Mitchell uses the parameter estimates of Park's ultimate penetration equation, but imposes his own maturity path, which he neither defends nor supports with statistical evidence. The differences between the Comanor-Mitchell, Park exponential, Park linear, and Mitchell maturity paths are given in Table C-1.

Note that Mitchell's assumption of maturation is more conservative than either of Park's, but Mitchell continues to use Park's mature penetration parameter estimates, imposing his own slower maturation path--a totally indefensible procedure. If Park's mature penetration results are to be accepted, they can only be accepted in conjunction with his linear maturation path.

There are numerous other problems in applying the Park equation to Mitchell's universe of CATV systems. First, the sample Park utilizes is supposed to represent the environment in the top 100

markets. Mitchell uses results for the purposes of projecting penetration in all markets and outside the defined markets. Second, Park finds that the impact of educational stations exceeds the impact of independent stations--a dubious result given all statistics on relative viewing of the two types of outlets. The elasticity of penetration with respect to the educational station variable is 0.204--meaning that an increase in the number of educational stations from 0 to 1 will increase penetration by 20.4 percent (of its ex ante value). A similar increase in independent signals will increase penetration by only 14.5 percent. Finally, Park makes no allowance for local origination even though in a subsequent publication he has argued that ambitious local originations will lead to a substantial increase in penetration in the Dayton-Miami Valley area. Because the form of the penetration equation (and its maturation factor) is important in predicting cable system profitability, we shall examine each published demand equation's ability to predict actual penetration for a randomly drawn sample of cable systems from the Factbook.

Our sample of CATV systems was obtained by selecting a system at random from the 1972-1973 Factbook and choosing every twentieth system sequentially thereafter. In this manner, we collected data on 153 systems, but the data required for fitting the Park and Comanor-Mitchell demand equations were incomplete for 66 of these (usually because the number of homes passed by plant was unavailable). Of the remaining 87, six were found to have erroneous data on homes passed; therefore, we were left with a sample of 81 systems--of which 20 were located in the top 100 markets.

None of the three demand equations predicted demand any better than one could by a random process. All three were rather strongly biased downward, and all three had root mean square errors

18L. L. Johnson, et al., op. cit., Addendum 2A.

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in excess of the standard deviation of the distribution of actual penetration rates. The performance of each demand equation is summarized in Table C-2.

Mitchell's adaptation of Park's equation performs the worst of all, providing the largest values for root mean square error. For the settings which Mitchell posits in his recent paper, Comanor-Mitchell provides much higher estimates of major penetration than the Park equation, but even these estimates are considerably below those derived by a group of Major System Operators (MSO's) themselves. These predictions appear with each demand function's estimates in Table C-3.

1These estimates are taken from Andersson, op. cit.; 1987 projections for penetration are coverted to mature penetration by utilizing Mitchell's growth path for homes passed in 1983-87. Thus, in the top 25 markets, 1987 penetration is 58.6 percent, but given an average increase of 882, 100 homes passed per year in 1982-87, mature penetration is estimated to be 64.6 percent in these markets.

Source: Mitchell, Table 4, without exclusivity calculation.

Given the poor performance of all three demand equations, we do not feel that use of any of them is justified in predicting future penetration for the purpose of calculating rates of return on cable investment. The considerable downward bias in each would create a similar downward bias in profitability calculations. Therefore, we are forced to rely upon the cable system operators' own projections of demand even though these estimates are derived from cable systems which provide little significant origination and only a minor amount of special services such as motion pictures or sports events by leased channels. When these services reach fruition, we can expect the attractiveness of cable to be enhanced considerably and penetration to rise accordingly.

Exclusivity. In its 1972 rulemaking, the FCC provided

exclusivity protection to local stations in the top 100 markets by requiring that cable systems black out imported signals when they contain programs which are also shown by local stations in a specified period. In order to allow for the effect of this exclusivity protection upon cable penetration, Mitchell reduces the number of imported signals by a proportion which purportedly reflects the percentage of time which the signals will be blacked out. Unfortunately, this calculation is based upon only the most scanty evidence assembled by Park. More importantly, there is no evidence that penetration will respond proportionately to reductions in the time independent signals are available. Thus, we do not attempt to replicate Mitchell's conjecture, but instead allow for the importation of two additional independent "standby" signals by building in six additional microwave hops (for importing the two signals) to our capital costs.

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The calculation of the necessary operating costs of cable systems is far from a simple matter. Comanor-Mitchell provide a very detailed breakdown of all operating costs of systems which they believe to be typical, but these data are not fitted by standard statistical techniques to the operating performance of extant systems. Rather, they are judgments derived by the authors after consultation with their clients and others in the industry. Not surprisingly, they have been viewed by some critics as rather high, but there is only scant evidence in published financial reports with which to compare them.

An important source of the apparent economies of scale in Comanor-Mitchell lies in the assumption that all cable systems with more than 3,500 subscribers will undertake the same origination expenses. This origination activity contributes $43,000 per year to operating costs

19R. E. Park, The Exclusivity Provisions of the Federal Communications Commission's Cable Television Regulations, The Rand Corporation, R-1057-FF/MF, June 1972.