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HB31
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woTicmg paper
department
of economics
How Effective Is Potential Competition?
Joseph Farrell
-
Number
3 75
May 1985
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
How Effective Is Potential Competition?
Joseph Farrell
Number
3 75
May 1985
JAN 2 5
/f^D
TN 84-407.2
How Effective Is Potential Competition?
by
Joseph Farrell
November 1984
Telecommunications Research Laboratory
GTE LABORATORIES INCORPORATED
40 Sylvan Road
Waltham, Massachusetts 02254
TN 84-407.2
1
1
INTRODUCTION
.
Competition among firms does many useful
things.
can prevent
It
from raising prices above (some appropriate definition of) costs.
firms
It can be a
means whereby differences in belief about v;hat the market wants can be tested,
mistakes corrected.
and managers'
It can be
a
means whereby production gets
All these and more are supposedly
carried out by the lov;est-cost producers.
benefits from actual competition among firms.
However, competition is often limited by economics of scale.
case
of
this
natural monopoly industry
the
is
scale exceeds market demand at minimum cost.
in which
,
The extreme
minimum
In this case,
efficient
there is an inef-
ficiency involved in having actual competition, and there are also likely to
be difficulties sustaining competition as an equilibrium.
Old-fashioned
anti-trust
industries:
for instance,
competition
than
the
is
it better
efficient
worried
economists
and
analysts
to have
such
some productively inefficient
unrestrained monopolist?
but
about
But
the
more
recent trend has been to assert that economics of scale in themselves need not
lead to any failure of the benefits of competition, as long as potential com-
petition is available:
"contestability
that is,
theory"
as
(Baumol,
long
Panzar
entry
as
not blocked.
is
and Willig,
In
suggests
1982)
fact,
that
if
entry and exit are costless, then an incumbent cannot charge more than average
cost.
In this paper,
tive
is
poteri lal
v;e
present
competition
a
in
simple analysis of the question,
doing what
actual
"How effec-
competition is meant
to
do?"
We study
a
model of an incumbent facing potential entry, and exa:-ine his
limit-pricing behavior.
testability's
The claim by Schwartz
conclusion
of
average-cost
and Reynolds
pricing
is
(1983),
not
robust
that conto
small
changes in assumption, is not borne out in our model; but neither is the claim
by Baumol,
Panzar
and
V/illig
(1983)
that
"where
costs, markets are almost perfectly contestable."
there
are
almost no
sunk
TN 84-407.2
2
A MODEL OF LIMIT-PRICING WITH SUNK COSTS AND RESPONSE LAGS
2.
Consider an industry with
per period.
a
flow demand which we normalize at
this demand is completely inelastic,
We suppose
one unit
both in order to
economize on notation and in order to focus on the price-discipline effects of
potential competition.
A firm can satisfy this demand at a (flow) cost c, but
only if it has invested an amount
S
in entering the
This cost
industry.
is
S
sunk and not recoverable if the firm leaves.
Initially,
there
is
an incumbent firm
serving
I
the market.
It
sets a
pre-entry price p, which it can change with a lag, called the response lag, L.
The
second active player in the game
is
(potential)
a
entrant,
The
E.
entrant observes p, and decides whether or not to enter.
If E does not enter, his payoff is zero.
a
Since there is no entry,
gets
I
payoff valued at
/q e""^ (p
-
c)
dt = Pl£
(1)
in present value.
However,
1982),
then,
I
E
arrives,
if E
chooses to enter,
is unable to
can
I
price
then
(as
in Baumol,
Panzar
and Willig,
react, by changing p or otherwise, until date L.
below
just
and
p,
get
the
whole market.
Once
Until
time
L
and E compete in some way we will not precisely specify,- possibly,
one of them will leave
the industry.
We
simply write W
and W
for
the pres-
ent values at date L of the two firms.
We can readily calculate E's payoff from entering:
n_
(p;
enter) =
c>
=
/J;
U
(p-c)e"'^^ dt + W^e""^^
(p-c)
-
S
Ci
1
-
r
e''^ ^ +
Wge'""^
-
S
(2)
TN 84-407.2
3
This enables us to find the entry-preventing price
which we denote p*
,
it is
:
such that (2) becomes zero.
p* =
c +
r
(S
e'"^
-
e
-
1
= c + r S +
rL
e
The last term in
c
+
(4)
W„)
(3)
E
r
~
-
1
(S
Wg)
-
measures the deviation of p* from the average-cost price
In assessing the robustness
rS.
(4)
of contestability theory to
small sunk
costs, we are thus concerned with the behavior of that term
6
-1
=
e^^-
when
S
1
is small but positive.
Proposition
I
exists S(e)
>
Proof
^'^
(S - W^)
Set
;
since W
E
:
Given strictly positive
such that if
S(e) = 1/2
> 0,
by free
•
z
S
S(e) then
<
(e"^^
6
<
(Equivalently, we
exit.
any
and for
there
0,
e
>
<
1/2
£•
Then
l)/r.
-
and L,
r
(5)
gives us
can say
6
that any
t
<
t,
exit costs
have been included in the sunkness of S.)
Can
6
be negative?
incumbent.
This would correspond to below-average-cost pricing by the
The analysis of
and
(7)
(8)
below tells us that this will happen
only if the incumbent's costs are higher than the entrant's.
Proposition
1
and Willig
(1983)
seems
almost perfectly
Proposition
2
to vindicate
that
"where
contestable."
will indicate:
(in our
there
But
are
the
model)
the
almost no
matter
is
claim of Baumol,
sunk
not
costs,
quite
so
Panzar
markets
simple,
are
as
2
TN 84-407.
4
Proposition
For any
2:
S
exists strictly positive
Proof
e^^
Take
:
-
1
<
r(S
Proposition
2
any
>
such that
L,
r,
r
however small, and any
VJ
and
>
0,
to
it only
6
>
A,
however large, there
A.
choose
L
sufficiently
that
W^)A.
-
has a bite
= 0.
if W
But this, of course,
and a very plausible one.
cisely the case normally considered,
rant's best strategy is "hit-and-run" entry, then certainly W
we will
small
have W^ =
after date
if,
E
entrant
L,
and
E
the ent-
If
= 0.
is pre-
Likewise,
incumbent play
mixed-
a
strategy equilibrium of the war-of-attrition game they find themselves in.
We now prove one
to the case of W„
E
Proposition
=
Proof:
=
E
0;
then we turn
0.
When W
3:
6
>
further simple result on (5) v;hen W
= 0,
E
and rL
is small,
>
(5)
is approximated by
S/L
(6)
The ratio of the claimed approximation to the correct formula is:
S/L
S/L
_
rS/(e^^ -1)
6
=
rL
e
-1,
rL
This
tells
us
(rL)/2! + (rL)^/3! +
1
+
1
for small rL.
that,
we
if
in every neighborhood of
Thus, simply knowing that
=
S
S
think
,
p*
of
L = 0,
5
as
a
function
of
S
and
takes on all nonnegative values
is small and L is positive
then
L,
.
tells us nothing at all
TN 84-407.2
5
about the extent to which potential competition will discipline the incumbent
price-setting.
his
in
in relation to L
as
a
Rather,
current costs that amount
running costs,
the
response
lag L
must expect
is
one
the
month,
sinking of two
6
equal
is
to
is only about 2% of c.
6
We now turn, as promised,
6
If entry costs are a week's running
twice c, representing a major distortion.
E
intuitively by expressing
if entry requires
Thus,
costs, and L is one year, then
small
is
S
depends on the number of time-period's
S
to S.
and
whether
then we can say that the proportional price
distortion allowed by the sunk cost
to obtain,
know
to
We can put this a little more
.
fraction or multiple of C;
months'
need
we
the case W^
to analysis of
either that
E
>
0.
For this case
will leave the market at date
I
L,
so
that E would become the incumbent, or else that the two firms could share the
market and make
profit (not allowing for sunk costs).
a
The latter case is
inconsistent with our motivating assumption that actual competition is infeasso we leave
ible,
it aside and concentrate on
E expects to displace
Such
"displacement" case:
as incumbent if he enters.
I
displacement is,
a
the former
of course,
one
equilibrium of the war-of-attri-
tion game which will result after date L on our assumption that the market is
unprofitable for two firms.
We can analyze the implications of equating W
to
the incumbent's value:
=
W
where p* =
c
P*
^
-
+ rS +
(7)
enforcing)
-W_)
(8)
E
-
e
Solving (7) and
(S
r
(8)
etiquette
1
gives W
is
for
=
,
p'^
=
c
incumbents
get average-cost limit-pricing,
not hard to understand:
S
since
+ rS.
to
leave
In other words,
if entered against,
and no entry in equilibrium.
there
is
if the
(self-
then we
This result is
no entry against incumbents in equi-
librium, a potential entrant contemplating entry will calculate on the assump-
tion that he would have the market forever,
basis.
and can thus amortize
S
on that
TN 84-407.2
6
Proposition 4
:
exit at date L,
If it is
the common expectation
should E enter,
that,
I
would
then equilibrium involves average-cost pricing (and no entry)
irrespective of the size of
S.
While Proposition 4 is of some interest in the model as we have described
it,
its main importance
lies
in
its extension to
initially the incumbent has costs
in c.
Suppose that
rant,
and potentially
that E would displace
other firms,
I
have costs
is very plausible
c
c
c
<
firms differ
case where
the
.
but that the ent-
Then
the
assumption
from being just one of
(as distinct
three equilibria of a war-of-attrition game), and it follows that,
if
I
is to
prevent entry, he must set price
p* = Cg + rSg
(9)
He will prefer to allow entry if and only if
Cj
which
is
>
c^ + rSg
precisely
the
(10)
condition under
which
it
socially
is
desirable
for
entry to occur:
Proposition
5
:
If
entrant's
and
incumbent's
costs
differ,
but
are
common
knowledge, then entry occurs precisely v;hen it saves costs overall (given that
I's
sunk cost is already sunk);
and the price
V7ill
be the entrant's
average cost if the incumbent chooses to prevent entry.
long-run
TN 84-407.2
7
CONCLUSION
3.
As
Panzar
Baumol,
dynamic
S
a
= 0,
function of
L = 0.
that positive
average
cost."
is
>
S
showed,
natural
to
monopoly
cost,
The
fixed;
and L
sunk
cost
does
even when we include
model is
however,
jointly,
continuous in
if we view the
there
is
an
S
the
in
raise prices above
model with sunk cost, we have investigated
and seen
in "average
response lag L
as
a
prices above
raise
cost
story,
In
(1982)
does not lead to monopoly power
absence of sunk costs
average cost.
Willig
and
enable
a
particular
incumbents
interest on the
(sunk
cost)
when
to
sunk
the
equilibrium limit price
essential
discontinuity at
This means that we cannot predict the relationship of price to
average cost based solely on the smallness of
S
have to have an estimate of their relative sizes.
and the positivity of L: we
TN 84-407.2
8
REFERENCES
Baumol,
William,
Panzar,
John
Robert
and
ble Markets and the Theory of Industry Structure
,
Contesta-
Willig,
San
Diego
:
Harcourt
Brace Jovanovich, 1982.
,
ing
in
the
Theory
and
of
,
Industry
"Contestable Markets-. An UprisStructure:
Reply,"
Ameri-
can Economic Review 73, June 1983, 491-496.
3.
Schwartz,
Marius, and Robert Reynolds,
ing
the
in
Theory
of
Industry
"Contestable Markets: An UprisStructure:
can Economic Review 73, June 1983, 488-490.
585^1
U7U
Comment,"
Ameri-
2r^'^C?
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