**On the Substitutability of Local Newspaper, Radio, and Television
Advertising in Local Business Sales**

C. Anthony Bush, Ph.D.

Chief Economist

Office of General Counsel

**Executive Summary**

A current policy issue is whether there is a single local media market
or several distinct local markets for newspaper, radio, and television
advertising. An important step in defining a market is the estimation of
elasticities of demand. In this study we present a model of local
business behavior in purchasing advertising for use in sales activities.
Using reported data on local radio and television advertising revenue
contained in the 2001 BIA's *Master Access Database* and using data from
the Newspaper Association of America on retail ad expenditures,
estimates of elasticities of substitution, ordinary own- and cross-price
elasticities are derived for a representative local business
establishment. The estimated elasticities of substitution and the
estimated ordinary cross-price elasticities suggest weak
substitutability between local media. In addition, the ordinary demand
elasticity for a retail ad in a newspaper is approximately unity and
negative. Demands for both local radio and local television ads are
inelastic. Finally, the data support the specified model of local
business advertising. An important caveat to these results is that
varying degrees of measurement error are associated with local radio
revenue and revenue from retail ads in newspapers. Due to these
limitations inherent in the underlying data, the results of this study
cannot be considered conclusive. The results, however, are consistent
with economic theory.

**Introduction**

Section 202 (h) of the Telecommunications Act of 1996 directs the
Federal Communications Commission to review its broadcast ownership
rules every two years in light of competitive developments. In
conducting such reviews, the Commission may need to consider the extent
to which established local media compete with each other for advertising
dollars. The specific policy concern is whether there is a single local
media market or several distinct local markets for newspaper, radio, and
television adverting. This study is intended to contribute to that
evaluation.

An important step in defining a market is the estimation of elasticities
of demand. Therefore, in this study, we estimate elasticities of
substitution for local newspaper, local radio, and local television
advertising media. Ordinary own- and cross-price elasticities of demand
are also estimated.

We note that this study evaluates the extent of substitutability of the
three largest local media -- television, radio, and daily newspapers. We
do not attempt to address whether cable television or other advertising
vehicles such as direct mail and outdoor advertising compete with local
television, radio and daily newspapers for local advertising dollars.

**Literature**

The literature on inter-media substitutability in advertising can be
divided into two broad categories. First, there is national advertising
that is associated with national sales of product/services. Second,
there is local media advertising by local businesses. Several authors
have studied national advertising. McCullough and Waldon (1998) examine
the substitutability of network advertising and national spot
advertising. They assume an aggregate sales function and rely on duality
in order to specify the share equations of a translog cost function.
Three share equations are considered: (1) the share of network
advertising, (2) the share of national spot television advertising, and
(3) and the share of a composite of all other advertising forms. Using
McCann-Erickson which spans the years 1960 to 1994, the authors estimate
Morishima elasticities of substitution. McCullough and Waldon find that
television network advertising and national spot television advertising
are substitutes.

Silk, Klein, and Berndt (2001) use a translog model in their evaluation
of inter-media substitutability. In addition, their analysis permits for
the complementary use of media in national sales. Their translog model
represents the advertising costs of national sales. The share equations
of the model are: (1) direct mail, magazines, newspapers, spot radio,
network television, network radio, spot television, and outdoor. The
parameters of the model are estimated based on national data for the
period covering 1960 to 1994. Estimates of own- and cross-price
elasticities for the various media are presented. Silk, Klein, and
Berndt conclude that demands for the various media are inelastic. In
addition, they suggest that weak cross-media effects are consistent with
industry practices in which media planning is conducted as a multistage
decision process. In this process inter-media choices are made primarily
on strategic and creative grounds. That is initial media buys are likely
to be a mix of media. Price-sensitivity is shown in subsequent
intra-media comparisons.

Sheldon, Jewell, and O'Brien (2000) investigate media substitutability
and economies of scale in advertising. These authors use a translog cost
function to model advertising cost of firms that manufacture beer. The
inputs to the sale of beer are print, television, and radio. Both the
translog function and media share equations are simultaneously
estimated. Their data are on U.S. beer firms. The data are quarterly and
cover the period 1983 to 1993. Morishima elasticities of substitution
and price elasticities of demand are estimated. Sheldon, Jewell, and
O'Brien find that all advertising media are substitutes in the selling
of beer. In addition, evidence of diseconomies of scale in advertising
is presented.

There is some research on inter-media substitutability in local
advertising markets.

Ekelund (1999) et al. evaluate whether a market for radio services by
advertisers exists independently of other local advertising markets.
Their method for identifying a radio market is based on the *DOJ Merger
Guidelines.* Their approach consists of determining whether conditions
exit such that a hypothetical monopolist could profitably and optimally
raise price. To this end, Ekelund compares a calculated Lerner Index for
radio with the reciprocal of the estimated own price elasticity of
demand for radio. The issue of media substitutability arises in their
specification of the functional from of demand. The authors estimated a
double-log model with the log of revenue as a dependent variable. Bona
fide explanatory variables are the prices of radio, television,
newspaper, and total retail sales.

The unit of observation in this cross sectional study is an Arbitron
market from BIA's *Master Access Database*. This BIA database also
provided information on total radio revenues or expenditures by firms on
radio in an Arbitron Market. All data are from the year 1995. The price
of radio and television are taken from the SQAD database. The prices for
both radio and television are both cost per rating point ("CPP").
Newspaper advertising prices are based on the price of a one-inch,
black-and-white, one day advertisement in \[Arbitron\] markets. These
price data are from the *Newspaper Advertising Source.*

Ekelund et al present estimates of own-price and cross-price
elasticities. Comparing measures of operating margins, e.g., cash flow,
and estimated own-prices elasticity of-2.101, these authors concluded
that the radio market constitutes an antitrust market. On the issue of
inter-media substitutability, demand cross-price elasticities are found
to be significant at the ten percent level.

In a separate paper, Ekelund and the same co-authors conduct an
analogous analysis of television. Again, the 1995 BIA *Master Access
Database* is used to identify revenues from Designated Market Areas
("DMA"). Both television and radio ad price is the cost per rating point
from SQAD. A double-log specification is used, where the log of
television advertising revenue or expenditure is the dependent variable.
Explanatory variables are the log of retail sales, the price of a
television ad, the price of a radio ad, and the price of a one-inch,
black-and-white, one day advertisement in DMA. Own- and cross- price
elasticities are estimated. Both the cross-price elasticities of demand
for radio and newspaper are positive, and the radio cross-price
elasticity is positive at a five percent level of significance. However,
in this analysis their calculated Lerner Index and the reciprocal of
their estimated elasticity does not suggest that a hypothetical
monopolist could profitably and optimally increase advertising prices.

The work of Ekelund et al. is limited in its generality for several
reasons. Due to data limitations Ekelund could not differentiate between
national radio (television) buys and local radio (television) buys
within an Arbitron (DMA) market. As Silk et al. (2001) argue,
aggregating national and local market demand for media may hide
different patterns and levels of inter-media
substitutability/complementarity among more finely disaggregated
components. In addition, our examination of the Newspaper Advertising
Source suggests that the explanation of newspaper ad price is
incomplete. The authors do not provide the details on which newspapers
are included in the geographic area of analysis. Also details on the
aggregation of newspaper prices into a single newspaper price are not
explained. The Newspaper Advertising Source data suggest that numerous
newspapers could have been included in the construction of the composite
price for local newspapers. Alternatively, a single newspaper's price
could have been used.

**Theoretical Framework**

Our focus is on the use of media by local businesses. Following Silk et
al. (2001) we hypothesize that inter-media buys by local firms are made
on strategic grounds and that a mix of media is used in advertising to
local consumers.

We began by developing the derived demand for broadcast television,
radio, and newspaper ads in a local market. Suppose that representative
firm A provides product/service
![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"} in a local market. For simplicity of
analysis, we assume that the geographic market for product
![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"} or area of geographic distribution of
![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"} is the same as the geographic market for
television, radio, and newspaper ads. That is the geographic market for
![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"}, the local television ad market, the
local radio ad market, and the local newspaper ad market all coincide.
In these local media markets, firm A is a price taker, and, given media
ad prices and the firm's media budget, firm A employs these local media
to sell![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"}.

We assume that all goods/services markets are competitive and that firms
are Bertrand competitors. Entrepreneurs of firms, e.g., firm A, regard
sales, however, as random variables. Sales of firms are random because
consumers face uncertainty. Given perfect information on prices and no
transportation costs, consumers must also decide where to spend.
Consumers' choices of firms to patronize are made in accordance with
consumer convenience in daily routine and with the degree of uncertainty
in daily events.

We assume that all firms advertise under the belief that advertising
reduces variability in sales and increases expected sales by reminding
consumers of the existence of the firm. In this model newspaper, radio,
and television are complementarily substitutable. Firm A uses a mix of
media in its outreach to the targeted demographic group of potential
buyers. If firm A buys television, it also buys some radio and some
newspaper. As relative media prices change or as the effectiveness of a
particular medium becomes know, firm A substitutes to a particular
medium without necessarily abandoning the remaining media.

Following Veblen (1919), capital and labor employed in advertising
(marketing) and in manufacturing are embedded in the constant return to
scale production function of the firm. The unit of output, from the
production of good ![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"}, is a *salable* good with specific
characteristics, including shape, color, material composition, and
consumer outreach through advertising (marketing) per unit for the
period. Since there is constant returns to scale in the production of
good ![](media/image1.wmf){width="0.1388888888888889in"
height="0.1388888888888889in"}, there is a constant unit (marginal)
cost, denoted ![](media/image2.wmf){width="0.16666666666666666in"
height="0.25in"} for firm A. With Bertrand competition the market price
is![](media/image3.wmf){width="0.5416666666666666in"
height="0.2361111111111111in"}.[^1] Profits of firm A are
![](media/image4.wmf){width="2.3465277777777778in"
height="0.2361111111111111in"}.

We assume that the entrepreneur of firm A maximizes expected profit and
that the entrepreneur of firm A prefers greater income from employment
of her capital and labor to less income. Thus, firm A maximizes
![](media/image5.wmf){width="1.7916666666666667in"
height="0.2361111111111111in"}.[^2] Expected sales
are![](media/image6.wmf){width="2.7083333333333335in"
height="0.2638888888888889in"}, where
![](media/image7.wmf){width="0.44375in" height="0.19375in"} and
where![](media/image8.wmf){width="0.2222222222222222in"
height="0.25in"}, ![](media/image9.wmf){width="2.9166666666666665in"
height="0.2222222222222222in"}, is the quantity of medium
![](media/image10.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"} purchased by firm A. The
parameter,![](media/image11.wmf){width="0.16666666666666666in"
height="0.25in"}, is the base quantity of advertising of medium
![](media/image10.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}, and the parameter
![](media/image12.wmf){width="0.4722222222222222in" height="0.25in"}is
the share of expenditures on medium
![](media/image10.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}. The problem of firm A is

![](media/image13.wmf){width="3.19375in" height="0.34652777777777777in"}
subject to ![](media/image14.wmf){width="0.9166666666666666in"
height="0.3055555555555556in"}

The advertising budget of firm A is
![](media/image15.wmf){width="0.2361111111111111in"
height="0.2361111111111111in"} which is in total outlays and which is
embedded in the constant per unit cost of a *salable* product. The price
per unit of medium ![](media/image10.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}
is![](media/image16.wmf){width="0.19375in" height="0.25in"}. Optimizing
expected sales is simply the problem of optimizing the Stone-Geary
utility function. The solution to this problem is the well known Linear
Expenditure System ("LES"). Expenditures on medium
![](media/image10.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"} are

![](media/image17.wmf){width="1.5416666666666667in"
height="0.3194444444444444in"} where
![](media/image18.wmf){width="1.4027777777777777in"
height="0.2638888888888889in"}, and
![](media/image19.wmf){width="1.19375in"
height="0.2638888888888889in"}[^3].

**Empirical Specification and Estimation Technique**

Leser's Transformation of the Linear Expenditure System ("LES")[^4]
permits us to directly estimate elasticities of substitution. Leser's
transformation of the LES is

![](media/image20.wmf){width="1.5in" height="0.4166666666666667in"},
where

> ![](media/image21.wmf){width="1.0555555555555556in"
> height="0.2638888888888889in"}
>
> ![](media/image22.wmf){width="1.5694444444444444in"
> height="0.5277777777777778in"}
>
> ![](media/image23.wmf){width="1.2361111111111112in"
> height="0.4166666666666667in"}

An observation, representative firm in a local market, is denoted
by![](media/image24.wmf){width="9.652777777777778e-2in"
height="0.16666666666666666in"}. The price of medium
![](media/image25.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}
is![](media/image26.wmf){width="0.2222222222222222in" height="0.25in"},
and expenditure on medium
![](media/image25.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}
is![](media/image27.wmf){width="0.19375in" height="0.25in"}. The sample
mean of expenditures on medium
![](media/image25.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}
is![](media/image28.wmf){width="0.19375in"
height="0.2638888888888889in"}. The sample mean values of the price of
medium ![](media/image25.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"} and total expenditures are
![](media/image29.wmf){width="0.2222222222222222in"
height="0.2638888888888889in"}and![](media/image30.wmf){width="0.6111111111111112in"
height="0.25in"}, respectively. Let
![](media/image31.wmf){width="0.20833333333333334in"
height="0.2638888888888889in"}be the mean quantity of medium
![](media/image25.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}, and
![](media/image32.wmf){width="0.625in" height="0.5in"}. The average
budget share at this coordinate set is
![](media/image33.wmf){width="0.9305555555555556in"
height="0.4722222222222222in"}. The parameter
![](media/image34.wmf){width="0.2361111111111111in"
height="0.2777777777777778in"}is the elasticity of substitution between
medium ![](media/image25.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}
and![](media/image35.wmf){width="0.1388888888888889in"
height="0.20833333333333334in"}. The parameter
![](media/image36.wmf){width="0.19375in" height="0.25in"} is the
marginal expenditure share. In this system, homogeneity, symmetry, and
adding up restrictions are imposed. Three equations are simultaneously
estimated for this derived demand system:

Due to singularity of the covariance matrix, which is a result of the
adding-up restriction, we estimate using the econometric technique of
Dhrymes (1984), (1987) and (1994)[^5]. In this procedure, different
variables can appear in different equations, and it not necessary to
drop an equation from the system. After estimation, own price
elasticities are calculated at sample means.

**Data**

Revenue data are from the 2001 BIA Master Access Database. Revenues are
reported for television by DMA. Radio revenues are listed by Arbitron
Radio Markets which are contained in DMAs. At the time of the work of
Ekelund et al. the BIA data contained an unknown mix of national and
local advertising revenue for broadcast media. The 2001 BIA database
contains, however, local advertising revenues for both television and
radio broadcasting[^6].

We took a random sample of DMAs. The sample contains 45 DMAs, and the
DMAs are listed in Appendix A. We assume that local radio revenues of
Arbitron Markets within a DMA are total local radio revenues for the
DMA. Spot Quotation and Data, Inc. ("SQAD") data are the source of both
local radio and television prices. Both radio and television prices are
in units of cost per point ("CPP")[^7].

Newspaper data are gathered and constructed from several sources. First,
the Newspaper Association of America reports categories of newspaper
advertising expenditures/revenue for the year 2000. The categories are:
(1) national, (2) retail, and (3) classified advertising
expenditures[^8]. Retail advertising expenditures of \$21,409 million
are allocated across the entire universe of DMAs. Thus, retail
advertising expenditure for a DMA is the product of \$21,409 million and
the allocation factor for that DMA. The allocation factor for a DMA is
the ratio of the population over 16 years of age in a DMA to the
population of the United States that is over 16 years of age[^9].
Second, newspaper retail prices are from the *Newspaper Advertising
Source*. Following Ekelund et al. (1999), price is the charge for a
one-inch, black-and-white, one-day advertisement i.e., a Standard
Advertising Unit ("SAU"). We used Monday through Friday-Saturday prices.
For every DMA of our sample, we manually collected these price data on
all identifiable newspapers. Since the number of newspapers varies by
DMA, our measure of local retail price for a DMA is the mean price for
newspapers in the DMA[^10].

Our theory predicts the use of local advertising by a local business in
the sale of its goods and/or services. This implies that we must
translate local media revenues in a DMA into media expenditures of a
representative local business in the DMA. For a given DMA, newspaper
retail revenue is divided by business establishments in that DMA, and
the result is local newspaper expenditures by a representative local
business[^11]. Expenditure on local radio advertising by a
representative local business is the result of dividing local radio
advertising revenue by business establishments in that DMA. The
expenditure of a representative local business on local television
advertising is the local television revenue in the DMA divided by the
business establishments in the DMA.

Two dummy variables are created to control for competitive effects that
are associated with the size or rank of a DMA. A dummy variable is
assigned the value of one when a DMA's rank is less than or equal to 10
(top 10 DMAs), and, the variable is zero, otherwise. A second dummy
variable is assigned the value of one when the rank of the DMA is
between 11 and 50, and, the variable is zero, otherwise.

**Results**

Economic theory predicts that elasticities of substitution can vary from
zero to infinity. For our function of expected sales, an elasticity of
zero would indicate that there is no substitutability between two media
since an elasticity of substitution[^12] is a measure of pair-wise
substitutability. Alternatively, an elasticity of substitution of
infinity indicates that two media are perfect substitutes, e.g.,
television is a perfect substitute for radio.

Our results suggest weak substitutability between local media in the
sales activities of local businesses. Specifically, with respect to the
three media pairs we studied, we find: [First]{.underline}, the
elasticity of substitution between newspaper retail ads and local radio
ads is 1.16936. [^13] Compared to the theoretical limit of infinity for
perfect substitutability this number is very small but statistically
significant. [Second]{.underline}, the elasticity of substitution
between newspaper retail ads and local television ads is 0.91459. This
number is also relatively small but statistically significant.
[Third]{.underline}, the elasticity of substitution between local radio
and local television is 0.3094, and this elasticity is not statistically
different from zero. These results are presented in Table 1 of Chart A.

Ordinary own- and cross-price elasticities are calculated at sample
means. The results are presented in Table 2 of Chart A. Ordinary
own-price elasticities of demand are negative. The ordinary own-price
elasticity for a retail ad in a newspaper is -1.0406. Demands for both
local radio advertising and local television advertising are inelastic.
Local radio's own-price elasticity is -0.8245, and the own-price
elasticity for television is -0.7960. Moreover, ordinary-cross price
elasticities of demand also suggest weak substitutability and suggest
that several media are gross complements[^14]. The cross price
elasticity between newspaper retail ads and local radio ads is 0.0178,
while the cross-price elasticity between local radio and newspaper
retail ads is 0.0981. The cross-price elasticities for newspaper retail
ads and local television ads are negative. In addition, the cross-price
elasticities for television and radio are negative. All ordinary
cross-price elasticities are presented in Table 2 of Chart A.

There are certain limitations associated with this study as a result of
the underlying data that informs our study. Specifically, the study
contains varying degrees of measurement errors on certain variables.
First, local radio revenue within a DMA is incomplete because BIA does
not report revenue data for all radio stations but only for Arbitron
markets, which generally are the larger markets. Second, newspaper
retail expenditure in a DMA results from an allocation process that
assigns retail revenues to DMAs based on a DMA's share of population 16
years or older. This methodology is used because there does not appear
to be a source for newspaper retail revenues by DMA. In addition, the
mapping of Census demographic data into DMAs involves some judgment
because some counties are contained in multiple DMAs. Moreover, the
reach of some newspapers may extend beyond the assigned DMA, and
business establishments outside the DMA could have spent advertising
resources on newspaper ads which are assigned to the DMA. Nonetheless,
acknowledging the limitations of the data, the results do not appear
unreasonable or inconsistent with economic theory.

**Summary and Conclusion**

This study examines the substitutability of local newspaper, radio, and
television advertising in the sales activities of local businesses. A
local business within a DMA is hypothesized to maximize expected sales
by selecting an optimal mix of newspaper retail ads, local radio ads,
and local television ads. The expected sales function for goods and/or
services of the local business is a scalar multiple of the Stone-Geary
utility function, and the resulting derived demand for local media is
the Linear Expenditure System. Leser's transformation of the LES permits
the direct and linear estimation of elasticities of substitution. Since
the LES gives rise to a singular covariance matrix, the econometric
technique of Dhrymes (1984) and (1994) is used to estimating this
singular system of equations. A random sample of 45 DMAs is used in the
study. Local radio and local television data are taken from the BIA
Master Access Database. Newspaper retail revenues for DMAs are
constructed from data published by the Newspaper Association of America.

Estimates of elasticities of substitution, ordinary own- and cross-price
elasticities are derived for a representative local business
establishment. The estimated elasticities of substitution and the
estimated ordinary cross-price elasticities suggest weak
substitutability between local media. The elasticities of substitution
are relatively small, and the elasticity of substitution between radio
and television is not statistically different from zero. The ordinary
cross-price elasticities for newspaper retail ads and local radio ads
are small but positive. The ordinary cross-price elasticities for
newspaper retail ads and local television ads are negative. In addition,
the ordinary cross-price elasticities for local radio ads and local
television ads are negative. This suggests that local newspaper and
television ads are complementary inputs in the sales efforts of local
businesses. These results also suggest that local radio and television
ads are also complementary inputs.

The following caveat must be acknowledged when considering this study in
communications policy. There are limitations inherent in the underlying
data. For example, local radio ad expenditures are not total
expenditures on radio within a DMA because total local radio revenue is
not reported. In addition, local newspaper ad expenditures are
constructed through an allocation process that introduces some degree of
measurement error. The allocation process used in this paper assigns
retail newspaper advertising expenditures in each DMA based on a DMA's
share of population 16 years or older. The estimated elasticities are
not, however, inconsistent with economic theory and do not appear
unreasonable.

**References**

BIA's *Master Access Database*, 2001

Bush, Clarence A. "Generalized Inverse Estimation of Partial
Elasticities of Substitution:

A Complete Demand System with Exclusion Restrictions and Autoregressive

Errors." 1994. Working Paper No. 384. Rochester Center for Economic
Research,

University of Rochester, Rochester, New York.

Dhrymes, Phoebus J. and Samuel Schwarz. "On the Existence of Generalized
Inverse

Estimators in Singular Systems of Equations." *Journal of Forecasting* 6
(1987):

181-192.

Dhrymes, Phoebus J. *Autoregressive Errors in Singular Systems of
Equations.* Discussion

paper no. 257, Department of Economics, Columbia University, New York.
1984.

Dhrymes, Phoebus J. "Autoregressive Errors in Singular Systems of
Equations."

*Econometric Theory* 10 (1994): 254-285.

Ekelund, Robert B. Jr., George Ford, and John D. Jackson. "Is Radio
Advertising a

Distinct Local Market? An empirical analysis." *Review of Industrial
Organization*

14 (1999): 239-256.

Ekelund, Robert B. Jr., George Ford, and John D. Jackson. "Are Local TV
Markets

Separate Markets?" International Journal of the Economics of Business 7
(2000):

79-97.

Leser, C.E.V. "The Pattern of Australian Demand." *Economic Record* 38
(August 1958):

212-222.

Newspaper Association of America. See website
<http://www.naa.org/artpage.cfm?AID=1556&SID=1022>

Powell, Alan A. *Empirical Analytics of Demand Systems.* Massachusetts:
Lexington

Books, 1974.

Seldon, Barry J., R. Todd Jewell, Daniel M. Obrien. "Media Substitution
and Economies

of Scale in Advertising." *International Journal of Industrial
Organization* 18

(2000): 1153-1180.

Silk, Alvin, Lisa Klein, and Ernst R. Berndt. "Intermedia
Substitutability and Market

Demand by National Advertisers." Working paper 8624. National Bureau of

Economic Research, December 2001.

United States Census Bureau. *County Business Patterns*, 1997.

United States Census Bureau. *Census 2000.*

Veblen,Thorstein. *The Vested Interests and the State of Industrial
Arts.* New York, B.W.

Huebsch, 1919.

![](media/image37.wmf){width="6.209027777777778in"
height="9.304166666666667in"}![](media/image38.wmf){width="5.948611111111111in"
height="8.99375in"}

**Appendix 1: A Note on Estimating Leser's Transformation of the LES**

In the procedure of Dhrymes (1987) and (1994), there is a condition
requiring each variable of the system to appear in at least two
equations. Except for the variable
![](media/image39.wmf){width="1.2083333333333333in"
height="0.4166666666666667in"}, no equation of Leser's Transformation of
the LES contains a set of variables common to any other equation. Bush
(1994) provided specific conditions where Leser's Transformation of the
LES can be estimated using the generalized inverse estimation procedure.
Through the requirements that partial elasticities of substitution be
symmetrical, i.e., ![](media/image40.wmf){width="0.6111111111111112in"
height="0.2777777777777778in"} and that the constraints imposed on the
parameters of the system satisfy the adding-up condition, each variable
of the transformed system appears in at least two equations of that
system. This is demonstrated through Lemma 1 and Proposition 1.

**Lemma 1.** Let ![](media/image41.wmf){width="1.5555555555555556in"
height="0.5138888888888888in"}where
![](media/image42.wmf){width="0.9027777777777778in"
height="0.4583333333333333in"} and ![](media/image43.wmf){width="0.75in"
height="0.2777777777777778in"}

Then ![](media/image44.wmf){width="1.8611111111111112in"
height="0.2638888888888889in"} where
![](media/image45.wmf){width="1.44375in" height="0.3333333333333333in"}

Proof.

![](media/image46.wmf){width="3.69375in" height="0.5277777777777778in"}

![](media/image47.wmf){width="2.125in" height="0.5138888888888888in"}.

![](media/image48.wmf){width="1.7777777777777777in"
height="0.2638888888888889in"} q.e.d.

**Proposition 1.** Suppose that we have Leser's Transformation of the
LES.

![](media/image49.wmf){width="1.4305555555555556in"
height="0.4166666666666667in"} (1)

> where ![](media/image21.wmf){width="1.0555555555555556in"
> height="0.2638888888888889in"}

![](media/image22.wmf){width="1.5694444444444444in"
height="0.5277777777777778in"}

> ![](media/image50.wmf){width="1.19375in"
> height="0.4166666666666667in"}.

If

*i)* ![](media/image51.wmf){width="0.2361111111111111in"
height="0.2638888888888889in"}replaces
![](media/image52.wmf){width="0.2638888888888889in"
height="0.2638888888888889in"} in the
![](media/image53.wmf){width="0.1388888888888889in"
height="0.20833333333333334in"}th equation and
![](media/image54.wmf){width="0.16666666666666666in"
height="0.1527777777777778in"}is the parameter associated with
![](media/image51.wmf){width="0.2361111111111111in"
height="0.2638888888888889in"}in the
![](media/image53.wmf){width="0.1388888888888889in"
height="0.20833333333333334in"}th equation; *ii)* the adding-up
constraints are imposed on the parameters of the system; and *iii)*
![](media/image55.wmf){width="0.6111111111111112in"
height="0.2777777777777778in"} (elasticities of substitution are
symmetrical), then system (1) is preserved.

Proof.

Replacing ![](media/image56.wmf){width="0.2638888888888889in"
height="0.2638888888888889in"}by
![](media/image57.wmf){width="0.2361111111111111in"
height="0.2638888888888889in"} in equation
![](media/image53.wmf){width="0.1388888888888889in"
height="0.20833333333333334in"} and recognizing that
![](media/image57.wmf){width="0.2361111111111111in"
height="0.2638888888888889in"}now occurs [only]{.underline} in the
![](media/image58.wmf){width="9.652777777777778e-2in"
height="0.18055555555555555in"}th and
![](media/image53.wmf){width="0.1388888888888889in"
height="0.20833333333333334in"}th equations,

![](media/image59.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

![](media/image60.wmf){width="2.4305555555555554in"
height="0.3611111111111111in"}

![](media/image61.wmf){width="2.4027777777777777in"
height="0.3611111111111111in"}

![](media/image62.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

The adding-up constraints
![](media/image63.wmf){width="0.8194444444444444in"
height="0.2777777777777778in"} and
![](media/image64.wmf){width="0.6805555555555556in"
height="0.4166666666666667in"}Thus,

![](media/image59.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

![](media/image65.wmf){width="2.375in" height="0.3611111111111111in"}

![](media/image66.wmf){width="2.4583333333333335in"
height="0.3611111111111111in"}

![](media/image62.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

![](media/image67.wmf){width="0.20833333333333334in"
height="0.16666666666666666in"}

![](media/image59.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

![](media/image68.wmf){width="2.375in" height="0.3611111111111111in"}

![](media/image69.wmf){width="2.513888888888889in"
height="0.3611111111111111in"}

![](media/image62.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

by Lemma 1.

Since ![](media/image70.wmf){width="0.6111111111111112in"
height="0.2777777777777778in"},

![](media/image59.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

![](media/image71.wmf){width="2.375in" height="0.3611111111111111in"}

![](media/image72.wmf){width="2.5416666666666665in"
height="0.3611111111111111in"}

![](media/image62.wmf){width="8.333333333333333e-2in"
height="0.20833333333333334in"}

which is system (1). q.e.d

[^1]: We can also think of the firm setting price at the intersection of
    marginal cost and the minimum of longrun average total cost.

[^2]: Because of constant return to scale, realized sales increase the
    entrepreneur's income.

[^3]: Alan P. Powell, *Empirical Analytics of Demand* (Massachusetts:
    Lexington Books, 1974), 36-38.

[^4]: Ibid., 62-66.

[^5]: The 1994 paper is the published version of the 1984 working paper.

[^6]: The share of local revenue is reported for each DMA. Local
    television revenue is the product of the local share and total
    revenue. Shares of local revenue out of total revenue are provided
    for each radio market. Local radio revenue is the product of the
    local share and total radio revenue within the radio market.

[^7]: SQAD reports CPP prices for both radio and television by quarter,
    and we use 4^th^ quarter 2000 prices. Late news rates were used for
    television and evening rates were used for radio. The rates are for
    Adults 18+.

[^8]: Newspaper Association of America at website
    http://www.naa.org/artpage.cfm?AID=1566&SID=1002.

[^9]: The source of the population data is *Census 2000*, U.S. Census
    Bureau. Census 2000 population data are mapped into DMAs.

[^10]: Newspaper prices are presented by month. We used prices for
    mid-4th quarter (November) 2000.

[^11]: Business establishments in a county are from *County Business
    Patterns*, U.S. Census Bureau (1997). We mapped county business
    establishments into DMAs.

[^12]: Elasticities of substitution are technical parameters that reveal
    the shape or curvature of the expected sales function.

[^13]: We assumed symmetry, and therefore, the elasticity of
    substitution between local radio and newspapers retail ads is also
    1.16936.

[^14]: For the Linear Expenditure System all goods should a priori be
    gross complements. The data support the LES specification.