The traditional Ramsey pricing and the Efficient Component Pricing Rule for access charges to a facility are modified in this paper, taking into account the constraint that profits per unit of investment must be the same between entrants and the incumbent (a general equilibrium requirement). It is shown that the required modifications are applicable even when the sustainability constraint is not operative. If this new condition is not satisfied, the incumbent will have an incentive to postpone the construction of the critical facility.Access Pricing; Exchangeability; Incentives to Invest

Chisari, Omar O.

English

Research Papers in Economics

  1
 
“A Note on Access Pricing, Role Exchangeability and Incentives 
to Invest” 
 
Omar Chisari 
 
Working Paper Nº 23 
 
ISBN: 978-987-519-134-1 
 
(May 2007) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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http://www.uade.edu.ar   2
“A Note on Access Pricing, Role Exchangeability and Incentives 
to Invest” 
 
 
 
Omar Chisari 
 
 
ISBN: 978-987-519-134-1 
 
 
Queda hecho el dep￿sito legal que marca la ley 11.723 
 
 
Catalogaci￿n en fuente: 
 
 
Chisari, Omar 
    Anote on access pricing, role exchangeability and incentives to invest. - 1a ed. -  
Buenos Aires : Universidad Argentina de la Empresa - UADE, 2007. 
    12 p. ; 29x21 cm. - (Working paper; 23) 
 
    ISBN 978-987-519-134-1           
 
    1. Econom￿a. 2. Servicios Pœblicos. I. T￿tulo 
    CDD 354 
 
 
Fecha de catalogaci￿n: 27/06/2007   3
 
 “A Note on Access Pricing, Role Exchangeability and Incentives 
to Invest” 
 
Omar O. Chisari
1  
Universidad Argentina de la Empresa 
October 2006 
 
 
 
Abstract: 
The traditional Ramsey pricing and the Efficient Component Pricing Rule for access 
charges to a facility are modified in this paper, taking into account the constraint that profits 
per unit of investment must be the same between entrants and the incumbent (a general 
equilibrium requirement). It is shown that the required modifications are applicable even 
when the sustainability constraint is not operative. If this new condition is not satisfied, the 
incumbent will have an incentive to postpone the construction of the critical facility. 
                                                 
1 I am grateful to Daniel Seeling for his assistance with the references and to Gustavo Ferro 
for this helpful comments.   4
1. Introduction. 
 
The Access Pricing literature is an excellent example of applied microeconomics to 
regulatory economics and competition policy. The Efficient Component Pricing Rule is one 
main result of a literature that addresses the problem of determining prices of access of 
entrants to a network owned by an incumbent, with the objective of maximizing social 
welfare under a condition of sustainability of the provider of the facility. 
 
There have been many elaborations and comments to the original Baumol-Sidak-Willig 
presentation, but we will discuss here a correction that seems to give the right incentives to 
invest in the long run. 
 
We will add to the basic model the constraint that profits per unit of investment of the 
incumbent must be at least that of entrants￿. Therefore, beyond the traditional sustainability 
condition of the provider of the essential facility,  we will ask that the incumbent must not 
find preferable to be an entrant. The reason is that without this condition, builders of 
facilities will find attractive to postpone the construction and become pure entrants. Who 
would then provide the essential facility? 
 
Next section is devoted to  a very brief summary of references. Section 3 discuss the basic 
elements of the traditional approach. Section 4 addresses the role exchangeability 
condition, and we conclude with the main result in Section 5.  
 
2.  A brief summary of the literature 
 
It is not our intention to present a detailed summary of this literature in this short note ￿in 
fact, the reader can find many good surveys-. For example, Valletti and Estache (1998) give 
a survey of different approaches and relevance of the problem. Laffont and Tirole (1996) 
suggested the use of ￿global-price-caps￿ considering access as a final good, not as an input; 
this allows to use Ramsey pricing with a cap on total revenues but without the need of 
knowing exact marginal costs of every activity. Crew and Kleindorfer (2002) have argued 
that the key weakness of the rule is in the evaluation of the opportunity cost in networks 
where a competitive fringe does not exist simply because there is an essential facility and 
the rule suffers from circularity. Vogelsang (2003) presents a summary and makes a 
distinction between ￿access￿ from ￿interconnection￿ and emphasizes the need of studying 
networks of similar hierarchy (like internet and not telephony). Valletti (2003) highlights 
the importance of examining incentives to investments. 
 
 
3. A model used to develop the ECPR. 
 
We will follow the presentation of Armstrong, Doyle and Vickers (1996) and use their 
model as our basic framework.  
So let us assume that: 1) There is an essential facility that is necessary to reach customers 
with a final product; this essential facility is a natural monopoly, a private network or 
transmission system (for example, providers of telephone cellular phones need the fixed 
line phones to complete calls). 2) The owner of the facility is also a producer of the final   5
product, and struggles with a competitive fringe in that market (the incumbent works in 
both markets). Therefore the problem we address here is to determine access prices to the 
network in such a way that total welfare is maximized. High access prices will cover the 
costs of investment in the network but will discourage entry of firms in the competitive 
fringe, while low prices will create competition in the market of the final product, but they 
will eventually eliminate the incentives to invest in the network (a sunk cost ex post).  
 
For the sake of simplicity, let us suppose there are only two firms: an incumbent and an 
entrant. Firm I is the owner of the facility while E is the entrant ; this firm requires one unit 
of network services (« access »). The original model assumes that there are no fixed costs 
for entry. Let  ) s , q ( ξ  be the cost for I of selling  q units of its own production in the final 
market and s units of access served to E and x(P) the demand function for the final product. 
 
Profits of firm E are given by 
 
f ) s ( c s ) a P ( + − −  
 
where P is the price of the final product and a is the price of one unit of access and c(s) the 
entrants· cost of producing s units, while f are the investment costs necessary to be an 
entrant. 
 
Notice that the difference here from the traditional presentation is that we are assuming that 
f is not zero. This is necessary for our results, but we can make these costs as small as we 
wish; f are not costs of access to the network.  
Profit maximization conditions require:    
 
  
) s ·( c m a P = = −  
 
with  0 ) s ( c > ′ ′ and therefore the supply function of E depends on prices net of access costs: 
 
) m ( s * s =  
 
Profits of the incumbent I can be written as: 
 
F )) m ( s ), m ( s ) p ( x ( ) m ( ms ) P ( Px − − − − ξ  
 
There are two sources of revenue for the firm. On the one hand it could charge an amount 
as to give entrants access to the facility. On the other, they could sell its own units to the 
market with a revenue  P(x-s). We have included here costs of investment in the facility, 
given by F. 
  
The sustainability condition is therefore: 
 
(S)  0 F )) m ( s ), m ( s ) p ( x ( ) m ( ms ) P ( Px ≥ − − − − ξ    6
 
Social welfare maximization requires to maximize customers surplus in monetary terms 
 
) P ( px )) P ( x ( u −  
 
plus profits of entrants and incumbents, subject to non negativity of profits of incumbents 
(the constraint imposed by the requirement of sustainability of the natural monopoly). 
Notice that entrants profits will be always positive if f is small enough. Variables of choice 
are P and m. Let us call λ the multiplier associated to the incumbents profits non-negativity 
condition. Optimal prices will be given by: 
 
(GE)              
s 2 1
x 1
/ m / ) ( m
/ P / P
η θ ξ ξ
η θ ξ
− = − −
= −
 
 
where   ) 1 /( λ λ θ + =  ,  and  x η  and  s η are the demand elasticity for the final product and 
the supply elasticity of entrants (both positive). 
 
We can see that this equations are Ramsey prices that take into account the elasticity of 
demand for the final product and the intensity of the revenue constraint to cover the cost of 
the transmission facility. 
  
There are several cases obtained under different assumptions.  
 
Firstly, let us assume that I  is not a Natural Monopoly (i.e. θ = 0), then:  
 
2
1
a
P
ξ
ξ
=
=
 
 
We can pose, instead, that if I is a natural monopoly and the condition is binding ( θ > 0) we 
will get: 
 
2
1
a
P
ξ
ξ
>
>
 
 
Hence, prices will exceed marginal costs simply because it is necessary to cover costs of 
the facility and not due to monopoly power (the monopolistic solution can be obtained by 
letting λ→∞). 
 
Third, when P is determined by the regulator exogenously,  i.e. P is not longer a variable to 
be used in the optimization process, and θ = 0 the outcome will become: 
 
1 2 P a ξ ξ − + = .  
   7
The first term of the second hand is the direct cost of providing access to an entrant, while 
the second term is the foregone profit or opportunity cost of the foregone market due to 
admitting access by competitors. This equation is the basic Efficient Component Pricing 
Rule.  
 
Thus the main lesson is that efficiency requires that incumbent charges himself the same 
cost for the use of the network that is imposed to entrants.  
 
 
4. The case without role lock-in. 
 
Let us consider now how we should adapt the above analysis for the case of role 
exchangeability. This means that profits per unit of investment should be the same for 
entrants and for the incumbent. If these rates of profit were different, it could be impossible 
to disregard situations where the incumbent could postpone investments simply because it 
is more profitable to be an entrant. Notice that the presentation by Armstrong et al (1996) 
assumes that profits of entrants are always positive while (in the same framework) to 
guarantee that result for the incumbent requires to impose a constraint on welfare 
maximization. 
 
Moreover, there is nothing that rules out cases where F is not enough to compensate the 
differences in the respective profits per unit of investment. 
 
So, let us reconsider the problem of welfare maximization when the following constraint is 
imposed: 
 
f / ) c ms ( F / ] ms ) P ( Px [ − = − − ξ  
 
that is, the rate of profits ￿in our sense- per unit of capital invested must be equal. This is 
what we call the Role Exchangeability (RE) condition, which can be written as:  
 
(RE)   0 c ms ) F / f ]( ms ) P ( Px [ = + − − − ξ  
 
Let  δ=f/F  and  φ be the multiplier associated to this last constraint. Then welfare 
maximization with respect to P and m gives: 
 
) / 1 )( 1 / ( m / ) ( m
) / 1 )( 1 / ( P / P
s 2 1
x 1
η ϕδ λ λ δϕ ϕ ξ ξ
η ϕδ λ ϕδ λ ξ
− + + + + = − −
+ + + = −
 
 
Notice that if the condition of exchangeability is relaxed (i.e. φ = 0) we will obtain the same 
conditions we already had for the traditional case.  
   8
But on the other hand, even if δ is small, the condition on m  will be different if profit rates 
are different; that is, even if entrants are not risking capital, it will be necessary to extract 
part of their rent to finance the network so that incentives to invest will be leveled.  
 
As in the traditional model, it is possible to distinguish several special cases: 
 
a)  (S) is operative but (RE) is not binding. In this case we go back to the traditional 
solution for λ ≥ 0 and φ = 0. 
 
b) (S) is not binding, but (RE) is operative, with  λ = 0 and φ > 0 (though it is not possible 
to discard φ = 0) .  
 
c) (S) and (RE) are both operative, with λ > 0 and φ> 0. 
 
d) Neither (S) nor (RE) are operative. 
 
The most interesting situations are b) and c). In both cases, access pricing is modified due 
to the presence of (RE); for example, take b) and assume that profits are enough to 
guarantee sustainability, but that does not mean that profits of the incumbent will be 
comparable on the same grounds with those of the entrants·. Therefore, access prices will 
have to be corrected upwards, and that will impact also on prices for the final product: 
 
) / 1 )( 1 / ( m / ) ( m
) / 1 )( 1 / ( P / P
s 2 1
x 1
η ϕδ δϕ ϕ ξ ξ
η ϕδ ϕδ ξ
− + + = − −
+ = −
 
 
The first equation says that even if condition (S) is not operative, prices will be increased 
over marginal costs, for it is necessary to have the same rate of profit in every segment of 
the market (except when entrants do not have fixed costs, i.e. f = 0). The second equation, 
says that entrants￿ net prices will be modified to increase the rate of profit of the incumbent 
(and that will happen even if f = 0, i.e. δ = 0; in fact, in this second case we will have 
s 2 / a η ϕ ξ + = ). 
 
And now the expression for the ECPR will be put as: 
 
)] / 1 /( ) ( P [ a s 1 2 η φ ξ ξ + − + =  
 
where  ) 1 /( ) ( ϕδ δϕ ϕ φ + + = . 
 
This implies that access price should be corrected. Let us put it in terms of the marginal 
cost and of the opportunity cost:   
 
))] / 1 /( ( P [ ) / 1 /( a s 1 s 2 η φ ξ η φ ξ + − + + =  
   9
The marginal costs of entrants will be reduced since it is preferable to dispatch less units of 
the incumbent and more of the entrants; this will reduce total costs for the incumbent.  
 
But at the same time, it will be necessary to compensate the loss of profits of the incumbent 
due to additional sales of the entrants, and hence the opportunity cost of each unit must be 
increased.  
 
The net effect will be positive if  1 2 ξ ξ < ; if marginal costs of entrants is lower then access 
prices will  be increased to compensate the differences in profits.  
 
 
5. Concluding remarks. 
 
There is an increasing interest in pricing rules for networks and for taking into account 
investment in those networks. Access conditions to railroads and telecommunications, for 
example, are critical for investment decisions in those infrastructure services. However 
most of the literature focuses more on treatment of entrants than on the incentives (explicit 
or implicit) given to incumbents for expanding capacity (an exception being Valletti 
(2003)). 
 
The main result of this note is that the traditional sustainability condition is not enough to 
discuss all the incentives to invest in a network facility. It asks for access prices that cover 
fixed costs but not for leveling profits per unit of investment between entrants and 
incumbent. Who would like to be an incumbent in an industry (or provide the facilities) if it 
were possible to fraction capital an get a higher rate of return on every piece? The ￿Role 
Exchangeability Condition￿ is a general equilibrium requirement to be imposed in 
industrial regulations. And when we take into account this role indifference (long run) 
condition, the Ramsey access prices and the ECPR must be modified. 
  
Therefore, if there is mobility of agents between different roles, it will be necessary to 
make a correction of the traditional formulas for access pricing. This corollary seems to go 
beyond the problem of access pricing, and could also be relevant for cases of Ramsey 
pricing when agents have more than one possible role in the market.  
 
 
 
 
 
 
 
 
 
 
 
 
   10
 
5. References. 
 
Armstrong M., Ch.Doyle and J.Vickers (1996), ￿The Access Pricing Problem: A Synthesis￿, The 
Journal of Industrial Economics, June. 
Crew M.A. and  P.R.Kleindorfer (2002), ￿Regulatory Economics: Twenty Years of Progress?￿,  
Journal of Regulatory Economics, 21:1, 5-22. 
Laffont J.J. and J.Tirole (1996), ￿Creating Competition Through Interconnection: Theory and 
Practice￿, Journal of Regulatory Economics, 227-256. 
Valletti T.M. (2003). ￿The Theory of Access Pricing and its Linkage with Investment 
Incentives￿. Telecommunications Policy 27 (2003) 659￿675. 
Valletti T.M. and A.Estache (1998), ￿The theory of access pricing: an overview for 
infrastructure regulators￿, The World Bank Institute. 
Vogelsang I. (2003), ￿Price Regulation of Access to Telecommunications Networks￿, Journal of 
Economic Literature, Vol.41, No.3, September, 830-862. 
 
   11
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WPS 1.  Laffont, Jean Jacques: Translating Principles Into Practice in Regulation Theory (March 
1999) 
WPS 2.  Stiglitz, Joseph: Promoting Competition in Telecommunications (March     1999) 
WPS  3.  Chisari, Omar, Antonio Estache, y Carlos Romero: Winners and Losers from Utility 
Privatization in Argentina: Lessons from a General Equilibrium Model (March 1999) 
WPS  4.  Rodr￿guez Pardina, Mart￿n y Mart￿n Rossi: Efficiency Measures and Regulation: An 
Illustration of the Gas Distribution Sector in Argentina (April 1999) 
WPS  5.  Rodriguez Pardina, Mart￿n Rossi and Christian Ruzzier: Consistency Conditions: 
Efficiency Measures for the Electricity Distribution Sector in South America (June 1999) 
WPS 6.   Gordon Mackerron: Current Developments and Problems of Electricity Regulation in the 
European Union and the United Kingdom (November 1999) 
WPS 7.  Mart￿n Rossi: Technical Change and Efficiency Measures:  The Post-Privatisation in the 
Gas Distribution Sector in Argentina (March 2000)  
WPS  8.  Omar Chisari, Mart￿n Rodriguez Pardina and Mart￿n Rossi: The Cost of Capital in 
Regulated Firms: The Argentine Experience (May 2000) 
WPS  9.  Omar Chisari, Pedro Dal-B￿ and Carlos Romero: High Tension Electricity Network 
Expansions in Argentina: Decision Mechanisms and Willingness-to-Pay Revelation (May 
2000). 
WPS 10.  Daniel A. Benitez, Antonio Estache, D. Mark Kennet, And Christian A. Ruzzier. Potential 
Role of Economic Cost Models in the Regulation of Telecommunications in Developing 
Countries (August 2000). 
WPS  11. Mart￿n Rodr￿guez Pardina and Mart￿n Rossi. Technical Change and Catching-up: The 
Electricity Distribution Sector in South America (November 2000).  
WPS  12. Mart￿n Rossi and IvÆn Canay. Measuring Inefficiency in Public Utilities: Does the 
Distribution Matter? (April 2001). 
WPS 13.  Quesada, Luc￿a. Network Competition and Network Regulation (July 2001). 
WPS 14.  Rossi, Mart￿n and Christian Ruzzier: Reducing the Asymmetry of Information Through the 
Comparison of the Relative Efficiency of Several Regional Monopolies (July 2001). 
WPS 15.  WPS 15. Ferro, Gustavo: Political Risk and Regulatory Risk: Issues in Emerging Markets 
Infrastructure Concessions (August, 2001). 
WPS 16.  Margaretic, Paula, Mar￿a Fernanda Mart￿nez and Diego Petrecolla: The effectiveness of 
Antitrust Enforcement in Argentina, Chile and Perœ during the 90￿ (March, 2005). 
WPS 17.  WPS 17. Chisari, Omar, Antonio Estache, GermÆn Lambardi and Carlos Romero: Trade 
balance effects of infrastructure services liberalization and of their regulation (March, 
2005). 
WPS  18. Chisari, Omar and Luc￿a Quesada: Trade balance contraints and optimal regulation 
(March 2005)   12
WPS 19.  Ferro, Gustavo: Options for Radical Reforms to Pension Systems: Chilean and Swedish 
Models Compared (April 2005) 
WPS 20.  Del Aguila, Virginia: Establishing global competition standards: Achievable Mission or 
Utopia? (April 2005) 
WPS 21.  Ferro, Gustavo and Carlos Romero: A cost frontier for Pension Funds in Argentina. (April 
2006) 
WPS 22.  Ferro, Gustavo and Carlos Romero: Efficiency in water and sanitation sector. A survey on 
empirical literature (May 2007) 
WPS 23.  Chisari, Omar: A note on Access Pricing, Role Exchangeability and Incentives to Invest 
(May 2007) 
    13
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