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Investment, Dynamic Consistency and the Sectoral Regulator’s Objective

  • Duarte Brito EMAIL logo , Pedro Pereira and João Vareda


This article explores the possibility of distorting the regulator’s objective function as a way of overcoming the dynamic consistency problem of regulatory policy toward investment. We derive general conditions under which having the legislator distort the regulator’s objective function away from social welfare allows increasing the range of parameter values for which it is possible to induce socially desirable investment. In particular, we show that when the regulator cannot commit to a regulatory policy, the legislator should give a relatively higher weight to the incumbent’s profit in the regulator’s objective function, if the incumbent invests, and a relatively higher weight to consumer surplus, if the incumbent does not invest.


Thresholds definitions

Formally Hence, a monopolist has a non-negative net profit after making the investment. Moreover, given Lemma 2, we know that:

Thus, our assumption assures that it is always possible to induce the incumbent to invest, when the weights are conditional on the investment decision.

Formally, . Assumption (A2) ensures that . However, our assumptions do not allow us to rank and . Therefore, the interval on Lemma 3 may be empty.

Formally This may be equal to zero.

Formally In fact, in the case of maximum distortion in favor of consumer surplus if there is no investment, the incumbent gets zero profits. In the case of no distortion if there is investment, the incumbent gets gross profit . Hence, the incumbent invests as long as: . Clearly, .

Formally, Note first that and . Two cases may occur. First, may be implicitly defined by: . When this occurs, since is strictly decreasing in k, is unique. Second, when there is no solution to in , is defined as the largest value for k that is inferior to the increase in welfare given that the weights are set optimally and induce investment. This second case may occur either because the equality is verified outside the interval or because, under monopoly, may be discontinuous.

Formally, is defined by

Proof of Lemma 1: Let . It follows from the definition of interior maximum and the implicit function theorem that:

Then (A3) and (A4) imply that . Let . Then, can only decrease, and only if increases. Let . Then, can only increase, and only if increases. Let . Then, may decrease or increase if or increases, respectively.

Proof of Lemma 2: Follows from (A3) and Lemma 1.

Proof of Proposition 1: Follows from Lemma 1, 2, 3 and 3′.

Proof of Lemma 4: Given assumption (A4), and knowing, by Lemma 1, that is non-increasing in and, from Section 4.4, that is non-decreasing in k, we have: . Assuming that then implies , for all If there is a such that , if and only if,

Proof of Lemma 5: Follows immediately from the differentiation of [4], assumption (A3) and Lemma 1.

Proof of Proposition 2: Follows from Lemmas 1 and 2 and the discussion above.


The authors gratefully acknowledge partial financial support from FCT- Fundação para a Ciência e a Tecnologia, program FEDER/POCI; and from Banco Santander-Totta. This paper was financed by national funds from the FCT under project PTDC/EGE-ECO/115451/2009

  1. The opinions expressed in this article reflect only the authors’ views, and in no way bind the institutions to which they are affiliated

  2. 1

    In some countries, regulators are appointed for longer periods than legislators. However, laws are usually the result of a complex political process and usually much harder to change than sectoral rules and regulations. Take, as an example, the longevity of the Telecommunications Act of 1996 in the USA. Another example of longevity is the Regulatory framework in the EU applicable to the electronic communications networks and services, known as the 99 Revision of the European Commission, which was enacted in 2003 and is still in place.

  3. 2

    See Guthrie (2006) for a discussion about the regulators’ inability to commit to a regulatory policy.

  4. 3

    This is related to the literature on strategic delegation, namely in the context of the relationship between the owner and the manager of a firm. See, for instance, Fershtman and Judd (1987, 2006) and Sklivas (1987) who argue that it may be profit maximizing for an owner of a firm to distort the manager’s objectives away from profit maximization.

  5. 4

    Other studies, which convey the idea of the existence of an optimal bias between the politicians’ and the regulator’s interests due to information asymmetries, include De Figueiredo, Spiller, and Urbiztondo (1999), Sloof (2000) and Spiller (1990).

  6. 5

    There is also some empirical literature on the link between the regulator’s preferences and investment, which has produced mixed results. Trillas and Staffiero (2007) point to evidence that in many developing countries, and especially in Latin America, some degree of industry orientation has been necessary to attract foreign capital in the utilities sector. On the other hand, Gutiérrez (2003) investigates the relationship between the regulator’s independence from the industry and from the government and investment in telecommunications infrastructure, finding that greater independence positively affects the number of phone lines per capita.

  7. 6

    An alternative to changing the regulator’s objective function is to constrain its future actions. The legislation behind the Kansas Telecommunications Agreement prohibits the regulator from carrying out earnings audits, thus making it harder for the regulator to review a price cap (see Weisman 2002).

  8. 7

    Strausz (2011) shows that regulatory risk, reflecting the uncertainty behind new or changing regulation over time, may actually benefit firms when aggregate consumer demand is convex.

  9. 8

    This solution, which follows the proposal by Rogoff (1985), is a second-best commitment mechanism, where the pricing decision is delegated to an independent regulator, whose preferences do not necessarily coincide with those of the government. Levine, Stern, and Trillas (2005) make an analogy of the Rogoff-delegation solution for central banks to other regulatory environments.

  10. 9

    We model the investment decision as a discrete choice since investment in many of these industries has a discrete nature. Take the example of the deployment of a next generation network. It involves two aspects: upgrading the core network and replacing the local access network. Upgrading the core network is clearly a discrete decision. Replacing the local access network amounts essentially to replacing copper lines by fiber optical lines, with the associated electronic control equipment, etc. Again this is a discrete decision. Furthermore, there are estimates that 68% of the costs of this investment relate to the construction of ducts. This means that most of the costs are fixed and irreversible and do not depend on the type of equipment installed.

  11. 10

    Given our assumptions about payoffs on Section 3.5, there is no need to give a weight higher than 1 to the entrant’s profit. The legislator can obtain a similar effect by adjusting the weights to the other parties’ payoffs.

  12. 11

    Note that in principle one should have , since the higher the quality of the network the entrant is using, the higher must the access price be for the entrant to prefer to stay out of the market.

  13. 12

    See DeGraba (2003) for a derivation of the relationship between the access price and the incumbent’s price.

  14. 13

    We assume that there is no price-squeeze regulation in place that would force the incumbent to charge a retail price above the access price.

  15. 14

    We assume that the legislator provides the regulator with a tie-breaking rule, such that the optimal access price is unique, e.g., choose the lowest value or the highest value.

  16. 15

    It is also possible that , in which case a higher weight to consumer surplus would make the regulator’s optimal access price equal to the first best.

  17. 16

    Suppose one assumed instead that the incumbent’s profit is increasing in the access price until a given , and decreasing afterward, i.e., the profit maximizing access price leads to duopoly. Then, for a sufficiently high weight to the incumbent’s profit the regulator would set , and the entrant would enter the market. Our results would continue to hold qualitatively.

  18. 17

    Note that if constraint [3] is binding, i.e., it follows from Lemma 2 that is increasing in k. Otherwise, is independent of k. Moreover, increasing k reduces the set of values for that verify constraint [3], thus is non-increasing in k.

  19. 18

    In case a bypass investments were possible, i.e., the entrant could invest after the incumbent, the optimal policy would involve the legislator setting weights conditional also on the entrant’s investment decision. If, for instance, a bypass investment were socially desirable, the legislator might set a policy such that the weight given to the entrant’s profit in case of no investment by the entrant was lower. Again, the solution would be such that the regulator would choose an access price after investment equal to the one a regulator able to commit would choose.

  20. 19

    The European Commission has been working on a regulatory approach intended to promote advanced access infrastructure investment in the telecommunications sector. As expected, incumbents are in favor of high access prices, whereas entrants argue for low access prices. In 2011, the European Competitive Telecommunication Association, ECTA, based on WIK (2011), suggested that the incumbents charge high access prices in the cooper network, with the excess profits reverting to the entrants in the absence of investment in fiber. This suggestion was eventually turned down. We thank one referee for pointing out this example.

  21. 20

    Note that a pro-incumbent regime is characterized by the regulator placing a weight on incumbent’s profits that is larger than the weight placed on the other parties. It is not necessary that value is explicitly stated in the regulator’s objective function. In fact, could be the focal point of the set of weights larger than one that verify some additional restrictions that constrain the regulator’s actions.

  22. 21

    As corresponds to the increment in the incumbent’s gross profit when the regulator’s objective function is not distorted, its value is the same both when the weights are and are not conditional on the investment decision. The same applies to .

  23. 22

    The determination of is similar to the case where the weights are conditional on investment with a difference in the incumbent’s constraint [3], which is now harder to verify as the regulator is unable to punish the incumbent in the case of no investment.

  24. 23

    The incremental profit of investment is maximized at Therefore, it is not possible to induce investment if k is on


Armstrong, M., and J.Vickers. 1996. “Regulatory Reform in Telecommunications in Central and Eastern Europe.” Economics of Transition4(2):295318.10.1111/j.1468-0351.1996.tb00174.xSearch in Google Scholar

Besley, T., and S.Coate. 2003. “Elected versus Appointed Regulators: Theory and Evidence.” Journal of the European Economic Association1(5):1176206.10.1162/154247603770383424Search in Google Scholar

Biglaiser, G., and P.DeGraba. 2001. “Downstream Integration by a Bottleneck Input Supplier Whose Regulated Wholesale Prices Are Above Costs.” The Rand Journal of Economics32(2):30215.10.2307/2696411Search in Google Scholar

Brito, D., P.Pereira, and J.Vareda. 2010. “Can Two-Part Tariffs Promote Efficient Investment in Next Generation Networks?International Journal of Industrial Organization28(3):32333.10.1016/j.ijindorg.2009.10.004Search in Google Scholar

Broer, P., and G.Zwart. 2013. “Optimal Regulation of Lumpy Investments.”Journal of Regulatory Economics: forthcoming. DOI 10.1007/s11149-013-9214-y.10.1007/s11149-013-9214-ySearch in Google Scholar

Che, Y.-K. 1995. “Revolving Doors and the Optimal Tolerance for Agency Collusion.” The RAND Journal of Economics26(3):37897.10.2307/2555994Search in Google Scholar

De Figueiredo Jr., R., P.T.Spiller, and S.Urbiztondo. 1999. “An Informational Perspective on Administrative Procedures.” Journal of Law, Economics and Organization15(1):283305.10.1093/jleo/15.1.283Search in Google Scholar

DeGraba, P. 2003. “A Bottleneck Input Suppliers’ Opportunity Cost of Competing Downstream.” Journal of Regulatory Economics23(3):28797.10.1023/A:1023364210896Search in Google Scholar

Edwards, G., and L.Waverman. 2006. “The Effects of Public Ownership and Regulatory Independence on Regulatory Outcomes.” Journal of Regulatory Economics29(1):2367.10.1007/s11149-005-5125-xSearch in Google Scholar

Evans, J., P.Levine, and F.Trillas. 2008. “Lobbies, Delegation and the Under-Investment Problem in Regulation.” International Journal of Industrial Organization26:1740.10.1016/j.ijindorg.2006.09.003Search in Google Scholar

Faure-Grimaud, A., and D.Martimort. 2003. “Regulatory Inertia.” The RAND Journal of Economics34(3):41337.10.2307/1593739Search in Google Scholar

Fershtman, C., and K.L.Judd. 1987. “Equilibrium Incentives in Oligopoly.” American Economic Review77:92740.Search in Google Scholar

Fershtman, C., and K.L.Judd. 2006. “Equilibrium Incentives in Oligopoly: Corrigendum.” American Economic Review96(4):13671367.10.1257/aer.96.4.1367Search in Google Scholar

Foros, O. 2004. “Strategic Investments with Spillovers, Vertical Integration and Foreclosure in the Broadband Access Market.” International Journal of Industrial Organization22:124.10.1016/S0167-7187(03)00079-1Search in Google Scholar

Gans, J., and S.King. 2004. “Access Holidays and the Timing of technology Investment.” Economic Record80:89100.10.1111/j.1475-4932.2004.00127.xSearch in Google Scholar

Grajek, M., and L.H.Röller. 2012. “Regulation and Investment in Network Industries: Evidence from European Telecoms.” Journal of Law and Economics55(1):189216.10.1086/661196Search in Google Scholar

Guthrie, G. 2006. “Regulating Infrastructure: The Impact on Risk and Investment.” Journal of Economic Literature44:92572.10.1257/jel.44.4.925Search in Google Scholar

Gutiérrez, L.H. 2003. “The Effect of Endogenous Regulation on Telecommunications Expansion and Efficiency in Latin America.” Journal of Regulatory Economics23(3):25786.10.1023/A:1023412226826Search in Google Scholar

Kotakorpi, K. 2006. “Access Price Regulation, Investment and Entry in Telecommunications.” International Journal of Industrial Organization24:101320.10.1016/j.ijindorg.2005.11.007Search in Google Scholar

Levine, P., and N.Rickman. 2002. “Price Regulation, Investment and the Commitment Problem.” CEPR Discussion Paper, vol. 3200.Search in Google Scholar

Levine, P., J.Stern, and F.Trillas. 2005. “Utility Price Regulation and Time Inconsistency: Comparisons with Monetary Policy.” Oxford Economic Papers57:44778.10.1093/oep/gpi021Search in Google Scholar

Levy, B., and P.T.Spiller, eds. 1996. Regulations, Institutions, and Commitment: Comparative Studies of Telecommunications. Cambridge: Cambridge University Press.10.1017/CBO9781139174589Search in Google Scholar

Newbery, D. 2000. Privatization, Restructuring and Regulation of Network Utilities. Cambridge: The MIT Press.10.7551/mitpress/5579.001.0001Search in Google Scholar

Rogoff, K. 1985. “The Optimal Degree of Commitment to an Intermediate Monetary Target.” Quarterly Journal of Economics100(4):116989.10.2307/1885679Search in Google Scholar

Salant, D.J. 1995. “Behind the Revolving Door: A New View of Public Utility Regulation.” The RAND Journal of Economics26(3):36277.10.2307/2555993Search in Google Scholar

Sklivas, S.D. 1987. “The Strategic Choice of Managerial Incentives.” The RAND Journal of Economics18:4528.10.2307/2555609Search in Google Scholar

Sloof, R. 2000. “Interest Group Lobbying and the Delegation of Policy Authority.” Economics and Politics12(3):24774.10.1111/1468-0343.00077Search in Google Scholar

Spiller, P.T. 1990. “Politicians, Interest Groups and Regulators: A Multiple-Principals Agency Theory of Regulation, or ‘Let Them Be Bribed’.” Journal of Law and Economics33:65101.10.1086/467200Search in Google Scholar

Spulber, D., and D.Besanko. 1992. “Delegation, Commitment, and the Regulatory Mandate.” Journal of Law, Economics and Organization8(1):12654.Search in Google Scholar

Strausz, R. 2011. “Regulatory Risk under Optimal Monopoly Regulation.” The Economic Journal121:74062.10.1111/j.1468-0297.2011.02441.xSearch in Google Scholar

Trillas, F., and G.Staffiero. 2007. “Regulatory Reform, Development and Distributive Concerns.” IESE Working Paper no 665.Search in Google Scholar

Vareda, J. 2010. “Access Regulation and the Incumbent Investment in Quality Upgrades and Cost Reduction.” Telecommunications Policy34(11):697710.10.1016/j.telpol.2010.09.003Search in Google Scholar

Vogelsang, I. 2010. “Incentive Regulation, Investments and Technological Change.” CESifo Working Paper Series no. 964.Search in Google Scholar

Weisman, D.L. 2002. “Is There ‘Hope’ for Price Cap Regulation?Information Economics and Policy14(3):34970.10.1016/S0167-6245(02)00046-XSearch in Google Scholar

WIK.2011. “Cost Methodologies and Pricing Schemes to Support the Transition to NGA.” WIK-Consult Report, December 2011.Search in Google Scholar

Published Online: 2013-08-10

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