In his seminal paper published in 1977 titled Nonlinear Pricing and Welfare Michael Spence demonstrated that a telecom regulator could maximize the benefit to society or a telecom supplier could maximize profit by using particular pricing structures he termed non-linear pricing. During the '70s and '80s the economist and his colleagues conducted an extensive research program on nonlinear pricing, which was encapsulated in Robert Wilson's book Nonlinear Pricing published in 1991.

The research program that Spence made such an important contribution to, however, is almost totally ignored by the telecom sector, except for the core tenet that profit cannot be maximized by using a simple variable price. With competition has come an explosion in the types of pricing structures employed across different telecom markets. Fixed voice structures are different in each country, and within countries the pricing structures across fixed and mobile, voice and data services are rarely the same.

This evolution in pricing complexity might be explained by a simple Darwinian principle, but it is not the principle most commonly associated with Darwin's theory - the so-called "survival of the fittest".

Darwin appealed to two drivers in the evolutionary process. One related to interaction between species and the environment. The second related to interaction within a species where individuals compete to attract a member of the opposite gender in order to reproduce.

Without the second principle Darwin was at a loss to explain the peacock's tail, a complex adornment that clearly did not assist in the competition with other species for the finite resources available in the environment. However, with the notion of sexual competition Darwin's theory could explain the peacock's tail through a process sometimes referred to as runaway sexual selection. Males with more exotic adornments reproduced.

A prime example of a peacock's tail in telecom pricing is the evolution of pricing propositions in the Australian mobiles market. In the early stages of competition standard offers were $40 per month, with $40 of included calls with modest underlying call rate. After the arrival of the fourth competitor. so called capped offers were introduced - typically $49 for $250 of included calls but of course with a not quite so modest underlying call rate. Some of these offers were even advertised as $49 = $250 - on the surface a false proposition.

A more recent entrant in this market has introduced the metaphorical peacock's tale: $49 for $1,000 of calls.

The exotic variation in pricing structures that has resulted from the "sexual" competition within each micro-market within telecom would be a benign feature of the industry if there were no systematic relationship between the profit that might be secured and the particular type of pricing structures that are employed. However, this is not the case.

The core result that came from Spence and others was that everyone could be better off (consumers and producers) by the use of optional two-part pricing. An example of a two-part pricing function is $10 per month and 10c per call. An example of optional two-part pricing is $10 per month and 10c per call or $20 per month and 5c per call.

For the telecom supplier the key challenge is to respond efficiently to the large range in the willingness and capacity to pay for the services. Variations in use can be as large as a factor of 100. Variations in willingness and capacity to pay may be as large as a factor of 10.

Using non-linear programming software and relatively simple mathematical models it is possible to model quite robustly the relative efficiency of different pricing structures. These models confirm, in general, the findings of Spence and the non-linear pricing research program. A supplier can indeed increase revenues by about 5% by simply using optional two-part pricing compared to a single variable rate.

However, the nature of the opportunity for the supplier is much greater when the acute skew in the distribution of willingness and capacity to pay is taken in account. Under these circumstances a supplier can increase revenues by about 25% using optional linear pricing.

Figure 1 clearly shows the optional two-part pricing generates a far greater proportion of the maximum revenues available that simple variable pricing.

What are even more striking are the results for the "rectangular" pricing structures employed. Some simple examples of "rectangular" pricing structures are:

- $40 per month for 1G (for fixed internet services)
- $60 per month for 500 minutes (for mobile services).

Again using numerical approximation techniques and non-linear programming tools we can assess relative efficiency of these "rectangular" pricing structures. Assuming (contrary to fact) that use is normally distributed, it turns out that a supplier using simple variable pricing can generate about 15% more revenue than by using an optional rectangular pricing proposition with four options.

Figure 2 shows how rectangular pricing generates a lower proportion of the maximum potential revenue than simple variable pricing.

The result is confirmed when the acute skew in use, and also willingness and capacity to pay, is taken into account. In these circumstances simple linear pricing and optional rectangular pricing propositions have a similar level of efficiency.

However, a supplier using optional two-part pricing can generate about 25% more revenue than if simple variable pricing or optional rectangular pricing are used.

Complex pricing structures are not universally superior to simple variable pricing. But optional linear pricing is, and in fact, it is superior to rectangular pricing. Spence et al effectively established optional two-part pricing as the benchmark for efficient pricing structures.

Furthermore, it is not just the economic analysis that indicates that two-part pricing is preferable. Optional two-part pricing delivers clearly superior stated intention to purchase metrics when tested in market research - a result that holds across residential or business customers and fixed or mobile services. It's not just the economists who prefer these structures - consumers as well prefer the simplicity and transparency of simple linear pricing.

Not all pricing structures are equal. The choice of structure is very material, not just the selection of price points and price level. The opportunities for producers that understand and attend to these affects are quite significant. The opportunity cost of ignoring or misapplying these important structural features is similar to the cost born by the peacock - his range is limited to environments where food is plentiful and predators are few.*Graeme Rhook** is a consultant specializing in telecom pricing strategy*