We consider two products traded in two duopoly markets, where competition is assumed a la Hotelling. Firms A and B are operating in Market 1, while Firm B is also competing in Market 2 with Firm C. Prices in Market 2 are pegged linearly to the average price in Market 1. We show that price indexation has anticompetitive consequences that always benefit Firm A, and that benefit Firm B operating in both markets if the size of the reference market is large enough.Hotelling, prices, indexation

Michèle Breton

Mohammed Kharbach

English

Research Papers in Economics

     
 
 
  
  
Volume 29, Issue 4 
  
Who benefits from price indexation? 
  
 
 
Michèle Breton  
GERAD and HEC Montreal 
Mohammed Kharbach  
Dolphin Energy
Abstract 
We consider two products traded in two duopoly markets, where competition is assumed a la Hotelling. Firms A and 
B are operating in Market 1, while Firm B is also competing in Market 2 with Firm C. Prices in Market 2 are pegged 
linearly to the average price in Market 1. We show that price indexation has anticompetitive consequences that always 
benefit Firm A, and that benefit Firm B operating in both markets if the size of the reference market is large enough.
 
Citation: Michèle Breton and Mohammed Kharbach, (2009) ''Who benefits from price indexation?'', Economics Bulletin, Vol. 29 no.4 pp. 
2732-2737. 
Submitted: Aug 04 2009.   Published: October 29, 2009. 
 
     1 Introduction
Indexation or pegging is a pricing mechanism that is used in diﬀerent markets, such as
commodities. For example, natural gas contract prices in most of European countries are
indexed to fuel oil prices, and LNG prices in Asia are linked to average prices of diﬀerent
imported crude oil streams. The link to a spot market helps reduce pricing uncertainties in
the contracts markets.
There is an important literature on long-term contracts. The economics of long-term
and-short term contracts in the gas industry are analyzed in Neuhoﬀ and Von HirchHausen
(2005); the authors show that, if the long-run demand elasticity is signiﬁcantly higher than
the short-term elasticity, then the strategic producers and consumers beneﬁtf r o ml o w e r
prices and larger volumes. The (anti) competitive consequences of long-term contracting are
discussed in Allaz and Vila (1983); the authors show that forward trading fosters competition.
Le Coq (2004) and Liski and Montero (2004) ﬁnd that forward trading induces collusions in
the spot market.
In this note, we consider the eﬀect of a linear indexation pricing in the two markets
involved: Market 2 which is using the indexation mechanism (gas for example), and Market
1, the "benchmark" market (oil for example). We analyze the situation where both markets
are competitive. Recent development in LNG markets, for example, support our assumption
for Market 2. Indeed, most of the LNG contracts that were signed in the 70s and 80s
have approached their maturation. Besides, an important train capacity was added in the
last decade. Therefore, some customers were able to proﬁtf r o ms u c has i t u a t i o nt os e c u r e
a competitive pricing. For example, in the recent tender for Guangdong LNG terminal,
Chinese buyers were able to secure a contract with a much better indexation (proportionality
coeﬃcient) than what was used for other Asian countries.
We analyze the interactions in the two markets in the presence of a common ﬁrm operating
in both markets. Note that the following analysis is conducted without reference to contracts:
we consider two diﬀe r e n td u o p o l ym a r k e t sw h e r e b yt h ep r i c ei no n em a r k e ti sp e g g e dt ot h e
average price in the other.
The remainder of this note is organized as follows: Section 2 describes the setting, Section
3 derives the equilibrium solution and Section 4 concludes.
2 The two duopoly markets
We consider two products traded in two seperate markets, labeled Market 1 and Market 2;
each market is represented by a set of consumers distributed with a density equal to 1 in
the interval [0,L i],i=1 ,2.T h r e e ﬁrms are competing on these markets: Firms A and B
are competing in Market 1 while Firms B and C are competing in Market 2. Firm B is
operating in both markets; it is located in the right (left) end of Market 1(2).A l lﬁrms have
zero marginal costs.
As in the standard Hotelling model, a consumer pays a price P for the product and a
linear transportation cost. All consumers derive the same intrinsic utility from consumption,
which is assumed large so that all consumers want to consume the product .
Market shares are deﬁned by the location of the indiﬀerent consumer. The indiﬀerent
1consumers’ locations in both markets are respectively:
x1 =
PB1 − PA1
2t1
+
L1
2
x2 =
PC2 − PB2
2t2
+
L2
2
where Pij is the price of ﬁrm i in market j and tj is the unit transportation cost in market
j. We assume that
t1L2
1
t2L2
2
≥
1
15
,
where Market 2 is the one where price indexation is used. Recalling that the total proﬁti n
a standard Hoteling model is tL2, this condition, which will be derived in the next section,
can be interpreted as a relative proﬁt condition: total proﬁti nt h er e f e r e n c em a r k e ti sn o t
too small compared to the proﬁt in the price-indexed market.
We consider the case where prices in Market 2 are indexed to the average of prices in
Market 1. Firms B and C independently choose their proportionality coeﬃcients, so that:
PB2 = α(PB1 + PA1)
PC2 = β(PB1 + PA1).
We assume that price information is conveyed instantaneously from Market 1 to Market 2.
3 Equilibrium
We ﬁrst we derive the equilbium prices and markets shares in both markets. We consider
the case where contract delivery time coincides with spot market clearing and abstract from
any time strategy behavior. Therefore, we need only one stage interaction.
The proﬁts of ﬁrms A, B and C are:
ΠA = PA1x1
ΠB = PB1(L1 − x1)+PB2x2
ΠC = PC2(L2 − x2).
The FOC for ﬁrm A yields
PA1 =
PB1
2
+
t1L1
2
Firm B maximizes its proﬁts by choosing PB1 and α, knowing the indexing rule and the
impact price PB1 has on the prices in Market 2. The optimality conditions for Firm B are
then:
2∂ΠB
∂PB1
=0 ⇒ 2PB1 (t2 + α(α − β)t1)=PA1 (t2 − 2α(α − β)t1)+( L1 + αL2)t1t2
∂ΠB
∂α
=0 ⇒ L2t2 =( 2 α − β)(PA1 + PB1). (1)
Finally, for Firm C,w eh a v e :
∂ΠC
∂β
=0⇒ L2t2 =( 2 β − α)(PA1 + PB1). (2)
Equations (1)-(2) imply that, at equilibrium,
α = β =
t2L2
(PA1 + PB1)
,
and therefore the equilibrium prices on Market 2 are given by:
PC2 = PB2 = t2L2.
Using α = β and solving for PA1 and PB1, we get the equilibrium prices:
PA1 = L1t1 +
1
3
αt1L2
PB1 = L1t1 +
2
3
αt1L2
which implies
α =
t2L2
2L1t1 + αt1L2
.
The only positive root of this equation is
α =
s
t2
t1
+
L2
1
L2
2
−
L1
L2
.
Now, under these prices, the indiﬀerent consumers locations are
x1 =
αL2
6
+
L1
2
x2 =
L2
2
;
where we need to have
x1 ≤ L1,
3which is equivalent to
α ≤ 3
L1
L2
or
t1L2
1
t2L2
2
≥
1
15
.
We have the following results:
Result.1 In the present framework, price indexing induces the same prices, in Market 2,a s
in the standard Hotelling prices: competition forces in Market 2 are not aﬀected by
the indexation.
Result.2 Indexing has anticompetitive consequences in Market 1; prices are higher than in
the standard Hotelling setup for both ﬁrms A and B.
Result.3 Firm A is better-oﬀ if indexation is used in Market 2:i t sp r o ﬁti sl a r g e rt h a ni n
the standard Hotelling framework since both its price and market share are higher.
For Firm B, the consequences are not so clear-cut, since its market share decreases in
Market 1 when prices are indexed. Firm B’s proﬁti nM a r k e t1i sg i v e nb y
ΠB = PB1(L1 − x1)
=
µ
L1t1 +
2
3
αt1L2
¶µ
L1 −
µ
αL2
6
+
L1
2
¶¶
=
1
2
t1L
2
1 +
1
18
αL2t1 (3L1 − 2αL2).
Therefore, its proﬁt in Market 1 is higher with indexation than in the standard Hotelling
case if 3L1 − 2αL2 > 0,o re q u i v a l e n t l y
α<
3L1
2L2
.
Replacing with the equilibrium value of α, this condition reduces to
s
t2
t1
+
L2
1
L2
2
−
L1
L2
<
3L1
2L2
,
or
t1L2
1
t2L2
2
>
4
21
. (3)
Result.4 Firm B’s market share is lower in Market 1 under indexation than in the standard
Hotelling case, and its Proﬁt is higher than in the standard Hotelling case if
t1L2
1
t2L2
2 > 4
21.
Otherwise, Firm B is better-oﬀ when the two markets are independent.
Again, an interpretation of condition (3) is that proﬁt in the reference market is large
enough with respect to the one in the price-indexed market. For equal transportation costs,
for instance, it means that the size of Market 1 is at least 44% of the size of Market 2.
44C o n c l u s i o n
Price indexing is a pricing mechanism used in diﬀerent markets. In a simple Hotelling
duopoly framework, we show that indexation does not aﬀect competition forces in the market
where indexation is used. However, indexation has anticompetitive consequenses in the
reference market since prices are then higher than if no indexation were used. Finally, if a
company is operating in both markets, its proﬁt is higher under indexation only if the size of
the reference market is suﬃciently large with respect to the size of the price-indexed market.
References
[1] Allaz, Blaise and Jean-Luc Vila (1993) “Cournot Competition, Forward Markets and
Eﬃciency”, Journal of Economic Theory 59,1 - 1 6 .
[2] Le Coq, Chloé (2004) “Long-Term Supply Contracts and Collusion in the Electricity
Market” Stockholm SSE/EFI Working Paper Series in Economics and Finance number
552.
[3] Liski, Matti, and Juan-Pablo Montero (2004) “Forward trading and collusion in
oligopoly” The Journal of Industrial Economics 37,8 5 - 9 7 .
[4] Karsten, Neuhoﬀ and Christian von Hirschhausen (2005) “Long term vs. Short-term
Contracts: A European Prspective on Natural Gas” Cambridge Working Paper Series
number CWPE 0539.
5

Who benefits from price indexation?

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