The demand for access for local telephone service is linked to the demand for usage of service. The ``service'' can be many varieties and bundles of telecommunication services and features. So some ask, what price should be charged for access and will the demand for access support that price? Mitchell and Vogelsang summarize, when network membership reaches near 100 percent of the customer base the usage externality is greater than the network externality (for access) and so you should charge below the marginal cost for access to the network, and make a profit on the usage price (price per call).[6] Others say buyer diversity leads to this approach being optimal.[14] Although we do not try to answer the question, ``what price should be charged for access'', we are interested in the question, ``what is the demand for access.'' We needed a study which examined the demand for access based on social and demographic characteristics, and not complex service offerings.
We briefly list some studies that have examined the issue of demand for access. The first 5 studies are reviewed and summerized in Lester Taylor, 1994 and the later two are newer studies done outside the U.S.[15][16][4] Of the collection, Perl's 1983 study with 1984 revision makes the most extensive use of sociodemographic data.
In our iterative game model, we make use of the Perl studies.[8][9] Perl has several varieties of an econometric model. He uses a discrete choice framework (logit model) to have or not have a telephone. The choice is related to monthly cost of service, income and many socio-demographic factors. The framework produces the logarithm of the odds of having a telephone to a list of variables and their estimated coefficients and asymptotic standard errors.
Perl has several varieties of his model. One includes a price variable for measured use service as an option to the flat rate price. Another model excludes the variables for measured use service. He states the results of the two models are similar.
To focus on access, we selected his model for Flat Rate Access Areas. These are areas where there is no measured use option available to subscribers. This model is stated in Figure 25, page 70 of the report.
Perl uses Census Track Household Data from 1980. We use Census Track Household Data from 1990, and have matched this to the 14 study service areas. The 14 service areas have a census of about 200,000 people in the urban region and 18,000 people in the rural region.
The model is represented in the following syntax. Here Pr is
the probability of having a telephone. Also, a is the Perl
model's intercept and 
are the coefficients to the
vector of social-demographic characteristics, 
.
In our use of the model, the values of all of the social-demographic characteristics are selected except the value for the flat rate price parameter. We leave that as an unknown. The equation is then reduced to the following form.
becomes
Where y is a compressed intercept of all the known parameters*coeficients plus the Perl intercept. The expression can also be written as follows.
This produces the probability of subscribing for the study service area or the penetration rate. Perl's model can predict probabilities of access by study areas and by states.
The above probability function is used to develop revenue functions for the reaction functions that are used in the interactive game model.
The reaction functions in the game model determine market quantities and market price. Perl's equation is then represented as an inverse demand function.
Here, 
and 
are the number of access lines for Provider 0 and
Provider 1.
The b is the coeficient for flat rate price in the Perl model.
The y is the compressed intercept. The interative game model
which is discussed in the next section, selects the quantites
that will be produced under described market conditions.
