dis-economies in communications networks

In the late 19’th and early 20’th centuries, local investment in telephone networks drove the spread of telephone service in the U.S.   Decentralized network investment made the U.S. a world leader in telephone coverage.   U.S. telephone development was especially successful in rural areas.  Dis-economies of scale in telephone networks help to account for the success of decentralized investment in early U.S. telephone networks.

While economies of scale tend to be abstractly associated with communications networks, actual communications networks can have dis-economies of scale.  The number of possible connections in a telephone network increases with the square of the number of subscribers to the network.  Then, as now, any given person typically only calls a small number of other persons.  Moreover, the number of persons called grows little with the size of the telephone network.   However, designing a switching system that realizes the switching economies that human social behavior implies wasn’t possible early in the twentieth century.  Because the number of possible connections provided increased with the square of telephone network subscribers, (manual) switching costs rose significantly with the size of telephone networks.[1]

Data for U.S. telephone companies in 1916 shows that dis-economies of scale were quite large.  Average operating expenses per telephone rose with the logarithm of the number of telephones that a telephone operating company served.  Average operating expenses per telephone for a telephone network serving a million telephones was about double that of a telephone network serving a thousand telephones.[2]  The impetus to consolidation in the telephone industry was not technological economies of scale.  Small telephone networks were more cost efficient than large telephone networks.

graph of scale dis-economies

Small telephone companies were innovative organizationally and technologically.  Like libraries, telephone companies arose in a wide variety of institutional forms.  They included unincorporated businesses, co-operatives, and private corporations.   Some grew out of telegraph companies; others combined telephone service with electricity or construction services.   The earliest telephone companies that installed automatic switches were small, independent telephone companies.

Economies of scale in communications networks should not be taken for granted.  Local soil, weather, foliage, topology, economic demography, politics, and institutional history all affect prospects for local broadband infrastructure.   Decentralized investment in local broadband infrastructure might address more cost effectively local heterogeneity than a centralized investment program could.   At the level of softer technology, while Facebook is plotting web domination and Ning is in trouble, don’t under-estimate possibilities for social dis-economies of scale in social networks.

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Data: Summary statistics and selected records for telephone companies in 1916 (Excel version); dataset of telephone company returns for calendar year 1916

Graph notes:  The sample plotted is telephone operating companies with > 1000 telephones, excluding companies with “long” or “interstate” in the company name (companies assumed to provide predominately long-distance telephone service).  Most independent telephone companies purchased long-distance telephone service from AT&T.  Some telephone companies with < 1000 telephones had abnormally high costs per telephone.  No over-all trend in cost per telephone is apparent as telephone network size rises from 500 to 1000 telephones, but some indication of declining average cost per telephone appears for telephone networks up to 500 telephones.

Notes:

[1] Milton L. Mueller (1997), Universal Service: Competition, Interconnection, and Monopoly in the Making of the American Telephone System (Cambridge, MA: MIT Press) pp. 15-19 notes that early telephone industry analysts recognized dis-economies of scale in telephone service.  Asserted demand-side value of “unified service,” meaning having everyone on the same network, motivated calls for large scale, not supply-side scale economies.  Miles of wire per telephone rose with the size of telephone networks.  While networks with a high number of telephones per working line, e.g. party lines, were typically small telephone networks, the number of telephones per line did not generally increase with network size.  The increase in miles of wire per telephone with increasing telephone network size might indicate greater use of two-wire circuits.  But the increase in mileage, from roughly 1 mile per telephone for a 1,000 telephone network to 3 miles per telephone for a 1,000,000 telephone network, is larger than a shift from ground-return to two-wire circuits can explain.  Whatever the reason for greater wire mileage per telephone with increasing telephone network size, it also undoubtedly contributed to higher costs.

[2] Fitting a linear regression to the plotted graph implies operating expenses per telephone of $12.5 for a 1000 telephone network and $23.6 for a 1,000,000 telephone network.  Aggregate statistics from the telephone census of 1917, which used a slightly different accounting of expenses, are consistent with cost dis-economies.  Bell Companies, which averaged 50,530 telephones per operating company, had average operating expenses of $35.6 per telephone.  Independent companies, with average size 1,278 telephones per company, had average operating expenses of $19.9 per telephone.  For large telephone networks with n telephones, total operating cost is proportional to nlog(n).  More recent abstract analysis of communication network value suggests that communication network value is proportional to nlog(n).  See Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly (2006), “Metcalfe’s Law is Wrong”, IEEE Spectrum.

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