Monopoly Prices versus Ramsey-Boiteux Prices:
Are they "similar", and: Does it matter?
Felix Hö- er1
August 29, 2005
1
Max Planck Institute for Research on Collective Goods, Kurt-Schumacher-Str. 10,
53113 Bonn, Germany. Phone: +49(0)228-9141646. hoe- [email protected]. I would like
to thank Felix Bierbrauer, Christoph Engel, Hendrik Hakenes and Thijs ten Raa for
helpful discussions. The comments of two anonymous referees are gratefully acknowledged. Any remaining errors are mine.
Abstract
Ramsey-Boiteux prices and monopoly prices are frequently regarded as being similar. This might suggest that sometimes monopoly pricing is close to
the Ramsey-Boiteux second best and welfare superior to imperfectly regulated
prices. This paper tries to specify what is meant by "being similar". Both sets
of prices are similar in a theoretical sense but di¤er not only with respect to
price levels but can even lead to di¤erent price orders. The paper discusses
the impact of competition and stresses the di¤erence between market and residual demand, which are important for the Ramsey-Boiteux and the monopoly
problem, respectively.
Key words: Ramsey Pricing, Regulation, Access Pricing, Termination
JEL-Classi…cation: L33, L50, L94
1
Introduction
Ramsey prices and monopoly prices are similar, aren’t they? It is widely acknowledged that the solution to the Ramsey-Boiteux problem of second best
price setting in an environment with increasing returns to scale and the price
setting of a monopolist are somewhat similar. Both can be expressed by an
”inverse elasticity rule”. Goods with low elasticities receive a higher mark-up
on their marginal cost than goods with high elasticities. A private …rm tries to
maximize pro…ts, thus taking money from those who are least likely to abstain
from buying the …rm’s products. A welfare maximizing social planner tries to
minimize distortion caused by the departure from marginal cost pricing. She
therefore uses high mark-ups only if this will cause little quantity reaction. It is
because of the similarity of this reasoning that Ramsey-Boiteux pricing is often
called ”business oriented” (La¤ont and Tirole, 2000, 63).
This similarity is sometimes used to suggest that withholding from monopoly
regulation might be welfare superior to imperfect regulatory interference. A
monopolist might set prices a bit higher, but at least this will re‡ect the ”right”
structure. Market participants and even academics involved in the political
discussion often informally refer to Ramsey arguments.
In the UK, mobile operators have strongly relied on Ramsey arguments when
trying to justify high prices for mobile call termination. The UK regulator
Ofcom reports:
"MNOs [mobile network operators] have made a number of comments in favour of the use of Ramsey prices". For instance, "TMobile claims that the own-price elasticities for the two types of
calls [on-net and o¤-net calls] are very similar and so are relative
mark-ups, as required by the Ramsey principle" (Ofcom, 2003, 297298).
For Germany, also in the context of mobile regulation, it has been argued
that
"companies already try to come close to the Ramsey pricing
structure because this is individually pro…t maximizing. Ramsey
prices are, however, also welfare maximizing for the whole economy."(Kruse, 2003, 11, own translation)
Prieger (1996) reports that in the 90s in the US, the …xed line telecommunication incumbents GTE, Paci…c Bell (and other local exchange carriers) have
argued to
"lower prices for services also provided by competitors (such as
intra-LATA toll calls) and to raise the price of basic phone service
of which they are the sole provider. To justify the price shift, the
…rms typically argue that demand for services that face competition
is highly elastic... Underlying such arguments is an appeal to the
traditional Ramsey rule..."(Prieger, 1996, 307)
1
In this short survey we discuss whether such arguments can be justi…ed
by economic reasoning. We want to provide some orientation in which case
reference to the Ramsey-Boiteux problem makes sense and in which it does not.
In a nutshell, monopoly prices and Ramsey-Boiteux prices are similar in
a theoretical sense. They are solutions to constrained maximization problems
which di¤er only with respect to the constraints. Therefore, the "logic" of
the solutions, i.e. the inverse elasticity rule, is similar. The actual solutions,
however, di¤er. Not only are monopoly prices higher, they also have a di¤erent
price structure, i.e. the order of prices might di¤er between the two sets of prices.
Furthermore, implications for regulatory policy from the theoretical similarities
are di¢ cult to draw. In practice, most regulated markets are subject to some
form of competition. Competition drives a wedge between the reasoning of the
Ramsey-Boiteux planner and a pro…t maximizing …rm. While the former is
concerned about the market demand elasticities, the latter is only concerned
about his own residual demand. For most practical regulatory questions the
fact that Ramsey-Boiteux and monopoly prices both apply an inverse elasticity
rule does not matter since the rule is applied to di¤erent demand functions.
The text is organized as follows. Section 2 provides the theoretical framework
and makes precise the similarities between the two sets of prices. Section 3
investigates the di¤erences for the case of independent demand functions. In
section 4 we introduce competition as a complication which is important for
policy issues. Section 5 elaborates this point buy investigating a selective entry
process. Section 6 discusses mobile termination as a policy example and section
7 concludes.
2
Model
The similarities become obvious when stating the original Ramsey-Boiteux problem and comparing it to the monopolist’s problem. We analyze a fairly general
formulation which is similar to e.g. Braeutigam (1989), or La¤ont and Tirole
(2000).
There are m; i = 1; :::; m; products. The m dimensional vector q represents
the quantities of these products. Consumer demand for each product is given
by qi (p); where p is the m dimensional vector of prices. Demand might be
interdependent, i.e. @qi =@pj need not be zero. There is a single technology to
produce the output, de…ning a cost function C(q); where C(q) is subadditive for
the relevant demand levels. Let CS denote the consumer surplus. Then a social
planner would – due to the subadditivity of costs – choose only a single …rm
to produce the output. Assume that the social planner is restricted to linear
pricing. Then she solves the following optimization problem:
max CS(q) + pq
pi
s.t.
= pq
C(q) = 0
C(q)
8i;
(1)
(2)
Assume that the restriction is binding (i.e. the Lagrange multiplier is nonzero) and that the solution is determined by the …rst order conditions. Then,
2
after some rearrangement, the …rst order conditions with respect to the relative
mark-up on marginal cost Mi can be stated as (La¤ont and Tirole, 2000, 64) :
MiRB =
X
1
"RB
ii
1+
MjRB
j6=i
|
where
Mi
=
"ji
=
RB RB
"RB
pj
ji qj
;
RB pRB
"RB
q
ii
i
i
{z
}
(3)
correction term
pi
@C
@qi
pi
@qj pi
:
@pi qj
This is the classical ”inverse elasticity rule” with interdependent demand.
In the case of independent demand, the mark-up in excess of the marginal cost,
which is necessary to cover the production cost (say, to cover …xed cost), is
proportionate to the inverse of the price elasticity of demand. In case of interdependent demand, this needs to be corrected: the mark-up should be smaller
(larger) for complements (substitutes). Otherwise the price for a complement
would not account for the distortion imposed on the other complementary products. The correction term must be larger in absolute terms, the more important
the complementary good is (the higher the revenue is) and the higher the distortion (i.e. the mark-up) of this product is.
A monopolist, with the same production technology available as the social
planner, and facing competition in none of the markets, solves the following
problem:
max pq C(q)
8i:
(4)
pi
The …rst order conditions can be expressed as:
MiM =
1
"M
ii
X
j6=i
|
MjM
M M
"M
ji qj pj
:
M
"ii qiM pM
i
{z
}
(5)
correction term
The monopolist also uses an ”inverse elasticity rule”. Where demand is less
elastic, the monopolist will be able to extract more rent, as consumers will be less
prone to abstain from purchasing the good. When demand is interdependent,
the monopolist will account for that similarly to the way a social planner will.
He will add a (positive) correction in case of substitutes in order to account for
the ”externality” among goods. Compare the case where the monopolist either
produces only one good i with the case where he also produces the substitute
j. In the …rst case, he will set a relatively low price, otherwise revenues and
pro…ts would decrease, since consumers would switch to the substitute if prices
were too high. If he, however, produces both products, he will account for that
3
e¤ect: he will set a higher price since he will also receive the payments from the
consumers switching to the substitute.
That a similar logic along the lines of an inverse elasticity rule applies is theoretically unsurprising. From a theoretical point of view there is no doubt that
the prices are similar since they are solutions to the same optimization problem
under comparative statics with respect to the social planner’s constraint (2).
One can transform the Ramsey-Boiteux problem into the monopolist’s problem
just by setting the pro…t in (2) equal the monopolist’s pro…t. Furthermore,
one could also get the marginal cost pricing outcome if in (2) is set equal
to the loss of the …rm if it would use marginal cost pricing (which is the same
as ignoring the constraint (2)). Viewed from this point it will also be not surprising that comparative statics within a given optimization problem will yield
di¤erences in the solutions.
3
Di¤erences with independent demand
Trivially, by construction Ramsey-Boiteux prices yield a higher welfare level
than monopoly prices. However, given the same "logic" of an inverse elasticity
rule, one is tempted to consent to the following statement:
"Put more crudely, the Ramsey-Boiteux prices are the same as those
of an unregulated monopolist, just a notch down." (La¤ont and Tirole, 2000, 63)
There are indeed situations where this statement is perfectly correct, namely
if one assumes constant elasticities of demand and zero cross-elasticities.1 In
this case the vector of monopoly mark-ups M M is just a scalar multiple of the
Ramsey-Boiteux vector of mark-ups M RB :
"ii constant and "ij = 0 ) M M =
1+
M RB ;
> 0:
If the assumption of constant elasticity of demand is not met, the statement
might actually be "too crude". Then the order of the mark-ups need not be the
same order under monopoly prices compared to Ramsey-Boiteux prices.
MiM > MjM ; MiRB > MjRB :
Therefore, it might well happen that product i is less expensive than product
j under Ramsey-Boiteux pricing, while under monopoly pricing product i will
be more expensive then product j: To see how this can happen consider the
1 ten Raa (2005) constructs an example where the …rst condition holds (constant demand
elasticities) while the second (independent demand) is violated and where this leads to a
reversal of the price structure. Thus, independence of demand is also essential for RamseyBoiteux and monopoly prices to have the same structure.
4
following kinked linear demand example, depicted in Figure 1.2 There are two
markets with independent demands. Market 2 has a linear demand function.
Market 1 has a piecewise linear demand function, e.g. because it is the sum
of linear demands of two di¤erent consumer groups. Note that the lower part
of the (inverse) demand functions are parallel. Assume marginal costs equal
zero. Monopoly prices (which equal the mark-ups) can be derived geometrically
M
M
M
as pM
1 and p2 ; p1 > p2 : Assume that the social planner has to set prices
such that some small amount of …xed cost F is covered. Consider …rst the case
where both prices would be the same, pRB
= pRB
= pRB : This would imply
1
2
j"1 j > j"2 j ; which, together with p1 = p2 ; cannot be optimal. Thus, the planner
has to raise p2 relative to p1 , which also increases "2 (p2 ); 3 until eventually
"2 (p2 )p2 = "1 (p1 )p1 = ( =1 + ); the optimality condition from (3). Thus, the
M
M
social planner would choose pRB
> pRB
2
1 , while p2 < p1 :
p
P1
P
2
p 1M
p 2M
RB
RB
ε^1 (p ) > ε^2 (p )
pRB
q
Figure 1: Linear Demand Example
Thus it might be misleading to think that Ramsey-Boiteux prices are equal
to monopoly prices minus, say, 20%. They are "a notch down" but the notch
might be di¤erent for each price such that the price order might be reversed.
Therefore, monopoly prices are not only higher but can also have a di¤erent
order of prices.
This has important policy implications for regulators. Regulators lack the
information necessary to identify the Ramsey-Boiteux prices. The regulated
…rm has superior information on costs and on demand elasticities. On the cost
side, …rms typical have an incentive to shift cost from the non-regulated sector
2 ten Raa (2005) shows that the break down of the similarity of Ramsey-Boiteux and
monopoly pricing does not hinge upon the lack of smoothness. He shows that the same occurs
with two di¤erentiable demand functions, where one exhibits constant demand elasticity while
the other is a linear demand function.
3 Note that the elasticity is given by the (negative) ratio of the distances from the point on
the demand curve to the intersection of the demand function with the x-axis and the y-axis,
respectively: The absolute value of the elasticity thus strictly increases in p along the demand
function. Since the lower part of the …rst demand function is parallel to the second demand
function, at pRB we have "1 > "2:
5
to the regulated sector in order to be able to get approval of higher prices in the
regulated sector. Even though regulators try to get reliable information on the
…rm’s cost structure4 there will always remain some degree of freedom for the
…rm how to allocate cost which the …rm will use to come as close as possible to
monopoly prices.
Consider a situation where the …rm proposes monopoly prices to the regulator, e.g. because these were the prices in the past. The regulator lacks
the information to derive the Ramsey-Boiteux prices. Vogelsang and Finsinger
(1979) have shown that under certain conditions (in particular: with a myopic
monopolist) a price cap regime converges to Ramsey-Boiteux prices. A price
cap is applied each period to a basket containing the di¤erent services of the
monopolist, where past revenues are used as weights for the di¤erent services in
the basket. Hence, the regulator circumvents the informational problem.
Although it is not the focus of the current paper to analyze speci…c methods of price regulation,5 two more general points are of interest in this context.
First, mechanisms like the one proposed by Vogelsang and Finsinger that converge to Ramsey prices must allow the price structure to change when moving
from monopoly prices to Ramsey-Boiteux prices. The kinked demand example
illustrates that this can be necessary. Just reducing the monopoly prices by x
% does not produce Ramsey-Boiteux prices even if x is chosen such that the
Monopolist just breaks even afterwards. This is a direct implication of the fact
that monopoly prices are not a scalar multiple of Ramsey-Boiteux prices. Second, prices will be equal to the Ramsey-Boiteux prices only if the monopolist’s
pro…t goes down to zero. Therefore, if the regulator leaves some pro…t to the
monopolist, the regulator cannot be sure that the price structure obtained is
similar to the Ramsey-Boiteux price structure.
4
Competition
In his seminal article Marcel Boiteux (Boiteux (1956)), who later became CEO
of Electricité de France, the French state owned electricity monopolist, derived
the "inverse elasticity rule" for a setting with a single monopolist serving different customer groups. At that time this description was by and large correct.
In many countries, as in France, there was only a single supplier for electricity,
supplying di¤erent customer groups with potentially di¤erent price elasticities.
Thus his argument was highly relevant for the pricing of a monopolistic utility,
e.g. setting prices for residential versus industrial customers. His considerations
were also perfectly adequate for the regulation of telecommunication tari¤s pro4 Legislators provide regulators with the right to collect cost data, see e.g. for the EU
the "Access Directive" 2002/19/EC (7 March 2002), art.13, which allows regulators even to
prescribe accounting methods for cost allocation. The UK regulator Ofcom just recently
obliged BT to provide separate accounts for network access and retail (see Ofcom (2005)).
5 There is an extensive literature comparing di¤erent regimes, in particular price cap versus
average revenue regulation. Most paper argue that average revenue regulation is welfare
inferior to price caps (Bradley and Price (1988), Bradley and Price (1991), Waterson (1992))
or even to no regulation at all, Cowan (1997).
6
vided by a monopolistic telecommunications operator for di¤erent products,
like long distance and local calls. The same is true for public transport, again
with respect to potentially di¤erent price elasticities of di¤erent destinations or
customer groups.
Times have, however, changed and competition has been introduced into
most of these markets formerly exclusively supplied by a monopolist. Liberalization has at least two dimensions, a horizontal dimension and a vertical
dimension. Horizontally, it implies that some of the …nal good markets a former
monopolist supplied are opened to competition, while others are not. In Europe
the EU required member states to open the non-household sector in the gas
industry for competition at July 2004 while markets for household customers
need not be opened to competition before July 2007.6
With respect to the vertical dimension it has often been argued that in
network industries some elements in the value chain are natural monopolies
("essential facilities") while others are not. For the former regulated access
prices are required to allow for competition in the latter. For instance in the
telecommunications industry it is standard to regard the local access as a natural monopoly while the distribution network (the backbone) is probably not a
natural monopoly.
Both aspects, the horizontal as well as the vertical, raise the question whether
and to what extent Ramsey-Boiteux ideas are still relevant for regulatory decisions. We want to discuss both issues in turn.
4.1
Competition in some …nal good markets
With adjacent …nal product markets opened to competition it is unclear in the
…rst place whether a Ramsey-Boiteux planner would actually like to have more
than one …rm active across markets. In the presence of economies of scale,
free market entry can be ine¢ cient (since the last entrant …nances his entry at
the cost of lower pro…ts for competing …rms rather than from additional social
surplus, see Mankiw and Whinston (1986)). This is of particular importance
since the Ramsey-Boiteux problem assumes scale economies. When talking of
the Ramsey-Boiteux problem we mean that setting price equal marginal cost
results in a de…cit, or more general, that the constraint (2) in the social planner’s
maximization problem is binding.
Only very speci…c cost functions imply that the social planner wants to have
more than a single …rm active across markets in the presence of the RamseyBoiteux problem. Three properties are required. (i) The cost functions of none
of the potential suppliers is subadditive for the relevant region (i.e. the region of
total market demand in equilibrium). Otherwise, due to the natural monopoly
character of the industry, least cost production requires production by this …rm
only. (ii) For n …rms to be socially
optimal, the production vector (x1 ; :::; xn) ,
Pn
providing total supply X = i=1 xi , must be such that the cost for each …rm is
6 Article 23, Directive 2003/55/EC of the European Parliament and of the Council of 26
June 2003 concerning common rules for the internal market in natural gas and repealing
Directive 98/30/EC.
7
subadditive at xi : Otherwise, the social planner could just split the production
of the …rm with non-subadditive cost and introduce a new …rm (provided, that
there is no scarcity of resources that prevent the social planner from replicating
…rms). (iii) Finally, as long as marginal costs are non-decreasing, the average
cost for xi must exceed the marginal cost at xi for at least some …rms. Otherwise,
the Ramsey-Boiteux problem would not occur since …rms could cover their …xed
costs by setting price equal to marginal cost. Few of the standard cost functions
used in economic modelling ful…l these requirements.7 Nevertheless, such cost
situations might exist in reality.8
Assume a cost situation where the social planner wants to allow for competition in one of the markets formerly served by the incumbent only. The
incumbent remains the monopolistic supplier in all other markets.9 Let us compare the monopoly prices with the Ramsey-Boiteux prices in this situation even
though before liberalization prices in regulated markets were neither monopoly
prices nor Ramsey-Boiteux prices. An imperfectly regulated …rm will nevertheless use any leeway to execute market power. Taking monopoly prices as a point
of reference therefore can serve as a useful benchmark.
Consider the model discussed in Section 2. Imagine now that one market j
is opened to competition and a competitor enters the market. This highlights
a key di¤erence between Ramsey-Boiteux and Monopoly reasoning. A private
…rm always focuses on the own residual demand function. Only in the case
of monopoly does this coincide with the market demand function and only
this coincidence is responsible for the similarities between Ramsey-Boiteux and
monopoly pricing.
In market j; the ”monopolist” will optimize against his residual demand
function and no longer against the market demand function (and demand in7 Examples for cost functions which do not ful…l the listed properties are: (i) Constant
marginal costs: If all …rms have a cost function Ci = Fi + ci xi ; then least cost production
always requires production by a single …rm. (ii) Symmetrically increasing marginal cost:
Ci = F +cxi ; > 1: Least cost production then has every …rm producing at the same marginal
cost where in the social optimum marginal cost equal average cost (otherwise - abstracting
from integer problems - the planer could reduce the number of …rms, shift production to the
remaining …rms and reduce industry cost).
8 In Baumol, Panzar, and Willig (1988), 337-338, another issue is highlighted which makes a
situation less likely in which it is socially desirable to have more than a single …rm while prices
equal to marginal cost lead to losses. They show that for any given number of …rms larger
than one, industry cost are typically not minimized if one requires that each …rm individually
breaks even. This is due to the fact that the social planner needs to deviate from the cost
minimizing situation in which the marginal costs are equal among …rms. In the absence of
subsidies, shifting quantities among …rms is the only way to provide those …rms (that would
otherwise not break-even) with additional revenue and pro…ts.
9 This is certainly disputable and there might exist good reasons to assume some "hybrid"
social planner who is able to perfectly control prices but not to prevent entry. A large literature
has made this assumption, see Braeutigam (1989) or Braeutigam (1979). Baumol, Panzar,
and Willig (1988), 334, discuss di¤erent restrictions on the budget balancing for each …rm
individually or at industry level only. In the latter case the social planner can tax or subsidize
di¤erent …rms, in the former he can not. None of these assumptions seem very realistic with
respect to what regulators can actually do. From this point of view assuming that the social
planner can restrict entry might seem even less unrealistic because this happens frequently,
e.g. whenever licences are required like in telecommunications or public transport.
8
terdependencies will also be considered with respect to the residual demand in
market j): The form of the residual demand function is not generally determined; instead, it hinges upon the assumptions about the strategic interaction
between the suppliers and the assumptions on the demand side behavior. Well
known examples for assumptions about the strategic interaction are: (i) Stackelberg leadership for the incumbent, which leads to a relatively inelastic residual
demand function (Fixed quantity qj of the incumbent, the entrant optimizes
against a residual demand function of the form qjE = qj qj :): (ii) Bertrand
competition, which yields perfectly elastic demand function. Examples of assumptions on the demand side are di¤erent rationing rules (”e¢ cient” versus
”proportionate”rationing in case of excess demand; the former implies a parallel
downward shift of the demand function; the latter reduces the inverse demand
at each point by a …xed percentage, see e.g. Tirole (1988), 213.)
It might nevertheless be reasonable to assume that for each quantity qj of the
former monopolist, the residual demand function is more elastic than the market
demand function, since customers can switch to the competitor. This view is
supported by evidence from the telecommunications industry. Estimations for
long distance telecommunications demand …nd a price elasticity for the residual
demand function of individual long distance telecommunications operators up
to 22.8 (Hartman and Naqvi (1994)), while market demand is usually found to
be price inelastic (i.e. price elasticity < 1, see Taylor (2002)).
By similar reasoning, the absolute value of the cross-price elasticity is likely
to be smaller for any given quantity vector of the monopolist if there is competition in market j: Consider an increase in price i: If products i and j are
substitutes, not all consumers’substitution away from i will arrive at the monopolist’s o¤ering in market j; since some consumers might buy good j from
the entrant. Vice versa for complements. The "monopolist", faced with competition in market j, sees less need for correcting the mark-up in market i since
part of the e¤ect from the correction will no longer bene…t the monopolist but
will be captured by the competitor in market j.
With these assumptions on the elasticities of the residual demand function,
we can state that (i) the mark-up in the competitive market j will decrease,
and the mark-ups in the other markets (ii) remain unchanged in the case of independent demand (iii) still have the same sign but become smaller in absolute
terms in case of interdependent demand. The mark-up Mj becomes smaller
due to the introduction of competition in market j: At the former (monopolistic) price level, demand will now be more elastic and the former monopolist
reacts by lowering the price. Prices of substitutes tend to decrease while prices
of complements tend to increase, due to our assumption that j"ij j decreases.
Furthermore, since the monopolist had formerly chosen a point on the demand
function where demand is elastic, i:e: ejj > 1; the monopolist’s revenue qj pj
decreases with the introduction of competition.
There is some evidence for the empirical validity of these theoretical claims.
In the electricity market, in Europe the opening of the market took place step
by step, opening …rst the market for large industrial customers, then for intermediate customers, and …nally for private households. These demands are
9
independent. Indeed, prices decreased only in the segment opened to competition, not in the other markets. See Figure 2 for a comparison of consumer prices
of electricity in Germany versus industry prices before and after liberalization
1998. Although liberalization encompassed both markets, for institutional reasons competition developed only for industrial customers. These prices have
decreased, while the price in the monopoly market (households) has remained
almost stable.
Electricity Prices
Germany
Index (1998 = 1)
1,1
1
0,9
0,8
0,7
Households
0,6
Industry
0,5
1997 1998 1999 2000 2001 2002 2003 2004 2005
Source: Eurostat
Figure 2: Partial market opening I: Electricity
A similar reasoning holds for the telecommunications market in Germany. While
long-distance and international calls were opened to competition in 1998 on the
basis of call-by-call competition, local calls were excluded until the second half of
2003. A similar situation is found: the price in the noncompetitive sector was
almost stable, the price of the competitive segments – unsurprisingly – went
down.
Telecommunication Prices
Germany
Index (1998 = 1)
2
local
national
to US
1,5
1
0,5
0
1997
1998
1999
2000
2001
2002
2003
2004
Source: Eurostat
Figure 3: Partial market opening II: Telecommunications
To summarize the "horizontal" case it is important to note that the (former)
monopolist’s price reaction to competition can formally be described by an "in10
verse elasticity" rule. However, since the monopolist now optimizes against the
elasticity of the residual demand while the Ramsey-Boiteux planner optimizes
against the market demand, the results can be very di¤erent.
4.2
Access Pricing
If some markets along the value chain are competitive, while …rms in the competitive segments require access to the monopolistic elements of the value chain,
the problem of access pricing arises.10 A standard result is that access prices
should contain some mark-up to cover the (…xed) costs of the essential facility
and that these mark-ups have a "Ramsey-property", which means that they
incorporate some form of an inverse elasticity rule.
Since the access pricing problem can be phrased in terms of the RamseyBoiteux problem all problems discussed so far carry over to this class of problems
(di¤erent price structures, incumbent orientated towards residual demand, not
…nal market demand). This is of particular regulatory importance in the presence of the asymmetric information problems already discussed. Imagine an incumbent controlling essential inputs for di¤erent …nal good markets, like access
lines, switches, and DSL infrastructure. As discussed in Section 3, monopoly
prices converge to the Ramsey-Boiteux prices if the price cap system on the
di¤erent products is adequately formulated. Following the logic of Vogelsang
and Finsinger (1979), the basket of products to which the price cap is to be
applied needs to contain all regulated products.
Regulators, however, are reluctant to allow for price cap regulation on inputs.
They are afraid of a price-cost squeeze an integrated incumbent could execute by
setting low …nal market prices and too high prices on (strategically important)
elements of the access services basket. The German legislator, for instance, has
spelled out high hurdles for the application of price cap mechanisms on access
services.11 This prevents the regulator from using a price cap regime which –as
discussed in Section 3 – might converge to the Ramsey-Boiteux result. By the
same arguments discussed in Section 3, just cutting the proposed (monopoly)
access prices by some percentage need not result in Ramsey-Boiteux prices, even
if the monopolist just breaks even with the set of regulated prices.
5
Selective Market Entry
When markets are opened to competition, competitors do usually not enter all
markets at the same time. Entrants typically choose to enter the most attractive
markets …rst ("cream skimming"). What is most attractive clearly depends on
the size of the mark-up the monopolist has established. However, since the
1 0 Seminal articles for the access pricing problem are La¤ont, Rey, and Tirole (1998a),
La¤ont, Rey, and Tirole (1998b) and Armstrong, Doyle, and Vickers (1996). A very accessible
overview is provided in La¤ont and Tirole (2000), Chapter 3.
1 1 Price cap procedures for access services can be considered only if abuse of monopoly power
is prevented by additional ex ante measures; see the legislator’s commentary ("Gesetzesbegründung") to § 32 of the German Telecommunications Act.
11
mark-up was subject to regulation this might not be the monopolistic markup. Nevertheless, it might be plausible to assume that the actual prices re‡ect
market power and the informational advantage of the monopolist and hence
monopoly prices can serve again as a reasonable point of reference.
If pre-liberalization prices were su¢ ciently close to monopoly prices, opening
of the market leads to a systematic bias between Ramsey-Boiteux pricing and
the prices resulting from pro…t maximization. Entry of competitors is biased
towards markets with low price elasticity. Therefore, the residual demand an
incumbent faces tends to be inversely related to the market demand. This is
illustrated in the following simple example. Assume n markets with market
demand Di (pi ) = pi i : Assume that markets di¤er only with respect to their
constant elasticity of demand i ; i = 1; :::; n; where i > 1 and i < j for
i < j:12 Markets are the same size, and marginal costs are identical for all
markets, ci = c for all i. Also the market entry cost Fi are the same, Fi = F;
for all i: Assume that initially all markets are served by an incumbent, who
then sets his mark-up on marginal cost equal to 1= i : Now consider an entrant
who can enter each market (and if he entered, is identical to the incumbent).
He will enter a market as long as he makes positive pro…ts, i.e. the pro…t from
competition (which we assume to be of the Cournot type) with the incumbent in
market i covers the …xed cost of market entry F: Straightforward computations
show that he would then enter the markets with the lowest price elasticities.13
Prices in these market then go down. If pre-entry prices were su¢ ciently close
among markets (which would be the case if the elasticities are close), this change
in the prices of the markets the entrant chose will su¢ ce to change the order of
prices.
Some empirical evidence can be found when comparing business and residential customer markets for phone calls. The demand of business customers is
usually regarded as less price elastic than residential demand, e.g. because they
1 2 With constant elasticities of demand, we need to assume elastic demand,
i > 1; in order
to ensure existence of a price equilibrium. For inelastic demand, i < 1; increasing prices
would always increase pro…ts.
1 3 The inverse demand function is:
1=
pi = Q
; where Q = q1 + q2 :
The Cournot pro…ts of the two symmetrical competitors in the market the entrants selects
are:
c) F:
i = q1 (pi
By symmetry, and assuming F to be small enough such that entry is pro…table, equilibrium
quantity for each …rm is given by:
(2c) i
qi =
:
2
Cournot pro…ts equal:
1
i
=2
i
i
c1
c
i
F;
thus, the no-loss condition is:
1
2
i
i
c1
i
c
F:
The left hand side is decreasing in the market’s price elasticity i : Thus, the entrant enters
all markets up to bi; the last market for which the last inequality holds.
12
are bound to o¢ ce hours and cannot postpone calls into less expensive o¤ peak
hours. Taylor (2002), 103-104, cites additional reasons for a lower elasticity for
business customers. While the regulatory regime is similar (in particular, there
are no di¤erences with respect to the regulated interconnection charges), competition for business customers is more intense than for residential customers.
This is re‡ected in the lower market share of BT, the British telecommunications
incumbent, in the business segment, as can be seen from Figure 4.
BT Market Shares (Volume)
Business Volume
Residential Volume
100,0%
80,0%
60,0%
40,0%
20,0%
Ju
n
D 96
ez
Ju 9 6
n
D 97
ez
Ju 9 7
n
D 98
ez
Ju 9 8
n
D 99
ez
Ju 99
n
D 00
ez
Ju 0 0
n
D 01
ez
Ju 0 1
n
D 02
ez
Ju 0 2
n
D 03
ec
Ju 03
n
04
0,0%
Source:
Ofcom
Figure 4: Stronger market entry in business segment
6
An example: Mobile termination rates
Mobile termination fees have to be paid by the telecommunications company of
the call-originating party to the mobile network operator of the called party in
order to deliver the call on the called party’s network. Under the "calling party
pays" principle the network operator of the call-originating party (typically a
domestic …xed line or mobile network operator) charges the own client for the
termination. The called party pays nothing.14
As it was mentioned already in the introduction, mobile operators made
frequent reference to Ramsey-Boiteux pricing in the discussion of termination
rates. Mobile network operators claimed that demand for termination is relatively inelastic compared to …xed monthly subscription fees or to call prices.
Therefore charging relatively high termination fees would be in line with social
1 4 Calling party pays is the standard rule in Europe. In the US, "mobile party pays"
is frequently in place. While for mobile phones in- and outbound calls are of the same
magnitude in Europe, in the US the ratio is about 1 (inbound) to 3 (outbound). See e.g.
http://www.mobilein.com/ calling_party_pays.htm, (download 26 July 2005). International
roaming is a similar topic since here often also the called party has to pay. A di¤erence,
however, is that the networks of the operators typically do not overlap, therefore the issue of
duplication infrastructure and desirability of more than one supplier is not relevant. A survey
on termination can be found in Armstrong (2002).
13
welfare maximization, as operators have to …nance the …xed and common cost of
the mobile telecommunications network (Competition Commission, 2002, para
1.7, and para 2.435).
This argument is ‡awed since it does not take into account that the di¤erence
in price elasticity might stem from di¤erent intensities of competition in the
markets compared and does not distinguish between …nal market demand and
residual demand. In the retail market, e.g. for subscribers, there typically is
high competitive pressure. Thus, the residual demand function of an operator
is highly price elastic.
Regulators have at the same time often ruled that mobile network operators
have signi…cant market power with respect to delivering the call on the own
network, since there is no substitute for this service. The mobile phone of a
called party can be reached only via the network of the called party’s mobile
network provider. Thus, the residual demand function of an operator for termination is very inelastic. However, the reference of the mobile network operators
towards the Ramsey-Boiteux logic must be with respect to the …nal market demand, not the individual …rm’s residual demand. OFTEL, the UK regulator,
employed precisely this logic in its arguments (Competition Commission, 2002,
para. 2.437).
High termination charges (compared to e.g. monthly subscription fees) could
be justi…ed only if the …nal market demand satis…ed with termination services
would be less elastic than the demand for other services. This would, for instance, be implied if the demand for "on-net" calls would be more price elastic
than the demand for "o¤-net" calls. On-net calls are calls where the calling party
and the called party have subscribed to the same network operator. Thus, no
termination fee is charged. With o¤-net calls di¤erent network operators are involved. Hence, a termination fee is charged which –assuming cost based pricing
–turns into a higher …nal customer price. If the market demand for o¤-net calls
(for whatever reason) would be relatively inelastic, such calls should contribute
more to the coverage of the network’s …xed cost and should be more expensive,
which could be induced by high termination fees. Vodafone, the largest operator
in the UK, however denied that termination fees could be justi…ed by di¤erences
in the price elasticities for on- and o¤-net calls (Competition Commission, 2002,
para. 2.432).
This discussion of termination points out another pitfall when naively referring to "Ramsey-Boiteux" arguments as a justi…cation for (relative) prices.
The Ramsey-Boiteux analysis is a welfare analysis maximizing the social surplus as the sum of producer and consumer surplus. This is meaningful only
when looking at …nal customer markets, where the consumer surplus is derived.
Termination is an intermediate product, an essential input to produce the …nal
product, namely voice calls.15 It needs careful investigation how input prices
relate to …nal market prices. If there exist monopolistic mark-ups in down1 5 An alternative view would be to think of termination and origination as (perfectly) complementary products, implying that the cross-price elasticities are non-zero. This – see the
discussion in Section 3 and example 2 in ten Raa (2005) – implies that monopoly prices are
not always scalar multiples of Ramsey-Boiteux prices.
14
stream markets even large changes in input prices might not yield changes in
…nal market prices. The case of mobile termination at least casts some doubt
on the hypothesis that changes in this input price has had a major impact on
the …nal market price, although at times termination accounted for almost 80%
of the call revenues, see Figure 5.
Pence/Min.
UK: Retail revenues and termination fees
33
30
27
24
21
18
15
12
9
6
3
0
Average Revenue / Call
Jun
98
Dez Jun
98
99
Dez
99
Jun Dez
00
00
Jun Dez
01
01
Termination
Jun Dez
02
02
Jun
03
Figure 5: Termination rates in the UK
There is a large economic literature on mobile termination. The seminal papers by La¤ont, Rey, and Tirole (1998a) and La¤ont, Rey, and Tirole
(1998b) discuss –among other things –questions of (i) overlapping versus nonoverlapping networks, (ii) uniform versus two-part retail tari¤s, (iii) price discrimination between on-net and o¤-net calls, and (iv) reciprocal versus nonreciprocal termination charges. Further research by Gans and King (2001) and
Behringer (2004) shows that the magnitude and even the sign of the mark-ups
on termination costs crucially depend on the question of reciprocal or nonreciprocal access. The issue of whether only the calling party has to pay for the
call is analyzed in Hermalin and Katz (2004).
None of this literature, however, is focused on the key question of a RamseyBoiteux planner: How to set prices if marginal cost pricing would lead to a
de…cit? How can of …xed (network) cost be recovered? The model of La¤ont,
Rey, and Tirole (1998a) which has been used by many subsequent papers on the
topic, does not even consider any …xed cost of network build-up.16 Discussing
the large network build-up cost in overlapping mobile networks begs the question (raised already in Section 3) whether a social planner would want to have
so many …rms active in the market. This implies that a regulator should be cautious in allowing all network operators to recoup their network build-up cost,
even if this happens with Ramsey-Boiteux prices. Ramsey-Boiteux mark-ups
might …nance an ine¢ cient amount of …xed cost of a duplicated infrastructure.
1 6 Their …xed costs are subscriber acquisition costs, e.g. subsidization of a mobile handset.
One exemption, which makes reference to network cost is La¤ont and Tirole (2000), 196: A
socially optimal termination fee would generally be below the marginal cost of termination in
case of monopoly power in the retail market. This might not be the case in the presence of
"common costs": The necessary mark-up might increase the termination fee above marginal
cost.
15
7
Conclusion
The classical Ramsey-Boiteux approach is based on a static model of a single
…rm producing for di¤erent …nal consumer markets. The Ramsey-Boiteux prices
are similar to the prices of a pro…t maximizing monopolist in this framework
only in the sense that at the implemented allocation (which is di¤erent in both
cases) mark-ups on marginal cost will be higher for goods where demand is less
price elastic. The size and order of the prices can, however, di¤er. Monopoly
pricing is not in any general sense "more e¢ cient" just because it is orientated
on the price elasticity at the point realized on the demand function.
It is therefore not surprising that reference to Ramsey-Boiteux pricing o¤ers
even less insights for welfare analysis if one departs from the original assumptions
of the Ramsey-Boiteux world. Allowing for competition in one or all markets
– which is sensible for almost all regulated industries – causes market demand
and residual demand of the "monopolist" to be di¤erent. The Ramsey-Boiteux
planner is oriented at the price elasticity of the former, the monopolist at the
price elasticity of the latter. Both typically deviate signi…cantly from each other.
Analyzing intermediate goods, network access, or termination also shows the
limits of naive analogies between monopoly prices and Ramsey-Boiteux prices.
Economics can say a lot about these things – but not by referring to RamseyBoiteux concepts.
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18