FEDERAL COMMUNICATIONS COMMISSION

MEDIA BUREAU STAFF RESEARCH PAPER 

Media Ownership Working Group 

Radio Market Structure 

and Music Diversity 

By George Williams , Keith Brown, and 

Peter Alexander 

September 2002 

2002 - 

9 
1

RADIO MARKET STRUCTURE AND MUSIC DIVERSITY 

George Williams 

Keith Brown 

 Peter Alexander1

* 

September 2002 

Executive Summary: We develop a unique measure of product diversity, and apply it to 

R&R playlists to examine changes in diversity following the 1996 Telecommunications 

Act. This represents the first attempt to measure diversity in radio markets using actual 

songs. We find modest changes in diversity, with a slight decrease in the diversity of 

songs within the same R&R format across local markets, and a slight increase in the 

diversity of songs within the same R&R format within each local market. 

* Media Bureau, FCC. For this study, we acknowledge and express our appreciation for the following 

assistants: Tierra Ford, Antoine Greene, Eli Levine, Brenda Lewis, Linda Senecal, and Diedre Whitehead. 

The views expressed in this paper are those of the authors alone and do not necessarily reflect the views of 

the Federal Communications Commission, any Commissioners, or other staff. 

 

1

We list names in reverse alphabetical order of surname. 
2

Introduction 

 With the wave of radio mergers following the 1996 Telecommunications Act, the 

radio market has captured more attention from observers and policymakers. Specifically, 

observers and policymakers wish to understand the consequences of consolidation in 

radio markets. In this piece, we employ unique data and a novel measure of product 

diversity to study the relationship between concentration and diversity in broadcast radio. 

Unlike past research, which employs formats as a proxy for diversity (Berry and 

Waldfogel, 2001), we employ R&R data on actual songs aired by radio stations to 

directly measure diversity. In addition, we employ a unique measure of product 

diversity, which allows us to directly estimate concentration’s effect on diversity. So far, 

our results are tentative, and we can make no definite statement regarding the relationship 

between concentration and diversity. 

 The 1996 Act made two major regulatory changes in the radio market. First, the 

1996 Act increased the amount of radio stations that a single radio owner could possess 

in any given locality. Under the 1996 Act, a single owner can own up to 8 radio stations 

in a market with 45 or more commercial radio stations, 7 radio stations in a market with 

30-44 radio stations, 6 radio stations in a market with 15-29 radio stations, and five 

stations in markets with less than 15 radio stations. Second, the 1996 Act eliminated all 

caps on national ownership, replacing the old cap of 20 FM stations and 20 AM stations. 

We combine R&R playlists with data on ownership of radio stations and concentration in 

various radio markets to assess the impact of this important regulatory change on product 

diversity in the radio broadcasting market. 
3

Literature Review 

Theoretical treatments of product diversity on media markets start with Steiner 

(1952). Steiner averred that a single monopolist would maximize product diversity and 

economic welfare in a broadcast market, because the monopolist would want to capture 

every single viewer, and would therefore not duplicate programming. Social welfare is 

therefore higher under monopoly, because more viewers receive their preferred 

programming. 

 Researchers have pointed out that Steiner’s finding relies on strict assumptions 

about preferences. For instance, if viewers may have lesser preferred substitutes in 

programming (Beebe, 1977), then Steiner’s finding may not hold. More importantly, 

Steiner ignores the issue of pricing in media markets. If viewers pay for programming, 

either explicitly by direct payment or implicitly by sitting through advertising (Becker 

and Murphy, 1993; Gabszewicz, Laussel, and Sonnac, 1999; Anderson and Coate, 2000), 

then Steiner’s conclusions may no longer hold. As Gabszewicz, Laussel, and Sonnac 

(1999) and Anderson and Coate (2000) point out, if programs of the same type are perfect 

substitutes to viewers, then competition will now actually maximize product diversity, as 

competitors air different types of programming to avoid competing on price. Anderson 

and Coate (2000) demonstrate that Steiner’s conclusions may hold only when programs 

of the same type are imperfect substitutes. 

 As theory itself does not reveal a clear relationship between concentration and 

diversity, researchers employ empirical methods to gauge this relationship. Notably, 

Berry and Waldfogel (2001) attempt to measure the effect of concentration on product 

diversity in radio markets between 1993 and 1997. This allows Berry and Waldfogel to 
4

use the 1996 Act as their source of exogenous variation, thereby allaying potential 

concerns about the endogeneity of market structure. Berry and Waldfogel use the 

number of unique radio formats (using the Duncan classification system) as their proxy 

for product diversity. Berry and Waldfogel find that reductions in the number of owners 

led to increases in the number of formats, making the case that increased concentration 

increases product diversity in radio markets, which is consistent with Schmalansee’s 

theory of spatial preemption (1978). 

Our Contribution 

 As Berry and Waldfogel point out, formats are merely taxonomic methods of 

roughly classifying various radio stations, and certain formats are more similar than 

others. Therefore, the change in the number of formats may not be an accurate measure 

of the change in product diversity. If the number of formats does not change, but the 

diversity of songs across formats increases by 5%, using formats as the measure of 

diversity would inaccurately lead a researcher to conclude that radio product diversity did 

not change when in fact it increased by 5%. The ideal method of measuring product 

diversity would use radio stations’ comprehensive playlists and would measure 

concentration based on the relationship between the number of unique songs played and 

the number of total songs played. 

 We do not have comprehensive playlists, but we do obtain from R&R magazine 

the top songs played by a large sample of radio stations in March, 1996 and March, 2001. 

Thus, we can measure product diversity more directly, based on songs themselves, rather 

than format classification. Thus, we can create new measures of radio product diversity 

based on samples of actual songs played by radio stations. In doing so, we do forgo one 
5

advantage of Berry and Waldfogel’s study. For the most part, our data is drawn from 

radio stations in the top tier markets. Therefore, our sample’s variation across markets is 

not as driven by differences in FCC rules, which raises the possibility of market structure 

endogeneity. In addition, our sample draws from a possibly non-representative sample 

within these large markets. R&R only lists stations that meet a minimum rating 

requirement, meaning that stations with very few listeners are not listed by R&R. In 

addition, R&R only lists stations that play new songs, so stations that specialize in older 

songs, like Oldies stations or Classical stations, are not included in our sample of R&R 

playlists. 

 Our approach allows us to create and exploit a new measure of product diversity; 

the distance measure. As one may imagine, measuring diversity in a market is a daunting 

task. However, as Alexander (1997) points out, if we can break down products into a 

bundle of characteristics and simply treat the existence or non-existence of each 

characteristic as a binary variable, then we can create a measure of product diversity. In 

this case, songs are individual product characteristics, and we can create a measure of 

diversity between any two stations by comparing the songs played on each station. 

Below, we detail the creation and application of the distance measure. 

The Distance Measure of Diversity 

 We compare the similarity of m different product characteristics (in this case 

songs) across n different producers (in this case radio stations). In this case, we compare 

10 songs across 2 stations. So, m = 10 and n = 2. Under this condition, we can define a 

distance function that embodies a measure of diversity. This distance function will 
6

conveniently equal the number of unique songs played by each station. Therefore, when 

comparing two stations and the diversity of their top ten songs, if there is no duplication 

of songs, the distance function = 10, if the two stations duplicate one song, the distance 

function = 9, etc. Below, we demonstrate the creation of the distance function: 

 In the present case, we are interested in a subset of a set of many characteristics. 

Let this finite vector of dimensionality (the number of characteristics) be equal tom , and 

let n be the number of objects in the system. We now define the following. 

 First, two objects, ) ( , , 1 2 m X x x Κ x and ) '( ', ', ' 1 2 m X x x Κ x are identical to each 

other provided all ' n n x = x , where 0 < n ≤ m . Second, an object ) ( , , 1 2 m X x x Κ x is 

unique if there is no other object ) '( ', ', ' 1 2 m X x x Κ x such that all ' n n x = x , where 

0 < n ≤ m . Third, two objects are divergent from each other provided ' n n x ≠ x for all 

0 < n ≤ m . Fourth, two objects ) ( , , 1 2 m X x x Κ x and ) '( ', ', ' 1 2 m X x x Κ x are analogues

provided some ' n n x ≠ x and some ' j j x = x , where 0 . Finally, two objects, < n, j ≤ m

( , , ) 1 2 m X x x Κ x and ) '( ', ', ' 1 2 m X x x Κ x have the th n degree of analogy to each other, 

provided there are exactly n characteristics such that ' n n x = x . The greater (lesser) the 

degree of analogy, the more similar (dissimilar) the objects. 

Proposition 1: Suppose that object A has the th i degree of analogy with object 

B and the th j degree of analogy with object C , where 0 . Then, the degree of < i, j ≤ m

analogy k between B and C is such that 0 ≤ k ≤ m − | i − j | . Proof in technical 

appendix. 
7

 We extend our measure to include binary systems. In this system, each 

characteristic takes the value of 0 or 1, indicating the absence or presence of a 

characteristic. We define the degree of divergence between objects Xi and X j as: 

∑=

= −

m

k

ij ik jk d x x

1

| |

The degree of analogy can be computed as: 

aij = m − dij

allowing us to calculate the nominal analogous diversity of the system as: 

| | / 2 / 2. 111 1 1

∑∑∑ ∑∑ === = =

= − =

n

i

n

j

jk ij

n

i

n

j

m

k

ik nd x x d

The higher the nominal analogous diversity (nd) of the system, the more diverse is the 

system. 

 Proposition 2: Minimum (nominal analogous) diversity, min nd , equals zero. 

Maximum (nominal analogous) diversity, ndmax , equals ( ) 2

4

1 m n when n is even, and 

( 1) 2

4

1 m n − when n is odd. Proof in technical appendix. 

 Therefore, when we compare playlists of m songs between n = 2 stations, 

maximal diversity equals ( )

2

4

1 m n = 1⁄4 (m)(4) = m, so that maximum diversity obtains 

when we have two completely unique playlists, and our distance measure is equal to the 

number of songs played. Note that these playlists must be of equal size. 
8

Data and Methodology

 We combine data on station playlists and station ownership from R&R magazine 

with BIA data on station-level market share and market-level concentration. Using the 

partial playlists displayed in R & R for March 15, 1996 and March 16, 2001, we count 

the total number of different songs within each format. Table 1 presents data on the 

number of unique songs in our sample by R&R format. In six out of twelve formats (AC, 

Active Rock, Adult Alternative, CHR Pop, Jazz, and Rock) the number of unique songs 

has remained the same or declined between these two time periods. The number of 

different songs played in the other six other formats (Alternative, CHR Rhythm, Country, 

Hot AC, Urban AC, and Urban) has increased. There is, of course, some overlap 

between these formats; some songs are common to a number of formats, especially 

similar formats, such as Rock and Active Rock. On the bottom row of Table 1, we 

present the total number of unique songs across all formats published in our selected R & 

R magazines: 1241 for 1996 and 1228 for 2001. 

 Table 1: Unique Number of Songs by Formats
9

 

 Our methodology raises some issues concerning our sample. First, R&R playlists 

draw mainly from the largest markets. Therefore, our sample draws mainly from the top 

markets and does not include data from smaller markets. However, the markets from 

which our data draw include over 60% of all listeners. First, we assess song diversity 

across every R&R station-pairs in March 1996 and in March 2001. For each station pair 

in 1996 and 2001, we calculate the distance function, which measures the number of 

unique plays between any two stations. For instance, if two radio stations each play 10 

songs and none of those songs are the same, then our distance function would be 10; if 

Format Number of 

Stations 

Number of Unique 

Songs 

 1996 2001 1996 2001 

AC 18 20 93 93 

Active Rock 20 19 152 120 

Adult Alternative 20 20 221 183 

Alternative 40 39 207 221 

CHR Pop 45 45 255 199 

CHR Rhy 15 15 179 187 

Country 45 30 138 166 

Hot AC 20 20 110 140 

Jazz 20 20 191 143 

Rock 20 20 152 149 

Urban AC 11 12 82 125 

Urban 28 28 153 160 

All Formats 302 288 1241 1228 
10

those two stations have one song in common, then the distance function would be 9, etc. 

In our case, we employ only the top ten songs played by each radio station. We do this 

because the entropy measure requires equality in the number of songs we compare 

between radio stations, and radio stations have playlists of varying sizes. All radio 

stations, however, have playlists with at least ten songs. 

 Given that we have 302 stations in our sample in 1996, we generate ∑=

301

i 1

i = 

45,451 station-pair distance observations. In 2001, we have 288 stations, so we generate 

41,328 station-pair distance observations. 

 We use the distance function to create some simple descriptive statistics. Table 2 

shows the average distance between top ten lists among stations within the same R&R 

format. 

Table 2 

Average Distance Within Formats 

Format 1996 2001 

Adult Contemporary 6.51 5.53 

Active Rock 6.84 6.02 

Adult Alternative 7.65 7.06 

Alternative 7.44 6.68 

CHR Pop 7.09 6.00 

CHR Rhythm 7.66 6.79 

Country 4.68 5.94 

Hot Adult Contemporary 7.09 6.49 

Jazz 8.05 6.39 

Rock 7.25 6.94 

Urban Adult Contemporary 6.75 7.21 

Urban 5.33 6.68 
11

 

 The first row in Table 2 shows that, on average, Adult Contemporary top 10 radio 

lists differ by 6.51 songs in March 15, 1996 and 5.53 times in March 16, 2001. Overall, 

Table 2 shows that the average difference between radio station top ten lists declined in 

our time period for nine out of twelve formats; these include Adult Contemporary, Active 

Rock, Adult Alternative, Alternative, CHR Pop, CHR Rhythm, Hot Adult Contemporary, 

Jazz, and Rock. Average diversity for top 10 songs increased in the remaining formats: 

Country, Urban AC, and Urban. These changes are statistically significant with 99% 

confidence except for Rock and Urban; these are statistically significant with 95% 

confidence. The overall changes for within format song diversity are more modest; we 

find that the average distance across all pairs within the same format in March 1996 is 

6.51, which declines approximately 2.4% to 6.35 in March 2001.2

We should note that of the three categories that showed an increase in song 

diversity between 1996 and 2001, two of them, Country and Urban, had the two smallest 

averages of distance for 1996. Thus stations in Country and Urban had relatively more 

uniform playlists among formats in the earlier time period for our sample. Their shift 

toward more diversity appears to place them closer to the others in terms of diversity, 

although Country, with a distance measure of 5.94, still appears to be slightly less diverse 

than most of the other formats. One additional point here is that the relatively large 

number of Country stations in our sample (and in the populations of stations) is an 

important factor why the overall decline in distance appears more modest than for the 

nine individual cases where distance declines. 

 

2

 This change is statistically significant with 99% confidence. 
12

As we noted above, we also compare songlists between radio stations in similar 

formats, such as Adult Contemporary and Hot Adult Contemporary. In many cases, 

however, radio stations in different formats have no top 10 songs in common. For 

instance, there will be no top ten Jazz song played on any Country station. Thus, for 

many format pairs, our distance measure yields 10 (meaning no top 10 songs in 

common). For our purposes at the moment, we focus only on relatively similar formats 

and discard format pairs that are highly dissimilar.3

 

Table 3 

Average Distance Across Selected Formats 

 

3

 We therefore ignore for the moment those format pairs whose average distance is equal or higher than 

9.5. 

Formats March 1996 March 2001 

Adult Contemporary Hot Adult Contemporary 8.21 9.06 

Active Rock Alternative 7.76 7.40 

Active Rock Rock 8.05 7.30 

Adult Alternative Alternative 8.80 9.37 

Adult Alternative CHR Pop 9.45 9.47 

Adult Alternative Hot Adult Contemporary 9.54 8.96 

Alternative CHR Pop 9.35 9.44 

Alternative Rock 8.23 8.33 

CHR Pop CHR Rhythm 8.84 8.49 

CHR Pop Hot Adult Contemporary 7.83 8.11 

CHR Rhythm Urban AC 8.21 9.41 

CHR Rhythm Urban 7.40 7.85 

Urban AC Urban 6.76 8.61 
13

 Table 3 presents the results of comparing radio stations across similar formats. 

Seven of the thirteen cases displayed show statistically significant increases in the 

average difference (more diversity) between top ten playlists. These format pairs 

include: Adult Contemporary / Hot Adult Contemporary, Adult Alternative / Alternative, 

Alternative / CHR Pop, Alternative / Rock, CHR Pop / Hot Adult Contemporary, CHR 

Rhythm / Urban AC, CHR Rhythm / Urban, and Urban AC / Urban. Two cases, Adult 

Alternative / CHR Pop and Alternative / Rock, show no statistically significant change. 

The remaining four format pairs show statistically significant reductions in song 

diversity, suggesting that playlists in Active Rock / Alternative, Active Rock / Rock, 

Adult Alternative / Hot Adult Contemporary, and CHR Pop / CHR Rhythm are sharing 

more songs in common now than in 1996. 

In general, the differences between these averages for similar but different format 

pairs show changes of less magnitude than those displayed in Table 2. Of course, we 

remind the reader that we’ve excluded all format pairs from our analysis here that have 

average differences greater than 9.5. Together, however, Tables 2 and 3 suggest that 

diversity may have declined between stations of the same format, while rising somewhat 

for stations across different formats. When we compute the average measure of diversity 

for our entire sample, we find that the overall diversity has increased very slightly, from 

9.26 to 9.32, only 0.74%.4

 Song diversity looks very stable overall, with some significant 

changes occurring within formats and across some format pairs. 

 

4

 Here we include all stations pairs, even those with categories that have no overlapping songs. This has a 

strong effect of raising the average and lowering the difference between the time periods. 
14

We use the distance function in a panel regression to determine the causes of 

these changes in diversity. In particular, we examine the role that market structure may 

have played, with particular focus on the consolidation of ownership that resulted from 

changes in ownership rules under the Telecom Act in 1996. In addition, we study the 

extent to which diversity reductions within formats reduce the alternatives available to 

listeners. 

To answer these questions we estimate a linear model of the change in distance 

between radio pairs using our R&R data. To do this, we select only those portions of our 

data where each radio station appears in both our selected time periods, giving us 174 

stations. We then compute the percent change of distance across our time period for all 

possible pairs of these 174 stations. 

We regress the percent change in distance (between top ten playlists of station 

pairs) on a set of variables indicating the status of format, market, and ownership between 

station pairs.5

 Our set of variables includes the following: an indication of whether or not 

both stations are within the same format (Same format); whether both stations broadcast 

within the same market or city (Same city); whether both stations share the same owner 

(Same owner); whether both stations share the same format and broadcast in the same 

city (Same format and city); whether both stations share the same format and owner 

(Same format and owner); whether both stations share same owner and broadcast in the 

same market (Same owner and city); whether either station has changed ownership over 

the time period (Change in ownership); whether there has been a change in ownership for 

 

5

 We set each variable to 1 or 0 to indicate whether or not a particular condition is satisfied. For example, 

the variable “Same format” is set to 1 if both stations in a pair have the same R&R format; otherwise it is 

set to 0. 
15

either station within a pair of stations sharing the same format (Change in ownership for 

pair in same format); whether two stations switch from separate to common ownership 

(Change from different to common ownership); and, finally, whether two stations within 

the same format switch from separate to common ownership (Change from different to 

common ownership within the same format). Table 4 summarizes our results. 

Table 4 

OLS Regression on Percent Change in Distance Between Radio Playlists, 1996-2001 
16

 We find that the variable indicating a station pair within the same format is 

significance with 99% confidence. The value on the coefficient suggests that song 

diversity between two top ten lists has declined between March 1996 and March 2001 by 

approximately 4%. However this does not appear to suggest that listeners in a given 

market have less choice when switching among stations of similar formats. The 

coefficient here suggests that diversity has grown significantly among stations within the 

same format and within the same city. Thus stations within the same R&R formats 

competing within the same market appear to differentiate themselves to appeal to their 

listeners. 

Coefficients Value t Value 

Intercept 2.12** 4.499 

Same format -4.16** -2.905 

Same city 0.84 0.713 

Same owner 0.33 0.368 

Same format and city 

 

11.48* 1.931 

Same format and owner -4.46 -1.607 

Same owner and city 0.43 0.155 

Change in ownership -1.04* 0.043 

Change in ownership for pair in 

same format 

11.46** 7.195 

Change from different to common 

ownership 

-0.18 -0.175 

Change from different to common 

ownership within the same format 

3.38 1.034 

Degrees of Freedom 14179 

R-Squared 0.009 
17

The role that concentration plays appears to be less clear. The variables we have 

indicating concentration or changes in ownership have different signs, muddying the 

overall story. The variable indicating the same owner between two station within the 

same format has a negative sign and is significant with 90% confidence.6

 Further, a 

variable indicating a change in ownership (but not necessarily an increase in 

concentration) leads to a slight, but statistically significant reduction in format diversity. 

This variable is for change in ownership for either of the two stations in a pair, regardless 

of whether or not they belong to the same city or format. However, our variable 

indicating ownership change for station pairs within the same format is strongly 

significant and positive, suggesting increases in diversity. Neither variable directly 

related to consolidation (change from different to common ownership) is statistically 

significant. 

Conclusion 

 We investigate the change in diversity among playlists within the radio industry 

since the passage of the Telecom Act in 1996. For this purpose we introduce a 

straightforward measure of diversity. Overall, we found that song diversity, whether 

measured as the number of unique songs or the difference between top ten playlists has 

remained stable between March 1996 and March 2001. While playlists for stations 

within the same format have grown slightly more uniform across local markets, playlists 

for same format stations competing in the same local market have diverged, so that 

 

6

 Thus it is not quite as statistically significant as the other variables we have discussed. 
18

listeners in local radio markets may have experienced increasing song diversity even 

absent an increase in R&R radio formats. 

We have not yet concluded how concentration in ownership affects playlist 

diversity. We speculate that concentration may be partly responsible for more uniformity 

for stations within formats and more diversity between formats. Changes in diversity 

may also stem from exogenous changes in market conditions that affect all owners 

simultaneously. Further, changes in ownership among stations within a format have led 

to increases in playlist diversity. Our results at this time suggest that recent consolidation 

has played very little role in playlist diversity, although this might not be the case in 

smaller markets, which are not represented in our sample. 

Technical Appendix 
19

 Proof of Proposition One: While 0 ≤ k is obvious, we must prove 

k ≤ m − | i − j | . First, assume that i = j . Clearly, | k ≤ m = m − | i − j . Now, let i ≠ j . 

Without loss of generality, we assume that i > j , and consider i characteristics such that 

an = bn . Note that there are at most j number of characteristics such that n n n a = b = c , 

and there are at most m − i characteristics such that n n n a ≠ b = c . Thus, 

k ≤ m− | i − j | = j + (m −i) . 

Q.E.D. 

 Proof of Proposition Two: When n = 1, . nd min = ndmax = 0 Now, assume that 

n >1. We consider two cases, m = 1 and m >1. 

Case 1: m = 1. We have n cases ) (i i X x which can take on a value of 0 or 1 and 

k objects such that 1 xi = and n − k objects such that 0 xi = . 

 Lemma 1: When the dimensionality m = 1, the nominal (analogous degree of) 

diversity in the binary system is given by ) nd = k(n − k , where k is the number of 

objects that have the same characteristic values. 

Proof of Lemma 1: Let k be the number of objects with characteristic values 

1. x1 = x2 = Κ xk = Note that we originally designated these objects as X X Κ Xk , , 1 2 . 

Thus, there are n − k number of objects Xk Xn , , +1 Κ such that 0 , , xk+1 Κ xn = . Notice that 

∑ ∑ = =

− = −

n

j

j k j

n

j

x x x x

1 1

1 | | | | and ∑ ∑ = =

+ − = −

n

j

j n j

n

j

k x x x x

1 1

1 | | | |. Therefore, 

| | / 2 ( ).

1 1

nd x x k n k j

n

i

n

j

= ∑∑ i − = − = =Q.E.D.
20

 As we stated in Lemma 1, ) nd = k(n − k , where n is given, and 0 ≤ k ≤ n. Noting 

that δnd δk = n − 2k , the function is maximized when k n

2

1 = . Note that when n is even, 

k is an integer, and 2

max 4

1 ) 21 ( 21 nd = k(n − k) = n n − n = n . If n is odd, the closet possible 

k to n

2

1 is ( 1) 21

n − or ( 1) 2

1

n + . In either case, ( 1). 4

1 ( 1) 21 ( 1) 21 2 nd = n + n − = n − This 

represents the maximum (nominal) diversity of the system when n is odd. However, if 

k is not n +1 or n −1, then k = ± q where q is a natural number greater than 1, and 

( 1). 4

1 ( ) 41 2 2 2 nd = n − q < n − Clearly, 0 nd min = when k = n or k = m . 

Case 2: m > 1. Now we consider the case where m > 1. We begin by noting that 

∑∑∑ ∑∑ ∑∑ === == = =

= − = − + + −

n

i

n

j

j im jm

n

i

n

j

m

k

n

i

n

j

ik jk i nd x x x x x x

1 1

1

111 11

1 | | / 2 | | / 2 Κ | | / 2 . It is then 

immediately clear that 2 2

4

1

4

1 nd ≤ Κ n + + n when n is even; 

( 1) 4

1 ( 1) 41 2 2 nd ≤ n − +Κ + n − when n is odd; and ) 41

( 2 nd = m n when n is even and 

( 1)) 4

1

( 2 nd = m n − when n is odd. 

Q.E.D.

 
21

Bibliography 

Alexander, Peter, 1997, ‘Product Variety and Market Structure: A New Measure and Simple 

Test,’ Journal of Economic Behavior and Organization, 32, 207-214 

Anderson, Simon and Coate, Stephen, 2000, ‘Market Provision of Public Goods: The Case of 

Broadcasting’, NBER Working Paper No. W7513. 

Becker, Gary and Murphy, Kevin 1993, ‘A Simple Theory of Advertising as a Good or a Bad,’ 

Quarterly Journal of Economics, 108 (4), 941-964 

Beebe, Jack H, 1977. ‘Institutional Structure and Program Choices in Television Markets,’ 

Quarterly Journal of Economics, 91 (1), 15-37. 

Berry, Steven and Waldfogel, Joel, 2001, ‘Do Mergers Increase Product Variety? Evidence from 

Radio Broadcasting,’ Quarterly Journal of Economics, 116 (3), 1009-25. 

Gabszewicz, J., Laussel, Didier and Sonnac, Nathalie, 1999, ‘TV-Broadcasting Competition and 

Advertising’, CORE Discussion Paper 2000/6 

R&R Magazine

Schmalensee, R., 1978, ‘Entry Deterrence in the Ready-to-Eat Breakfast Cereal Industry,’ Bell 

Journal of Economics, 9, 305-327 

Steiner, P.O., 1952, ‘Program Patterns and the Workability of Competition in Radio 

Broadcasting,’ Quarterly Journal of Economics, 66 (2), 194-223