ESTRECHO DE GIBRALTAR

Summarizing, the model developed in this chapter analyzes a cost-based regulation is- sue over multiple periods. In the specific model setup, investments overlap in the second considered period. The model answers the questions what effect the actual price deter- mination has on the affected company’s investment decision in all periods, and which determination results in the highest social welfare.

In one sentence, under the assumption that investment becomes cheaper for the com- pany, i.e. capacity costs decrease, section 4.3 demonstrates that the smallest possible price should be chosen. This is because the higher the regulated price the higher is the underin- vestment for total capacity over all periods and consequently the loss in social welfare. A higher regulated price would result in an NPV of greater than zero for the company. This by itself would not be a problem for a social welfare maximizing regulator, but as under- investment and hence the loss in social welfare increase with a higher regulated price, the regulator only allows an NPV of zero. This is the minimum NPV at which the company is still willing to invest.

Whereas the fact that the company invests less with a higher price might sound coun- terintuitive at first, the reason is the demand restriction the company is subject to. Only the amount of capacity is provided that can actually be sold. Even with the best possible price choice under these circumstances, one severe problem remains: no investment can be induced in period 1.

It could further be proven that the optimality of choosing the smallest possible price also holds for increasing capacity costs with the difference that no investment can be induced in period 2. This means that for both increasing and decreasing capacity costs, the feature of overlapping investments de facto ceases to exist. There is no overlapping investment, the company invests either in the first or the second period. As already discussed in sec- tion 4.3.1, this is not considered a shortfall regarding the initial research questions. It is an unexpected result that is due to the specific deterministic model setup, in which the company decides upon both investments simultaneously. It is likely that the overlapping feature does not fall away for a sequential setup of the investment process.

The analysis has been conducted under some strict assumptions which provide room for further investigation.

First, it is a discrete-time model in which investment is made only once at the beginning of each period. As one extension, ongoing but still discrete investment within one period would be interesting to implement into the model. Consequently, in such a setting, more than just two investments are relevant for the regulated price. Thereby, the real situation of the German incentive regulation would be better reflected. Moreover, in this setting the influence of the exact timing of the price review could be assessed. It is likely that different effects can be observed depending on whether the photoyear is three, two, or just one year before the new regulation period. With the photoyear being close to the new regulation period, the time lag between an investment outlay and its recognition in the revenue cap is reduced. As another extension, the model could be analyzed in a complete continuous time setting. This analysis would mainly be interesting from a theoretical perspective.

Second, the model only considers one monopolist that does not face competition at all. Although this does reflect the situation in the German electricity grid, analyzing different market structures and hence the effects of an oligopoly or even perfect competition would be natural extensions to the analysis.199Furthermore, only a one-product case was consid- ered, and the extension to several products would be a natural extension. However, for the electricity industry assuming just one product is still a reasonable assumption.

Third, one could think of a different objective function for the regulator. The model assumes that the regulators pursues the maximization of social welfare subject to the com- pany’s NPV being zero, but there are other possibilities as well.200 For instance, the regu- lator might be concerned with the speed of investment. He might want to induce fast and immediate investment instead of a formally maximizing welfare. In this matter, the strict assumption of allowing a maximum NPV of zero might be relaxed as well. This seems to be particular appropriate in the context of the thesis with the necessity of grid investment today.

Fourth, the way capacity is chosen is simplified. It is assumed that at any time, the amount of invested capacity can freely be chosen. In other words, the company can decide to provide another x units of new capacity, with x being any natural number. In many real life applications, this is not the case. In fact, investment is lumpy. If one thinks of a unit of capacity as one meter of power grid, it is impossible to just invest e.g. 150 meters of new line if the two nodes needing to be connected are 200 meters apart from each other. For the model, that means that capacity can only be increased by certain fixed amounts. Most

199_{However, it has to be noted that perfect competition would make the regulator obsolete. Nevertheless, it is}

not uncommon in the literature to analyze a competitive setting, see for instance Dixit (1991).

200_{Recall that as illustrated in section 4.3.1, a deviation of the NPV=0 requirement causes an immense loss in}

4 Model on the Influence of Multi-period Investment on Optimal Regulatory Pricing

likely, accounting for this aspect will strong affect the model results.

Concerning the capacity choice, one might furthermore wonder why it is important that capacity and demand match in every single period.201 One can imagine that it might be beneficial for the company to provide excess capacity today to be able to serve tomorrow’s demand as well. The effects of such shifts in demand require further investigation too.202

Fifth, one further strict assumption is constant demand which has been used throughout the analysis. Allowing changing demand will most likely tremendously change the anal- ysis and would be very important to further investigate analytically. For instance, Friedl (2007) analyzes the effects of changing demand. He considers linear demand functions with constant saturation quantity. He is able to show that in his setting, instead of the annuity depreciation rule, the relative benefit cost allocation rule203 leads to efficient in- vestment. Furthermore, he is able to prove that straight-line depreciation only results in efficient investment, if the maximum willingness to pay decreases at a very specific rate. Hence, Friedl (2007) is a convincing example for how different assumptions about the de- mand function lead to different results.

Moreover, not only changing demand will most likely make a big difference, but also other forms of the demand function. The demand function can be piecewise constant, which includes perfectly inelastic demand up to a certain point and not demand beyond that point. As another option, it could even be modeled as a very general demand function, without explicitly specifying it. All these possibilities in modeling demand will make a big difference, in particular because the assumed linear demand function is very crucial in the model.

As for another restriction concerning the parameters, the interest rate used throughout the analysis was exogenous and its influence was not analyzed. The same interest rate was used for both regulator and company, which is also a very strong assumption.

Sixth, the model is completely deterministic. Before all decisions are made, all relevant influencing factors are known and do not unexpectedly change later. This holds for de- mand, capacity costs, pricing procedure and interest rates. Of course this is a very strong assumption which can have a great impact on the model outcome. Uncertainty about any of these factors is very likely to dramatically influence the results and needs to be

201_{See the capacity restrictions in section 4.1.3.}

202_{However, in this case the restriction to NPV=0 projects would have to be relaxed.} 203_{In this thesis, the rule is illustrated in section 3.3.2.}

accounted for in future research.204 Furthermore, the deterministic setup also results in the fact that the regulator can fully commit to a certain pricing procedure which is known to the company ex ante. The company’s investment decision relies very strongly on this fixed price in period 2. Knowing that the regulator might change his policy again will also significantly change the model outcome.

The deterministic nature of the present model with the resulting full certainty and full commitment of the regulator is considered an important limitation which requires further investigation. This has not been achieved by the presented formal model, and naturally, there are not any contributions which analyze the issue of information, commitment and uncertainty, but the discussion of these topics in section 3.4 provided a basis idea of their importance.

In addition to the level of information and uncertainty there are more important drivers which were left out in the formal model. In the model, the cost base used for the determin- ing depreciation charges was chosen in the simplest way possible, namely just taking the original historic cost. This in another important limitation of the analysis. In analogy to section 3.4.1, section 3.4.3 discussed existing literature which deals with this issue. Based on this discussion, starting points for an extension of the model can be identified.

Lastly, in the model only capital costs, i.e. depreciation and interest, were included into pricing. In fact, as illustrated in section 3.4.4, there is a large stream of literature which suggests other forms of pricing, for instance peak-load pricing. These other pricing approaches are not incorporated in the model too, which is another limitation of it. Here again, the discussion in section 3.4.4 provides the literature framework for possible future research.