Entry and Competition in the Postal Market: Foundations for the Construction of Entry Scenarios

Journal of Regulatory Economics; 19:2 107±121, 2001

# 2001 Kluwer Academic Publishers. Manufactured in The Netherlands.

Entry and Competition in the Postal Market:Foundations for the Construction of Entry Scenarios*

HELMUTH CREMERIDEI and GREMAQ, University of Toulouse and

Institut Universitaire de France,Place Anatole France, 31042 Toulouse Cedex

ANDREÂ GRIMAUD,

JEAN-PIERRE FLORENSIDEI and GREMAQ, University of Toulouse,

Place Anatole France, 31042 Toulouse Cedex

SARAH MARCYIDEI, University of Toulouse,

Place Anatole France, 31042 Toulouse Cedex

BERNARD ROY, JOEÈ LLE TOLEDANOLa Poste,

4 Quai du Point du Jour, 92777 Boulogne Billancourt Cedex

AbstractThis paper presents a model of entry and imperfect competition, which is inspired by the product

differentiation literature and incorporates facts pertaining to the postal sector. There are two operators:incumbent and potential entrant. The entrant offers only one of the products (commercial mail) with a

speci®c technology and delivers only to part of the addressees (located in low cost areas). Its degree of

coverage is viewed as a quality attribute; it affects demand and hence market share. The incumbent

faces a USO while the entrant is an unregulated pro®t maximizing ®rm. To illustrate the potentialapplications of our approach, we provide some numerical simulations of entry scenarios.

* The views expressed in this paper are those of the authors and do not necessarily re¯ect the views of La

Poste. This paper has been presented at the Seventh Conference on Postal and Delivery Economics (June

23±26, 1999, Sintra, Portugal). We thank the participants and, in particular, our discussants JosÂe Soares and

David Storer for their comments and suggestions. Last but not least the very helpful and detailed remarks of

the referees and the editor, Michael Crew, are also gratefully acknowledged.

1. Introduction

Many current issues of regulatory and competition policy hinge crucially on the nature and

on the properties of the market equilibrium that will occur in a ( partially or totally)

liberalized postal sector. The universal service obligation (USO) provides one of the most

prominent examples. It is the equilibrium after entry has occurred, which effectively

determines the burden that the USO imposes on an operator.1

Similarly, the design of the ®nancing mechanism has to rely on a forward looking

analysis, accounting for its implications for competitive market equilibrium. Competition

policy and, in particular, the design of competition rules for the incumbent operator

provides another example. To distinguish sound and ef®ciency enhancing competition

from predatory behavior, an in-depth understanding of the nature of competition is

required. The construction of the relevant entry scenarios certainly raises a number of

empirical issues, like demand estimations. However, ®rst and foremost, it gives rise to a

theoretical (and methodological) problem, namely the modelling of competition in the

postal sector. Existing industrial economics models can provide some guidance but they

fail to account for the crucial speci®cities of the postal sector. What is needed is a model

which matches the characteristics of the postal sector suf®ciently well to capture its main

features and to yield predictions which are relevant for the policy issues under

investigation.

This paper proposes a model which is intended to represent a step in that direction. We

present a model of imperfect competition inspired by the product differentiation literature

and by Cremer et al. (1995, 1997), which incorporates stylized facts from the postal

sector.2 The main features of the model are as follows. The incumbent operator offers two

products, x (single piece mail) and y (bulk or ``commercial'' mail). The (potential) entrant

offers only product y. The population of addressees is ranked according to their delivery

cost and the entrant serves a fraction m of the total population (measured starting from the

individual with the lowest delivery cost). The products y offered by the incumbent and the

entrant are not perfect substitutes. The degree of coverage affects the entrant's demand in

two ways. First, it determines its potential market share. Second, it affects the demand per

addressee it faces, hence determining (along with prices) its effective market share.

Formally this second effect is introduced by considering m as a ``quality attribute'' of the

entrant's product. The larger m, the more attractive is the entrant's product, and the lower is

the price differential (conceded by undercutting the incumbent's price) at which it can

capture a positive market share. Observe that in reality this parameter is likely to change

(and increase) over time once entry has occurred and as the entrant's reputation becomes

established. Our static model abstracts from such dynamical phenomena, but this caveat

1 See Cremer et al. (2000) and Toledano and Gallet (1997).

2 The only predecessors to our calibration oriented approach we found are Dobbs and Richards (1991,

1992) who present and calibrate a simple model of entry in the postal sector. Though interesting, their

speci®cation is, however, not suf®ciently elaborate to account for the relevant entry scenarios. However,

there do exist other theoretical models of entry in the postal sector; see e.g., Crew and Kleindorfer (1998)

and Panzar (1999).

108 HELMUTH CREMER ET AL.

has to be taken into account for the interpretation of the results. We study essentially short-

run equilibria and in the short run, the incumbent has a competitive advantage which may

not persist in the long run. Finally, the entrant uses a distinctive single product technology.

Its speci®cation is based on a technico-economical analysis of the relevant process,

developed by Roy (1999).

The regulatory context we consider is as follows. The incumbent faces a USO on both

products which includes a uniform pricing requirement. In addition, its pricing policy is

subject to standard regulatory constraints (e.g., zero pro®t constraint, price cap, etc.). The

entrant, on the other hand, is an unregulated and pro®t-maximizing ®rm. Our setting can,

however, easily be combined with alternative regulatory arrangements. To illustrate this,

we also consider the possibility of relaxing the uniform pricing constraint on the

competitive product.

The main objective of this paper is to contribute to providing the methodological

foundations for the construction of entry scenarios. To illustrate the potential applications

of our setup, we also provide some numerical simulations of entry scenarios. The demand

and cost functions we use there have some realistic ¯avor and re¯ect some stylized facts

from the postal sector. However, they are not meant to represent fully ¯edged empirical

estimations of the underlying model. Consequently, our results are only of illustrative

nature and we refrain from drawing policy recommendations.

In this simulation part, we characterize the market equilibrium for a range of scales of

entry and under different assumptions on the regulatory rules that restrict the incumbent's

price adjustments. In particular, we study a ``passive incumbent'' scenario in which the

prices of the historic operator do not change as entry occurs. We also study various

alternative scenarios under which the incumbent adjusts (at least) some of its prices as

entry occurs. For each scenario, we assess the implications on the operator's pro®ts and

market share and on welfare. The viability of entry at different scales is also addressed.

2. The Model

We now turn to the presentation of the theoretical model. Even though we use speci®c

forms for the utility and cost functions, closed form solutions cannot be obtained.

Consequently, we study different scenarios through simulations. The calibration procedure

on which these simulations are based is explained in the Appendix. Even though, they

re¯ect some stylized facts from the postal sector, they are only meant to be illustrative.

2.1. AgentsThere is one representative sender who sends mail to a large number of individuals.

These N addressees are ranked according to their delivery cost, starting with the lowest

cost individual. There are two operators: the incumbent, indexed by m and a (potential)

entrant, indexed by c. The entrant delivers mail only to a fraction m (with 0 � m � 1) of the

addressees, namely those with the lowest delivery costs. In other words, the population of

addressees is partitioned into two subsets (market segments). The fraction m of households

with the lowest cost are served by the two operators while the remaining households can be

reached only via the incumbent operator.

ENTRY AND COMPETITION 109

2.2. Mail ProductsThere are two products. Single piece mail, x, is offered only by the incumbent operator,

irrespective of the location of the addressee. Bulk (commercial) mail, y, on the other hand,

is offered by both operators or solely by the incumbent, depending on the location of the

addressee. To be more precise, entrant and incumbent deliver y to the low-cost segment,

representing a fraction m of the addressees, while only the incumbent serves the remaining

(high-cost) individuals.3

We shall use the following notation. First, subscripts identify the operator while

superscripts identify the location of the addressee (competitive or monopolistic segment).

Second, the number of pieces sent to an addressee is denoted by lowercase letters.

Speci®cally ycm and ym

m denote the number of units of y sent through the incumbent's

network to each addressee in the competitive and monopolistic segments respectively. The

number of units carried by the entrant is denoted by yc. The corresponding prices are pcm

and pmm for the incumbent and pc for the entrant. Observe that pc

m � pmm � pm corresponds

to uniform pricing by the incumbent (as is imposed in some of the scenarios below).

Total demand for the incumbent's bulk mail product is then given by

Ym � Ycm � Ym

m ;

where

Ycm � Nf�m�yc

m; �1�

and

Ymm � N�1ÿ f�m��ym

m; �2�

similarly, total demand for the entrant's product is

Yc � Nf�m�yc; �3�

where f�m� is the fraction of mail which corresponds to the fraction of the m lowest cost

addressees. This function, satisfying f�m�4m is introduced to take into account the

empirically observed property that low-cost customers tend to receive more mail.4

Finally, X is total demand for single-piece mail. Even though this product is offered by

the incumbent only, it is sometimes useful to distinguish between Xc and Xm, that is

according to the location of the addressees. The price of X, denoted pX, is assumed to be

uniform throughout the paper.

3 Our calibration are based on a de®nition of y which aggregates direct mail and invoice mail or, more

generally, presorted mail.

4 This is a shortcut for the additional dimensions of heterogeneity which are not accounted for in our

model; see footnote 8.


2.3. PreferencesPreferences are quasi-linear and separable between goods and addressees. The utility

(surplus) of the representative sender is given by

S � U�X� � f�m�Nvc�ycm; yc; m� � 1ÿ f�m�� Nvm�ym

m� � Z; �4�

where Z is consumption of the numeraire good, which is determined by the budget

constraint:

Z � Rÿ pXX ÿ f�m�� pcmyc

m � pcyc� ÿ �1ÿ f�m��pmmym; �5�

where R denotes exogenous income. Before proceeding, it is useful to have a closer look at

each of the remaining terms of equation (4).

2.3.1. Good YThe function vc�yc

m; yc; m� represents utility (gross surplus) derived from the units of ysent to one of the addressees in the competitive segment. Observe that products are

differentiated in this segment; the variant offered by the incumbent, ycm, and that offered by

the entrant, yc, are substitutes, but not in general perfect substitutes. The variable mcaptures the ``network effect'' and it effectively plays the role of a quality attribute of the

entrant's product. Everything else equal, the entrants product is more attractive the more

addressees it can reach. We shall use the following speci®cation for this function:

vc�ycm; yc; m� � ayc

m ÿa2�yc

m�2 � byc ÿb2

y2c

� �g�m� ÿ gyc

mycg�m�; �6�

where g�m� is an increasing ( possibly nonlinear) function which represents the weight

attached to the entrants product, while a, a, b, b and g are positive constants.5

The role of g�m� can best be understood by looking at the marginal utilities (marginal

willingness to pay) of the two products:6

qv

qyc

� �bÿ byc ÿ gycm�g�m� �7�

and

qv

qycm

� aÿ aycm ÿ gycg�m�: �8�

5 Satisfying the usual regularity conditions to obtain a well behaved utility function.

6 Marginal utilities and marginal willingness to pay are equivalent because of the quasi-linear speci®cation.


Expression (7) shows that the marginal willingness to pay for the entrant's product

increases as the coverage of the entrant, m, increases. Expression (8) on the other hand

implies that the willingness to pay for the incumbent's product decreases as this coverage

increases.

The senders utility for the units of y sent to an addressee on the monopolistic segment is

given by

vm�ymm� � aym

m ÿa2�ym

m�2: �9�

Observe that vm�y mm �:vc�y m

m ; 0; 0�: the utility function on the monopolistic segment is a

special case of the utility function on the competitive segment; it is simply obtained by

setting the consumption of the entrant's variant to zero.7

Finally, vc and vm are de®ned on a per address basis. To obtain the utility the sender

derives from the bulk mail sent to all addressees, the terms are multiplied by N times the

relative weight of the segment (f�m� for c and �1ÿ f�m�� for m).8

2.3.2. Good XFor single piece mail, utility is directly speci®ed in terms of total consumption. Since X

is offered by a single operator at a uniform price, this does not involve any loss of

generality. Our calibrations will be based on a quadratic speci®cation given by

U�X� � aXX ÿ aX

2X2: �10�

2.4. Demand FunctionsDemand functions can now be derived by maximizing S de®ned by (4), subject to the

budget constraint (5) with respect to ymm, yc

m, yc and X, while making use of the de®nitions

(6), (9), (10). This problem is simpli®ed by the speci®c preference structure, which allows

one to consider the different market segments separately.

It can be veri®ed that ymm is determined by maximizing:

7 In which case the value of m no longer matters.

8 As mentioned in footnote 4, our speci®cation is a reduced form of a model where different weights are

attached to the addressees. To show this formally, let us concentrate on a single mail ¯ow y. Addressees

are indexed by e [ [0,1] which represents the proportion of individuals with lower or equal delivery cost.

The utility from mail to a given addressee is then given by

Z�e� y�e��Z�e��

:

Under uniform pricing, the sender's problem then yieldsy�e��Z�e� � cst. � y

which corresponds to the ``per capita'' variable in our setting. Summing over addressees then gives our

expressions with f�m� de®ned as

f�m� � R m0Z�e�de:


aymm ÿ

a2�ym

m�2 ÿ pmmym

m:

Using boldface characters to denote demand functions we then get

ymm�pm

m� �a

aÿ pm

m

a: �11�

Observe that ymm is independent of the prices in other segments and does not depend on m.

Using (2) total demand (on the monopolistic segment) is then de®ned by

Ymm�pm

m; m� � �1ÿ f�m��Nymm�pm

m�; �12�

which, unlike the demand per addressee, does (of course) depend on m.

Next, ycm and yc can be determined by maximizing:

aycm ÿ

a2�yc

m�2 � byc ÿb2

y2c

� �g�m� ÿ gyc

mycg�m� ÿ pcmyc

m ÿ pcyc:

First-order conditions are given by:

aycm � gg�m�yc � aÿ pc

m;

gycm � byc � bÿ pc=g�m�:

Solving this system of equations yields the demand functions:

ycm�pc

m; pc;m� � Aÿ Bpcm � Cpc; �13�

yc�pcm; pc; m� � H ÿ Ipc � Cpc

m; �14�

where

A � abÿ bgg�m�D

; B � bD; C � g

D; H � abÿ ag

D;

I � ag�m�D ; D � abÿ g2g�m�: �15�

Using (2) and (3) we obtain the aggregate demand functions (units send to all addresses

in the competitive segment) for the incumbent

Ycm�pc

m; pc; m� � Nf�m�ycm�pc

m; pc; m�; �16�

and for the entrant


Yc�pcm; pc; m� � Nf�m�yc�pc

m; pc; m�: �17�

The degree of coverage of the competitor affects these demands in two ways. First, it

has an impact on the demand per addressee (network effect); see (13)±(14). Second, it

determines the potential market share of the entrant, that is the number of addressees in the

competitive segment.9

Finally, optimization with respect to X yields:

X�pX� �aX

aX

ÿ pX

aX

: �18�

2.5. Cost functionsThe cost function of the incumbent is given by

Cm�X; Ymm ; Y

cm; m� �Cmÿ cts�X; Ym

m � Ycm�

� Cmÿ d�Xm;Xc; Ymm ;Y

cm; m�; �19�

where Cmÿ d is the cost of delivery, while Cmÿ cts is the cost of the other activities

(collection, transportation, sorting and overhead). Observe that Cmÿ cts depends solely on

the total output for each of the products, while the location of the addressees matters for

delivery cost. Further, we use a more sophisticated formulation for delivery cost than for

the cost in the other segments. This is because delivery is the crucial activity for the entry

scenarios we consider.

The cost function of the potential entrant is given by Cc�Yc; m�. This function is

estimated by using data generated from an engineering model of the entrants process; see

section B.1.1.

We now turn to the study of some entry scenarios. These are based on a calibrated

version of the model, where the parameters are chosen to re¯ect some stylized facts from

the postal sector. A description of the calibration procedure is provided in the Appendix.

3. Entry Scenarios

Our model can be used to study the market equilibrium in a liberalized market under a

variety of assumptions regarding the behavior of the incumbent, the regulatory

environment, the scale of entry etc. In the current paper, we shall restrict ourselves to

presenting some illustrative scenarios and sketch their policy implications.

9 The interpretation of m depends in part on the assumption that we have a single entrant. Demand would

certainly be affected in a different way if there were several entrants, serving different (disjoint) areas

which add up to the equivalent of a coverage of m. If several entrants serve the same area, the analysis

becomes much more complex for one then would have to worry explicitly about the interaction between

entrant's demands.


We start by considering the case of the ``passive incumbent'', that is the situation where

the operator m does not change its prices when entry occurs. Next, and on the opposite

extreme, we study the ``aggressive incumbent'' scenario, in which the operator engages

in limit pricing behavior to deter entry. Finally, we study the Nash equilibria with and

without a uniform pricing constraint.

In all our examples pX is held constant. Variants in which pX is also adapted e.g., to

maintain the initial pro®t level or to maximize welfare can easily be constructed.

In each of the scenarios considered, the entrant sets its price pc to maximize its pro®t:

pc�pcm; pc; m� � pcYc�pc

m; pc; m� ÿ C�Yc�pcm; pc; m�; m�; �20�

given pcm and m.

Before proceeding, some additional de®nitions are in order. The incumbent's pro®ts are

given by

pm � pcmYc

m � pmmYm

m � pXX ÿ Cm: �21�

Total (unweighted) surplus is de®ned by

W � S� pc � pm: �22�

Finally, it is useful to consider a weighted surplus, given by

Wl � S� pc � �1� l�pm; �23�

where l can be set for instance equal to the marginal cost of public funds.

3.1. Passive IncumbentWe ®rst assume that the incumbent does not change its prices as entry occurs. Operator

m's prices thus remain at their initial level, that is pX � 3:69 and pcm � pm

m � 2:33; see

Appendix A. A full characterization of the market equilibrium then only requires the

determination of the entrant's pro®t maximizing price level. The solution for different

levels of m is reported in table 1, where Ms-t denotes total market share ( for good Y) of the

entrant, c, while Ms-c denotes the entrant's market share on the competitive segment. The

pre-entry outcome (monopoly) is recalled in the ®rst line. Details on the speci®cation of

the parameters of the model are given in the Appendix.

For a low scale of entry (10%), pc is small (the entrant serves only the addressees with

the lowest cost) so that the price differential with the incumbent is large. Nevertheless the

entrant only captures a rather small market (10% of the total Ms-t, 54% on the competitive

segment Ms-c). This is because with a low m the entrant's product receives low weight in

the utility. When the entrant covers 50% of the population, the price differential is much

more limited but the entrant now captures more than 80% of the market on the competitive

segment.

Not surprisingly, the incumbent's pro®t decreases, and thus becomes negative, as mincreases. The entrant, on the other hand realizes a larger pro®t for a larger scale of entry.


This property is the result of two con¯icting effects that occur when m increases: demand

increase and cost increase. To understand the demand increase, recall that the potential

market share increases when m increases. In addition m acts as a quality attribute via g�m�;see subsection 2.4. The unit cost increase, on the other hand, follows from the very

de®nition of m and the ranking of consumers; see 2.5. Our results suggest that the demand

effect dominates, at least up to the considered scale of entry. Observe that the entrant

realizes positive pro®ts in all cases: with a passive incumbent, entry is thus feasible.

Finally welfare decreases. Unweighted surplus decreases because the duplication of the

delivery network is inef®cient.10 Weighted surplus declines even more because the

incumbent's pro®ts decline (and this pro®t is weighted at one plus the marginal cost of

public funds).

3.2. Aggressive IncumbentLet us now assume that the incumbent adopts a limit pricing behavior. In other words, it

sets its price so that the maximum pro®t that can be achieved by the entrant is equal to zero;

consequently, entry will not occur.11 The plausibility of this scenario is admittedly

debatable. First, it is well known that entry pricing strategies are not credible and may thus

not be suitable to deter entry. Second, even when the incumbent can credibly commit to the

limit price, it may be prohibited by competition authorities. In spite of these quali®cations,

the derivation of the limit price appears to be an interesting exercise.

Results are reported in table 2, once again for different scales of entry. The indicated

pro®t is that of the incumbent both for the case of uniform and non-uniform pricing. Notice

that if uniform price is imposed, operator m has to apply the low limit price also to the

monopolistic segment.

Interestingly, it turns out that the limit price ®rst increases and then decreases with m.

Once again, demand and cost incidence of m induce contradicting effects. For a low level

of ( potential) entry the limit price is low because the entrant has low unit cost; this

Table 1. Passive Incumbent

m Pc Ms-t Ms-c pm pc W Wl

0 Ð Ð Ð 0 Ð 38,047 38,047

0.1 1.11 0.10 0.54 ÿ647 316 37,983 37,7890.2 1.22 0.16 0.54 ÿ993 397 37,886 37,588

0.3 1.34 0.24 0.59 ÿ1,557 577 37,750 37,283

0.4 1.46 0.34 0.69 ÿ2,395 989 37,728 37,010

0.5 1.56 0.47 0.81 ÿ3,414 1,508 37,713 36,689

10 This is because of the properties of the delivery technology. Roughly speaking, the incumbents

multiproduct technology implies an incremental (unit) cost of y which is lower than the (unit) cost

implied by the (otherwise ef®cient) single product technology used by the entrant.

11 Strictly speaking, the indicated price leaves the competitor indifferent between entering and not entering.

However, a slightly lower price yields strictly negative pro®ts and thus no entry.


advantage tends to decrease as m becomes larger. However, for high levels of m the demand

for the potential entrant's product is large, and a low price is once again necessary to deter

entry.

The incumbent's pro®ts are inversely related to the limit price; this does not come as a

surprise. Notice the signi®cant impact of the uniform pricing constraint on the incumbent's

pro®t, especially for m � 0:1.

3.3. Nash EquilibriumSo far we have considered two extreme cases, neither of which is meant to predict the

effective post-entry equilibrium. Instead, they have provided two interesting benchmarks

and have illustrated the different effects which drive our model. We now turn to a more

meaningful modelling of the market equilibrium by adopting a solution concept which is

probably the most prominent one in the industrial economics literature, namely the Nash

equilibrium.

We consider a simultaneous game with two players (operators m and c), where prices are

the strategic variables (Bertrand competition with differentiated products) and where the

incumbent's objective is weighted surplus Wl with l � 0:3, with or without a uniform

pricing constraint.12 Recall that the entrant maximizes its pro®t.

The results are given in table 3a (uniform pricing) and 3b (no uniform pricing

constraint); they call for the following observations. First, the incumbent's pro®ts are

negative in all cases. Not surprisingly, losses are less important if there is no uniform

pricing constraints. Second, the incumbent's pro®ts are in some cases smaller than in the

passive incumbent scenario (subsection 3.1). This may appear surprising at ®rst, but it is

easily explained when one considers the fact that the entrant's prices are lower in these

cases than in the passive incumbent scenario.13 Third, entry is viable at all the considered

scales when the incumbent has to price uniformly. When non-uniform pricing is allowed,

on the other hand, only large scale entry is pro®table.

Table 2. Aggressive Incumbent; Limit Prices and Pro®ts With and Without Uniform Pricing

m pcm puniform pnon-uniform

0.1 1.50 ÿ 6,040 ÿ768

0.2 1.78 ÿ 3,603 ÿ8360.3 1.85 ÿ 3,095 ÿ 1,028

0.4 1.80 ÿ 3,434 ÿ 1,473

0.5 1.77 ÿ 3,688 ÿ 1,939

12 One can easily generate alternative scenarios by varying the objective of the incumbentÐranging from

the maximization of unweighted welfare �l � 0� to pro®t maximization �l??�. Further, one can

consider a different timing. For instance, if the incumbent commits itself to a price in a ®rst stage we

obtain a Stackelberg type equilibrium.

13 A Stackelberg leader can never do worse then in the passive incumbent case, but a Nash competitor can.

The problem is that it cannot credibly commit to the passive strategy.


4. Concluding Remarks

Let us ®rst recall that the objective of this paper has been mainly to provide a

methodological contribution. The speci®c results we have provided are mainly of

illustrative nature; they do not lead to direct policy recommendations. However, our model

could be used to make such recommendations when calibrated and/or estimated properly.

Furthermore, in spite of their illustrative nature, some of the results are worth mentioning

as they point towards possibly more general properties. For instance, the ®nding that the

limit price is not a monotonic function of the entrants degree of coverage can be expected

to have some robustness. Similarly, the discussion of the relationship between the entrant's

pro®t (in the passive incumbent case) and its degree of coverage can be expected to remain

valid in a more general setting. Furthermore, the property that the incumbent's pro®ts are

in some cases smaller at the Nash equilibrium than in the passive incumbent scenario is an

interesting reminder of the fact that ®rst intuitions may be misleading in a setting where

strategic interaction is involved. Finally, the rather signi®cant impact of the uniform

pricing constraint on the incumbent's pro®ts and on the possibility of entry, suggests that

such regulatory constraints may potentially play a large role.

To conclude, let us revisit the assumption that there is a single potential entrant. At this

point it is not entirely clear whether this effectively imposes a restriction or whether it

merely anticipates the equilibrium outcome in a model with several potential entrants.

However, the relevance of multiple entry has to be quali®ed in light of our illustrative

scenarios which suggest that small scale entry may not be viable. This is of course mainly

due to the technology, characterized by some degree of increasing returns to scale (even

Table 3a. Nash Equilibrium With Uniform Pricing

m pcm pm

m pc Ms-t Ms-c pm pc W Wl

0 2.33 2.33 Ð Ð Ð 0 Ð 38,047 38,047

0.1 2.02 2.02 1.02 0.07 0.43 ÿ2,256 178 38,643 37,9660.2 2.00 2.00 1.13 0.11 0.41 ÿ2,579 138 38,577 37,804

0.3 1.95 1.95 1.23 0.16 0.42 ÿ3,124 110 38,510 37,573

0.4 1.92 1.92 1.33 0.23 0.48 ÿ3,708 187 38,496 37,384

0.5 1.89 1.89 1.42 0.30 0.54 ÿ4,307 274 38,455 37,163

Table 3b. Nash Equilibrium Without Uniform Pricing Constraint

m pcm pm

m pc Ms-t Ms-c pm pc W Wl

0 2.33 2.33 Ð Ð Ð 0 Ð 38,047 38,0470.1 1.56 2.33 0.91 0.05 0.28 ÿ 867 ÿ 16 38,269 38,009

0.2 1.71 2.33 1.07 0.09 0.30 ÿ 1,281 ÿ 42 38,227 37,843

0.3 1.71 2.33 1.17 0.13 0.31 ÿ 1,846 ÿ127 38,218 37,664

0.4 1.73 2.33 1.28 0.20 0.38 ÿ 2,431 ÿ102 38,227 37,4980.5 1.75 2.33 1.37 0.27 0.45 ÿ 3,067 48 38,218 37,298


for the entrant), but also to demand considerations. A detailed examination of this issue

would, however, go beyond the scope of this paper. It is therefore left for future research.

AppendixÐCalibration of the Model

The values of the demand parameters and the cost functions are not derived from an

econometric analysis. We have selected the values of the parameters in order to reproduce

some stylized facts of the French postal sector.

A. Preferences and Demand

A.1. Good XWe assume a price elasticity of ÿ 0.5 for a price px � 3:69 and a level of demand

X � 7274. We then obtain the following demand function:

X�px� � 10911ÿ 985:6368px:

A.2. Good Y

* We restrict the possible values of the entrant's degree of coverage, m, to f0, 0.1, 0.2,

0.3, 0.4, 0.5g, where m � 0 corresponds to the initial situation. We have then ranked

the addresses by increasing delivery cost and matched them with the corresponding

mail ¯ows described by f�m�.* The values of a; a; b; b and g are then set at the following levels:

a � 5:2425 a � 3:785610ÿ 4 b � 4:84763

b � 3:8647610ÿ 4 g � 3:2610ÿ 4:

The parameters a and a correspond to a demand elasticity of ÿ 0.8 at the current

price of 2.33 in absence of competition. The other parameters are selected in order to

determine ``plausible'' demand scenarios. For example if the price of good Y by the

incumbent is 2.33 and if the price of the entrant is 1.80 for a value of m � 0:5 we get

Ymm � Yc

m � 6116 and Yc � 2002.* The function g�m� is normalized so that g�0:5� � 1. Recall that g�m� is the weight

attached to the entrant's variant: this weight determines, along the operator's prices,

the entrant's market share in the competitive segment.

In table A.1 the value of h�m� are assumed and g�m� is computed from the model.


B. Cost Functions

B.1. Operator m

Delivery. The cost of the delivery does not depend of the nature of the good and is a

function of Zc � Xc � Yc and Zm � Xm � Ym (mail delivered on the competitive segment

and on the non competitive segments). For any value of m the cost can be written as

C � Cc � Cm where Cc and Cm are obtained by a polynomial approximation of ln Cc and

ln Cm as functions of ln Zc and ln Zm.14 These cost functions are not derived from an

econometric study but they are consistent with our previous econometric analysis of the

delivery cost.15

Collection. The estimations are based on two assumption. First, good X and good Y enter

the network independently and, second, this process is characterized by increasing returns

to scale. Speci®cally, cost depends linearly on the square root of the two output levels of

each of the two products.

Sorting and Transport. We assume that the costs of sorting and of transport are linear in

the two goods X and Y.

Overhead cost. We assume that 1/4 of the overhead cost is variable and proportional to

others costs (collection, sorting, transport and delivery). The other 3/4 is supposed ®xed

and indivisible.

B.2. Operator cThe cost function of the competitor is based on the technico-economic developed in Roy

(1999). The underlying process is a 2 days per week delivery for bulk mail only. This

process is used for instance by CityMail in Sweden. The cost is evaluated for each delivery

of®ce, conditional on traf®c volumes. The of®ces are arranged in ascending order of unit

costs.

14 The detailed expressions for the functions referred to in this section are available from the authors upon

request.

15 See Cazals et al. (1997).

Table A.1: h�m� � market share of the entrant for a price differential of 40% �pc � 1:398�g�u� � estimated values normalized by g�0:5� � 1)

m h�m� g�m�

0.1 14% 0.7622796

0.2 22% 0.80166696

0.3 34% 0.85945169

0.4 52% 0.93698387


The per unit sorting cost increases from 0.1 FF to 0.3 FF as coverage increases from 10%

to 50% of the addresses. The entrant's cost is increasing in its two arguments, m and Yc and

we have:

Cc � Ccÿd � Ccÿs;

where Ccÿ d is the delivery cost and Ccÿ s is the sorting cost.

The estimated functions are given by:

Ccÿ d � 81:0207316Y0:51275c m0:73402

and

Ccÿ s � �0:5m� 0:05�6Yc:

References

Cazals, C., M. De Rycke, J.-P. Florens, and S. Rouzaud. 1997. ``Scale Economies and Natural Monopoly in the

Postal Delivery: Comparison between Parametric and Non Parametric Speci®cation.'' In Managing Change inthe Postal and Delivery Industries, edited by M. A. Crew, and P. R. Kleindorfer. Boston: Kluwer Academic

Publishers, pp. 65±80.

Cremer, H., M. De Rycke, and A. Grimaud. 1995. `Àlternative Scenarios for the Reform of Postal Services:

Optimal Pricing and Welfare.'' In Commercialization of Postal and Delivery Services, edited by M. A. Crew,

and P. R. Kleindorfer, Boston: Kluwer Academic Publishers, pp. 247±267.

Cremer, H., M. De Rycke, and A. Grimaud. 1997. ``Costs and Bene®ts of Universal Service Obligations in the

Postal Sector.'' In Managing Change in the Postal and Delivery Industries, edited by M. A. Crew and P. R.

Kleindorfer. Boston: Kluwer Academic Publishers, pp. 22±41.

Cremer, H., A. Grimaud, and J.-J. Laffont. 2000. ``The Cost of Universal Service in the Postal Sector.'' In

Current Directions in Postal Reform, edited by M. A. Crew, and P. R. Kleindorfer, Boston: Kluwer Academic


Crew, M., and P. Kleindorfer. 1998. `Èf®cient Entry, Monopoly and the Universal Service Obligation in the

Postal Sector.'' Journal of Regulatory Economics 14: 103±126.

Gallet, C., and J. Toledano. 1997. ``The Cost of the Universal Service in a Competitive Environment.'' In

Managing Change in the Postal and Delivery Industries, edited by M. A. Crew and P. R. Kleindorfer. Boston:

Kluwer Academic Publishers, pp. 304±320.

Dobbs, I., and P. Richards. 1991. `Àssessing the welfare effects of entry into letter delivery.'' In Competitionand Innovation in Postal Services, editied by M. A. Crew and P. R. Kleindorfer. Boston: Kluwer Academic


Dobbs, I., and P. Richards. 1992. Entry and component pricing in regulated markets. Mimeo.

Panzar, J., 2001. `À methodology for measuring the cost of universal service obligation'', In Future Directionsin Postal Reform, edited by M. A. Crew and P. R. Kleindorfer. Boston: Kluwer Academic Publishers.

Roy, B. 1999. ``Technico-Economic Analysis of the Costs of Outside Work in Postal Delivery.'' In EmergingCompetition in Postal and Delivery Services, edited by M. A. Crew and P. R. Kleindorfer. Boston: Kluwer

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Entry and Competition in the Postal Market: Foundations for the Construction of Entry Scenarios

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