Allocating Spectrum Efficiently

This practice note shows in more detail how ‘compromises’ over the division of spectrum amongst competing users can be found.  The problem is illustrated in Figure 1.0.

The total spectrum available for the two uses, A and B, measured in MHz, is shown by the horizontal line.  The amount used is Use A is measured from the left, the amount used in Use B is measured from the right.  Any point on the line, such as Y, thus shows how the available spectrum is divided.  Suppose initially that Use A is mobile telephony and Use B commercial broadcasting.   

The two curves, MB_A and MB_B (which are not necessarily linear) show the net benefit to the economy of allocating another MHz of spectrum to respectively Use A or Use B.   This measures the benefit (in $) which consumers derive from the extra units of service provided by the additional spectrum, minus the costs of producing the additional service.

Consider point X again.  At X, a fair amount of spectrum has already been allocated to mobile telephone (Use A).  Assigning a further MHz will increase the number of calls which can be made a little, but once the other costs of providing the service has been subtracted from what end users are willing to pay for those extra calls, the net benefit to consumers is quite small.  The same situation applies to Use B, where at X extra spectrum is used to increase the number or coverage of a reasonable number of commercial broadcast channels.

However, the first MHz allocated to a particular use – to meet the most urgent needs for telephone calls or to provide the first broadcast service, will yield much bigger benefits.  For this reason the curve MB_A (from left to right) and MB_B (from right to left) is initially high, but falls as a greater amount of spectrum is assigned to the respective use.

Following this argument, it is possible to go further and define the best allocation of spectrum to the two uses.  Consider point X again.  At that point, curves MB_A and MB_B cross, indicating that the net benefit to a MHz of spectrum is equal in both uses.  This means that taking spectrum from A and applying it to B, will not improve the situation and vice versa.  At Y, for example, ‘extra spectrum clearly has a higher value in Use A and in Use B.    X is then the allocation which achieves the objective of maximising economic benefit from both uses.  While at Y, spectrum should be shifted from B to A.

In the example above, Uses A and B were both commercial ones – revenue-generating services provided to end users.  Now suppose Use B is spectrum utilised for national defence - a public service provided directly by the government.  Here the government will place a value, on behalf of its citizens, of different levels of provision of defence services which utilise spectrum.  The net value of an additional MHz will diminish as now spectrum is utilised, so the shape of use MB_B  (where B is a defence use) will be as before.  And as before, the optimal allocation is where the curves cross, where the net benefits of spectrum are alternative use are equal.

The figure thus provides a fairly general way of thinking about how spectrum allocations decisions can be made to maximise end user benefits.  The competing uses can be two commercial uses, one commercial and one public use or two public uses.  One of the major conclusions of this analysis is that spectrum’s usefulness stems from the benefits in terms of services to end users whom it can provide; its allocation should thus be driven by the valuation people place on the commercial or public services it can make.