N_{j,M}}}}{{\left( {1 - {S_{j,m}}} \right)}} \times \left( { - 1} \right)} \right) = 0} \hfill \\ { \Rightarrow \left( {\beta - \beta \frac{c}{p_j}} \right) \times \left( {\frac{{{N_{j,m}}}}{{{S_{j,m}}}} - \frac{{{N_{j,M}}}}{{\left( {1 - {S_{j,m}}} \right)}}} \right) = 0} \hfill \\ { \Rightarrow \frac{{{N_{j,m}}}}{{{S_{j,m}}}} - \frac{{{N_{j,M}}}}{{\left( {1 - {S_{j,m}}} \right)}} = 0 \Rightarrow {S^*_{j,m}} = \frac{{{N_{j,m}}}}{{\left( {{N_{j,m}} + {N_{j,M}}} \right)}}} \hfill \\ { \Rightarrow {S^*_{j,M}} = 1 - {S^*_{j,m}} = 1 - \frac{{{N_{j,m}}}}{{\left( {{N_{j,m}} + {N_{j,M}}} \right)}} = \frac{{{N_{j,M}}}}{{\left( {{N_{j,m}} + {N_{j,M}}} \right)}}.} \hfill \end{array} $$

It is straightforward to show that at optimum values \( \frac{{\partial E\left\{ {{\Pi_j}} \right\}}}{{\partial {p_j}\partial {p_j}}} < 0;\,\,\frac{{\partial E\left\{ {{\Pi_j}} \right\}}}{{\partial {S_{j,m}}\partial {S_{j,m}}}} < 0 \); and \( \frac{{\partial E\left\{ {{\Pi_j}} \right\}}}{{\partial {S_{j,m}}\partial {p_j}}} = 0 \).

Q.E.D.

Appendix 3

Because consumers do not pay for traditional broadcast media, the relationship between broadcast media and preference externalities is explained in this appendix. The case of broadcast media is treated by recognizing the multi-stage nature of a consumer’s problem. First, assume that the consumer made a decision on labor and leisure. That is, we assume that the consumer has an income and an amount of leisure. The second stage consists of the general problem of a consumer optimizing utility by choosing consumer expenditures. The third stage consists of the consumer maximizing another utility optimand by choosing among leisure activities, where one such leisure activity is listening/viewing a broadcast.

Advertising and status in consumption

Following Bush (1994), an alternative presentation of a consumer’s maximization problem includes advertising components that affect taste for goods and services. Let ADV i denote advertising spent by firms to promote good i, i = 1, 2,...,n. For simplicity of analysis, it is assumed that a media firm does not purchase advertising to promote its own medium. The constrained optimization problem for consumer z is

$$ \mathop {\max }\limits_{\left\{ {v_j^{(z)},v_1^{(z)},v_2^{(z)}, \ldots, v_n^{(z)}} \right\}} {V^{(z)}} = {\left( {v_j^{(z)} - {\psi_j}g\left( {p_j} \right) - {\alpha_z}{\Omega_j}} \right)^{{\beta_j}}}\left( {{{\prod\limits_{i = 1}^n {\left( {v_i^{(z)} - {\psi_i}{p_i} - {\omega_i}AD{V_i}} \right)} }^{{\beta_i}}}} \right) $$

subject to

$$ \sum\nolimits_{k = 1}^{n + 1} {v_k^{(z)} = {I^{(z)}}} $$

where a z  > 0, Ψ k  > 0, ω i  > 0, β k  > 0, and Σ k β k  = 1. We explain Ω j in Section 2.1.2.

Subscriber z’s equilibrium expenditure on good/service k is

$$ v_k^{(z)} = {a_{kj}}g\left( {p_j} \right) + \sum\limits_{i = 1}^n {{a_{ki}}{p_i} + } \sum\limits_{i = 1}^n {{c_{ki}}AD{V_i} + \left( {{I_{\left\{ {k=j} \right\}}} - {\beta_k}} \right){\alpha_z}{\Omega_j} + {\beta_k}{I^{(z)}}}, k = j,1,2,3, \ldots, n. $$
(A1)

Let \( {a_{kk}} = \left( {1 - {\beta_k}} \right){\psi_k} \), \( {a_{kl}} = - {\beta_k}{\psi_l} \), \( {c_{kk}} = \left( {1 - {\beta_k}} \right){\omega_k} \), and \( {c_{kl}} = - {\beta_k}{\omega_l} \) .

Leisure Time

It is assumed that a consumer assigns a monetized value to total leisure time which is denoted VL (z). The monetized value of time spent with a broadcast medium is \( VL_B^{(z)} \), and the monetized value time spent in other leisure activities is \( VL_o^{(z)} \). The consumer maximizes utility from leisure activities:

$$ \mathop {\max }\limits_{\left\{ {VL_b^{(z)},VL_o^{(z)}} \right\}} {L^{(z)}} = {\left. {\left( {VL{}_B^{(z)} - {\chi_B}g(p_B^{(z)}} \right) - {\alpha_z}{\Omega_B}} \right)^{{\theta_B}}}{\left( {VL_o^{(z)} - {\chi_o}{p_o}} \right)^{{\theta_o}}} $$

subject to

$$ VL_B^{(z)} + VL_o^{(z)} = V{L^{(z)}} $$

where p B is the monetized opportunity cost of a unit of broadcast leisure. The parameter p o is the monetized opportunity cost of a unit of other leisure activity. Let a z  > 0, χ B  > 0, χ o  > 0, θ B  > 0, θ o  > 0, and θ B  + θ o  = 1.

Subscriber z’s equilibrium “expenditure” on broadcast leisure is

$$ VL_B^{(z)} = \left( {1 - {\theta_B}} \right){\chi_B}g\left( {p_B^{(z)}} \right) - {\theta_B}{\chi_o}p_o^{(z)} + \left( {1 - {\theta_B}} \right){\alpha_z}{\Omega_B} + {\theta_B}V{L^{(z)}} .$$
(A2)

Equation 2 states that a consumer’s optimal consumption of broadcasting is a function of opportunity costs and the effects of subscriber groupings (preference externalities) on the mix of content offered by the broadcast outlet. This effect is captured in Ω B .

Broadcaster behavior

Equation A1 states that advertising affects consumers’ expenditures on products, and, therefore, firms would demand advertising, including broadcast advertising. Equation A2 states that the leisure consumers spend with broadcasting is determined by the mix of broadcaster content which depends on preference externalities. Equations A1 and A2 together imply that the local market demand for broadcast advertising is influenced by preference externalities and prices of broadcast advertising. We assume that a broadcaster offers a differentiated product in a broadcast market and that the broadcaster is a Bertrand competitor. Other advertising markets remain perfectly competitive.

Let \( {r_B}\left( {pad{v_B},{q_B}} \right) = pad{v_B} \times {q_B} \) denote expected sales/revenue to a broadcaster from advertising, where padv B is the price for an ad to appear on a broadcaster’s station. Let q B denote expected demand. A broadcaster’s revenue is

$$ {r_B}\left( {pad{v_B},{q_B}} \right) = {G_B}\left( {pad{v_B}} \right) + \beta \left( {{N_{B,m}}\ln {S_{B,m}} + {N_{B,M}}\ln {S_{B,M}}} \right). $$
(A3)

The function G B is a well-behaved concave function on the price of the broadcast outlet. Again, the parameter β maps the influence of preference externalities into their dollar equivalents. Using Eq. A3 all results of our previous analysis apply; however, all price effects determine the welfare (surplus) of firms that purchase broadcast advertising. Alterations of broadcaster’s quality or mix of content due to preference externalities affect viewers of broadcasting and the price of broadcast advertising.

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Bush, C.A., Zimmerman, P.R. Media Mergers with Preference Externalities and Their Implications for Content Diversity, Consumer Welfare, and Policy. J Ind Compet Trade 10, 105–133 (2010). https://doi.org/10.1007/s10842-009-0057-2

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