Abstract
Contrary to copper, fiber is a segmented vital input. This means that, even though a National Regulatory Authority may regulate active fiber, the owner of the fiber network infrastructure may distort retail competition and obtain a sufficiently high wholesale revenue through the sale of dark fiber if this is not subject to regulatory intervention. Given the recent trend in favor of access price regulation of dark fiber in Europe, the analysis evaluates which wholesale price control method should be applied considering that the market structure of the telecommunications industry is the monopolistic bottleneck. Three regulatory options are tested against each other: active-minus regulation, cost-based regulation applied to both layers of the segmented vital input and equivalence of inputs. The imposition of active-minus regulation improves investment incentives and social welfare compared to the alternative methods.
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Notes
As explained and demonstrated in Brito and Tselekounis (2017)’s analysis, the trade-off between static and dynamic efficiency may be solved because the profit of the service-based entrant may increase (decrease) as the wholesale access price charged by the incumbent increases (decreases), respectively. The immediate effect of this mechanism is the higher investment realization. Moreover, the gain in producer surplus outweighs the loss in consumer surplus such that social welfare increases.
In light of the above categorization regarding the different types of access obligations, regulation of the price of dark fiber should be understood, similarly to the price of access to the ducts, as a form of intervention at a lower layer of the value chain because, by definition, dark fiber is an inactive element of the fiber circuit. Hence, regulation of the price of dark fiber corresponds to a regulatory intervention at the passive layer of the incumbent’s fiber network. See the Online Appendix for a detailed clarification.
This point is clarified through the analysis of the unregulated dark fiber regime relegated to the Online Appendix. Moreover, common carriage laws and supervision of the passive access price are gaining increasing strength. See the Online Appendix for a detailed clarification.
It is mandatory understand that regulation of the price of dark fiber differs from regulation of the price of access to the ducts. We focus on the first type of regulation. We exogenously assume that the price of access to the ducts is set at marginal cost level which, in turn, is normalized to 0. This assumption is verified in European jurisdictions whose deployment of NGA networks is more advanced (e.g., Portugal). The second type of regulation goes beyond the scope of this study.
On the one hand, cases \(0<1/2<\rho <\tau \le 1\) and \(0<1/2<\tau <\rho \le 1\) seem unlikely since the other licensed operator would use most of the active and passive fiber. On the contrary, under cases \(0<\rho<\tau<1/2<1\) and \(0<\tau<\rho<1/2<1\) the incumbent’s subsidiary would use most of the active and passive fiber which would reinforce the incumbent’s market power, thus, constituting a case study with little interest since both layers of the segmented vital input would be subject to marginal cost pricing.
Since the investment cost function has a quadratic and convex specification, quality underprovision is emaciated as we move towards rural regions.
On the one hand, this consideration reflects that the development infrastructure phase is influenced by the allocation infrastructure phase under active-minus regulation and cost-based regulation applied to both layers of the segmented vital input. On the other hand, the other licensed operator is always excluded from retail market when both regimes are implemented. In the Online Appendix, we demonstrate that such an exclusionary behavior is valid for a broader range of parameters’ space in which \(\rho =0\) and \(\tau =1\) are included. In particular, we confirm that the other licensed operator is always excluded from retail market as long as:
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the fraction of active fiber sold to the other licensed operator is sufficiently low
$$\begin{aligned} \rho \in \left[ 0,\dfrac{1}{2}-\frac{\gamma (3-\beta )}{4\beta ^{2}}\right] , \end{aligned}$$ -
for any given sufficiently high fraction of dark fiber sold to the other licensed operator
$$\begin{aligned} \tau \in \left( \dfrac{1}{2},1\right] . \end{aligned}$$
This result implies that the conclusions obtained for the analysis developed under the restrictions \(\rho =0\) and \(\tau =1\) are qualitatively valid for a broader range of parameters’ space. Thus, we have full legitimacy to impose \(\rho =0\) and \(\tau =1\) without loss of generality (w.l.o.g.), thus, keeping the qualitative nature of the main results beyond doubt. Imposing \(\rho =0\) and \(\tau =1\) heavily simplifies computations that are already sufficiently complex per se.
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Since demand is not dependent on \(\lambda\), the regulatory intervention on the infrastructure allocation phase under equivalence of inputs not only influences but also turns the infrastructure development phase irrelevant.
In addition, strategic effects between wholesale market and retail market can be even more complex if we take into account that there may not exist a complementary relationship between quality of service and retail price, for instance, due to the adoption of penetration pricing strategies or personalized bundles by the owner of segmented vital input in the retail market. This implies that even if a study that adopts a general specification for retail demand may generate biased results because, in spite of the generality, quality of service and retail price may be strategic substitutes. In this sense, any research can be subject to criticism.
The definition of active access price follows the cost-based principle of Sarmento and Brandão (2007) who have applied this methodology in the context of copper. The main difference is that, in the NGA framework, active access price only reflects the cost structure of the active elements of the fiber network infrastructure. Otherwise, if incorporating the passive cost structure, active access price would be too high. Obviously, a leveraged active access price would reflect a wrong evaluation of the active network infrastructure.
Assumption 1 has a twofold interpretation. From the mathematical point of view, the concavity of investment cost function is neither too smooth nor too steep. From the economic point of view, the investment effort is neither too low nor too high, otherwise, an equilibrium fails to exist once introducing passive access price regulation.
Where superscript AMR denotes ex-ante active-minus regulation regime.
Formally
$$\begin{aligned} \frac{\partial q_{I}}{\partial x_{I}}:=\frac{\beta (3\lambda -1)}{3}>0,\quad \forall \lambda ^{AMR*}\in \left( \frac{2}{3},1\right] , \end{aligned}$$while
$$\begin{aligned} \frac{\partial q_{E}}{\partial x_{I}}:=\frac{\beta (2-3\lambda )}{3}<0,\quad \forall \lambda ^{AMR*}\in \left( \frac{2}{3},1\right] . \end{aligned}$$For instance, the incumbent may have incentive to define low physical equipment costs or low amount of active input to decrease the active-minus discount in order to set passive access price at sufficiently high level thereby decreasing the wholesale price gradient, i.e. the difference between active and passive access price. The reader can easily observe that the investment cost formulas are not subject to bias. Under active-minus regulation, active fiber acts as anchor of the passive access price, thus, transparency and confidence only must prevail in the active layer of the segmented vital input. However, under cost-based regulation applied to both layers of the segmented vital input, transparency and confidence must be extended from the active to the passive layer of the segmented vital input.
See the Online Appendix for a detailed clarification.
Where superscript CBR denotes ex-ante cost-based regulation regime.
Where superscript EoI denotes equivalence of inputs. Note that this regime holds for \(\gamma >\beta ^{2}/8\), which is a parameter space less stringent than Assumption 1.
Note that
$$\begin{aligned} \left\{ \begin{array}{c} w^{P*,CBR}<w^{P*,EoI};\\ w^{P*,CBR}\ge w^{P*,EoI}; \end{array} \right. \Leftrightarrow \left\{ \begin{array}{c} \gamma \in \left( \widetilde{\gamma },\dfrac{2\beta ^{2}}{3}\right] ;\\ \gamma \in \left( \dfrac{2\beta ^{2}}{9},\widetilde{\gamma }\right] , \end{array} \right. \end{aligned}$$$$\begin{aligned} {\text {with }}\,\widetilde{\gamma }:=\frac{\beta ^{2}\left\{ 39-\lambda (9+6\beta )+\sqrt{1089-3\lambda \left[ 90-27\lambda +128\beta -4\beta \lambda (2+3\beta )\right] }\right\} }{3(36-7\beta \lambda )}\quad \text { and }\quad \frac{\partial \widetilde{\gamma }}{\partial \lambda }<0. \end{aligned}$$Furthermore, wholesale price gradient \(w^{A*,i}-w^{P*, i}\) is positively related with ratio
$$\begin{aligned} \widetilde{w}^{i}:=\dfrac{w^{A*,i}}{w^{P*,i}},\quad i=\{AMR,CBR,EoI\}. \end{aligned}$$Note that
$$\begin{aligned} \frac{\partial w^{A*,CBR}}{\partial \gamma }\,\lessgtr\, 0\Leftrightarrow \gamma \,\lessgtr\, \widetilde{\widetilde{\gamma }}:=\frac{2\beta ^{2}\left( 3-\beta +\sqrt{6}\sqrt{6-\beta }\right) }{27-\beta ^{2}}, \end{aligned}$$where \(\widetilde{\widetilde{\gamma }}\) corresponds to the minimum of \(w^{A*,CBR}\) since
$$\begin{aligned} \left. \frac{\partial ^{2}w^{A*,CBR}}{\partial \gamma ^{2} }\right| _{\gamma =\widetilde{\widetilde{\gamma }}}>0. \end{aligned}$$The expression ‘over time’ means as \(\gamma\) moves from the extreme \(2\beta ^{2}/3\) to the extreme \(2\beta ^{2}/9,\) thus, each curve exposed in Fig. 2 should be analyzed from the right to the left extreme of \(\gamma\)’s domain.
An unsuccessful entry is verified due to the ex-post adjustment in the incumbent’s network topology, and not because of a wrong definition of the wholesale price gradient. A statutory duty considered transversal to all national regulatory authorities is the promotion of competition. This is achieved by disseminating the use of dark fiber at an affordable price because the replication of a competitive market in the passive layer requires passive access price oriented to marginal cost.
Similar applies to passive fiber given the assumption of input substitutability. Computations show that both wholesale price control methods imply \(\partial \lambda ^{i*}/\partial \gamma >0\) and \(\partial \lambda ^{i*}/\partial \beta <0\), \(i=\{CBR,\) \(AMR\}.\) Needless to say, \(\lambda ^{EoI*}\) can take any value between 0 and 1.
When consumers observe a systematic price increase over time, they learn the strategic behavior of downstream operators and, thus, tend to attribute more relevance to retail price and less relevance to quality of service. The rigidity of the retail demand curve is softened, thus, it becomes flatter (Ribeiro 2017). Although our analysis does not capture this effect because retail demand is assumed linear, we have clarified such a limitation in the ‘Model’ section and we have explained the implication of introducing a more elastic retail demand: the regulator is expected to impose passive access price at marginal cost level, regardless of the regulatory regime adopted.
Note that
$$\begin{aligned} \left\{ \begin{array}{c} PS^{EoI*}<PS^{CBR*};\\ PS^{EoI*}\ge PS^{CBR*} \end{array} \right. \Leftrightarrow \left\{ \begin{array}{c} \gamma \in \left( \widehat{\gamma },\dfrac{2\beta ^{2}}{3}\right] ;\\ \gamma \in \left( \dfrac{2\beta ^{2}}{9},\widehat{\gamma }\right] , \end{array} \right. \end{aligned}$$with \(\widehat{\gamma }\) representing the break-even point between \(PS^{EoI*}\) and \(PS^{CBR*}\).
The exception holds for \(\gamma =2\beta ^{2}/3\), that is, when investment effort is excessively high, i.e. in the early rollout of fiber network infrastructure. The regulator is indifferent between active-minus regulation and cost-based regulation applied to both layers of the segmented vital input, hence, active-minus regulation is still socially desirable.
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Acknowledgements
The work was supported by ANACOM through Post-Doctoral Grant ref. 02 2014 DAC-AE. The views expressed in the paper are exclusively of the author, thus, not representing the view of ANACOM or BEREC. Vitor Miguel Ribeiro appreciates the valuable comments and discussions provided by two anonymous referees and the suggestions made by the Editor-in-Chief Carlo Cambini. These have drastically improved the quality of the manuscript, hence, my immeasurable gratitude goes to you. Finally, no conflict of interest is declared by the author.
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Ribeiro, V.M. Dark fiber price regulation in the absence of facilities-based competition. Econ Polit Ind 45, 243–278 (2018). https://doi.org/10.1007/s40812-017-0075-8
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DOI: https://doi.org/10.1007/s40812-017-0075-8
Keywords
- Vertical integration
- Dark fiber
- Active fiber
- Wholesale price discrimination
- Active-minus
- Equivalence of inputs