When Member States impose PSOs they are never allowed to grant even a single euro in excess of the net extra costs of the PSO. That is prohibited for the simple reason that it results in over-compensation.
Introduction
The Lexxion seminar on state aid for transport and transport infrastructure that took place in Brussels on 21-22 September (view the agenda here), examined, among other things, the imposition of public service obligations [PSO] on transport undertakings. There was a lively discussion on how best to define the PSO, and how to calculate the public service compensation [PSC].
When Member States impose PSOs they are never allowed to grant even a single euro in excess of the net extra costs of the PSO. That is prohibited for the simple reason that it results in over-compensation.
At the same time, Member States need to incentivise transport providers to increase their efficiency. This can be achieved only if the providers are allowed to keep some of the profits from the increased efficiencies. Otherwise, why would they try harder if they cannot reap at least some of the benefits from their own efforts.
But allowing them to make more profit creates a new problem. Higher efficiency means lower costs. The question that inevitably arises is how it can be possible that they reduce their costs and make more profits without at the same time receiving any overcompensation. The answer lies in how costs are defined.
This is a conundrum that extends far beyond the confines of transport. It is a problem that emerges in any case of a service of general economic interest [SGEI] where a public authority imposes a PSO, offers PSC and seeks to induce the provider of the SGEI to become more efficient.
The purpose of this article is to explain the nature of the problem, illustrate how the problem can be solved and indicate how both the public authority and the SGEI provider can gain from efficiencies.
Optimum output without PSO
We start by defining the profit-maximising and the break-even levels of output of an undertaking that provides services before a PSO is imposed.
Assume there is an undertaking whose total operating costs are given by this equation:
TC = 2N^{2}
where N is the amount of services it provides [assume that we can define a unit of service and that we can count the output of this undertaking in terms of these units]. This cost equation implies that the average and marginal costs of the undertaking are given by the following:
AC = TC/N = 2N and MC = dTC/dN = 4N
Also assume that the price that can be charged for each unit of service is constant at 100 [this means that marginal revenue, MR, is 100].
Economic theory indicates that the profit-maximising output is that for which
MR = MC = 100 = MC = 4N
Therefore, the profit-maximising output is N = 25, and at this output AC = 50 and MC = 100.
The profit that this undertaking makes is Revenue – Costs = 100×25 – 50×25 = 2500 – 1250 = 1250.
The output at which it breaks even is N = 50. At this output its total revenue is 5000 [= 100×50] and its total cost is 5000 [= 2×50^{2} = 5000].
For the rest of this article, it is assumed that this undertaking operates in a sector where licensing is required and that the terms of the licence are such that it has to supply at least 50 units of services. In other words, before the imposition of a PSO, the undertaking breaks even.
PSO & PSC
Now assume that a public authority imposes a PSO forcing this undertaking to provide its services to a wider market so that its output is raised to N = 60. The wider market can be some rural area where demand is low and costs of supply are high.
A parameter of compensation, which must be defined on an ex ante basis, can be as follows:
Parameter: Compensation is calculated as the Net Extra Costs at 60 units – Net Costs at 50 units.
At an output of 60 its total cost increases to 7200 [= 2x60x60], while its revenue is only 6000 [= 100×60]. The SGEI provider faces a revenue shortfall of 1200. It can claim that, if it starts from a break-even position, it needs compensation or subsidy, S, of 1200.
Indeed, its extra cost, EC, is 7200 – 5000 = 2200, while its extra revenue, ER, is 6000 – 5000 = 1000. Therefore, its net extra cost, NEC, is NEC = EC – ER = 1200 [= 2200 – 1000]. By applying the ex ante parameter, 1200 – 0 = 1200. It follows that the subsidy it can receive may not exceed 1200.
Efficiencies, other gains and the role of the ex ante parameters
Before examining how the public authority may incentivise this undertaking to increase its efficiency, by decreasing its costs, let’s consider what may happen when the undertaking becomes more efficient.
Assume that the achieved efficiencies result in lower costs which are given by this equation:
TC = 1.7N^{2}
The reduction of the cost parameter from 2.0 to 1.7 is a measure of the production efficiency of the firm. Now, the new extra cost for the provision of the 10 extra units is EC = TC of 60 units – TC of 50 units = 1.7x60x60 – 1.7x50x50 = 6120 – 4250 = 1870. The extra revenue is ER = 6000 – 5000 = 1000. The next extra cost is therefore, NEC = 1870 – 1000 = 870. It would appear that this undertaking needs to be compensated with a subsidy of only 870.
However, when we apply the ex ante parameter of compensation we obtain a different result. This is because the net cost at 50 units is NC = TR – TC = 100×50 – 1.7x50x50 = 5000 – 4250 = 750. Now the undertaking makes a profit of 750 on its first 50 units of output.
The formula of the ex ante parameter results in lower compensation: 870 – 750 = 120. Indeed if we calculate the total costs of the undertaking for the whole output of 60 we get TC = 1.7x60x60 = 6120. The total revenue for the whole output is TR = 100×60 = 6000. Therefore, the revenue shortfall that needs to be compensated is only 120 [= 6120 – 6000].
It is often asked why do the SGEI rules require Member States to define ex ante parameters of compensation if compensation cannot exceed the net extra costs of PSO? In general, the ex ante parameters determine the relevant revenue and cost items that should be taken into account. This is indeed demonstrated by the example above. In addition, the ex ante parameters determine what increases in costs are permitted. Otherwise, the failures and inefficiencies of an SEGI provider would have to be covered by public money through the PSC.
Efficiencies and the scope of PSO
Whether our hypothetical SGEI provider should receive the higher [i.e. 870] or the lower [i.e. 120] compensation depends on how the PSO is defined. Normally, the PSO should be limited to the identified market gap; i.e. the output that the market cannot provide. But the example above also shows another important issue. If costs between the SGEI and the non-SGEI are inter-related, it may make sense for the public authority that imposes the PSO to define it more widely or to use formulas that take into account the gains in the non-SGEI part. The reason for doing this is to reduce the amount of aid that may be necessary to compensate the SGEI provider.
Sharing efficiencies
Now we can turn to the question how this undertaking can be incentivised to increase its efficiency. The public authority that imposes the PSO does want to offer such incentives because when costs go down, so does the subsidy that is needed to enable the undertaking to cover those extra costs. The public authority can do the following. It can allow, for instance, the undertaking to keep half of the gains from the efficiencies it achieves.
At first glance this seems impossible if the undertaking is not to be overcompensated. On the other hand, this firm will not make the extra effort to achieve any efficiencies unless it can also benefit from them. Sharing the gains from efficiencies means that we have to calculate an “assumed” cost parameter of 1.85 because that is the middle point between 2.0 and 1.7.
Now the extra cost of the 10 units is EC = 1.85x60x60 – 1.85x50x50 = 6660 – 4625 = 2035. The extra revenue is ER = 6000 – 5000 = 1000. Therefore, the next extra cost is NEC = 2035 – 1000 = 1035. The compensation has declined from 1200 to 1035.
Moreover, if we take into account the gains on the first 50 units of output, then TR = 5000, TC = 1.85×2500 = 4625, which means that there is a profit of 375 [= 5000 – 4625]. By subtracting 375 from 1035 we derive compensation of only 660. We can verify that indeed this is what the firm should get by calculating the revenue shortfall over the total output which is TC – TR = 1.85x60x60 – 100×60 = 6660 – 6000 = 660.
By sharing the gains from efficiencies, the needed compensation is still lower at S = 660. Nevertheless, the authority has gained 1200 – 660 = 540.
The undertaking is also better off. It has a true revenue shortfall of 120 [= 6120 – 6000]. Therefore, it makes a profit of 540 [= 660 – 120] which it can keep. There is no overcompensation because an assumed higher cost is used for the calculation of the compensation.
The table below presents all the scenarios discussed above.
Profit-maximising output | Break-even output | PSO [without efficiency requirement] | PSO [with efficiency requirement but no other gains considered] | PSO [with efficiency requirement and other gains considered] | |
Units of output | 25 | 50 | 60 | 60 | 60 |
Extra output [PSO] | — | — | 10 | 10 | 10 |
Price of output | 100 | 100 | 100 | 100 | 100 |
Total costs | 1250 | 5000 | 7200 | 6660 | 6660 |
Extra costs | — | — | 2200 | 2035 | 1660 |
Total revenue | 2500 | 5000 | 6000 | 6000 | 6000 |
Extra revenue | — | — | 1000 | 1000 | 1000 |
Profit (+)/Loss (-) | 1250 | 0 | -1200 | -1035 | -660 |
Compensation | — | — | 1200 | 1035 | 660 |
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