Download 9.4 Predation

Lecture Notes: Industrial Organization
Joe Chen
9.4
138
Predation
The exit inducement game is essentially the same as the entry deterrence game, as discussed
when we studied the taxonomy of business strategies. Hence, one shall not be surprised
that the limit pricing model also applies to the inducement of exit. A more “colorful” term,
used frequently by IO people, for the exit inducement game is predation. Loosely, an
aggressive behavior (e.g., charging an abnormally low prices) aims to drive out rivals can be
considered as predation. An incumbent can prey on a potential entrant(s), or on another
firm already in the market (a predator preys). Nevertheless, predation usually refers to exit
inducement.
It is difficult to define predation theoretically. In general, we can decompose a predator’s
action into two components. The first (direct effect) indicates how this action directly affects
the predator’s profit, if we take the rival’s behavior, e.g., an exit decision, as fixed. The
second (strategic effect) reflects the influence of this action on the rival’s behavior. One may
then define predation as the reflection of this strategic effect on the predator’s behavior.
It is even more difficult to define predation in practice. The observation of a low price
may simply be an innocent competitive act intended to maximize profit. But it may also
have strategic purpose of inducing exit. The early tests of predatory behavior were based
on cost. The Areeda-Turner test, used in many antitrust cases, states that a price below
the short-run marginal cost should be unlawful and that the short-run marginal cost can be
approximated by the average variable cost. Put aside the question that if the approximation
is proper, the Areeda-Turner test undermines the underlying driving force of predation.
What is important is the trade-off between the sacrifice of the current profit and the gain
from monopolization.
One possibility is to look at the incumbent’s intertemporal price path. For instance,
suppose that the incumbent firm cuts its price when entry occurs. This might indicate
predatory behavior to drive the entrant out of the market. However, the incumbent’s
residual demand falls when a competitors enters, which may justify a lower price. The
labeling of a truly competitive price cut as predation is called a “type-I” error. Conversely,
Lecture Notes: Industrial Organization
Joe Chen
139
suppose that the incumbent does not lower its price when entry occurs. This does not mean
that the incumbent does not engage in anticompetitive behavior. The incumbent may have
been practicing limit pricing before entry, and—having been unsuccessful in deterring entry—
may have felt no need to cut its price further. A predatory behavior goes undetected is
called a “type-II” error. The design of any test will have to face these two types of errors.
9.5
Predation for Merger
The Chicago School argues that it cannot be rational to engage in predatory (limit) pricing
in order to induce exit. The arguments is that merging with the rival is a dominant
strategy to realize monopoly power. For example, the predator can make an offer to the
prey that would be preferred by both to the predatory outcome. Competition—especially
predatory competition—destroys industry profit, and therefore, firms have incentives to avoid
it.
This argument has been attacked on two fronts. First, The predator may face potential
entrants in the market in question or in other markets where it operates. If it does not fight
in the market in question, it can be seen as a sign of “weakness”. This may encourage other
firms to enter the market in question and/or other markets, because potential entrants
anticipate that, rather than being preyed upon, they will make profits in those markets
or else will be bought out at good prices. Second, the buyout price can depend on the
predator’s pre-merger behavior. If predatory pricing lowers the buyout price to the extent
that it covers the cost of predation, predation seems natural. In this subsection, we examine
the second idea.
Let’s go back to the structure of the limit pricing model except that after the entrant
enters and before the second-period price competition takes place, the incumbent can make
a merger offer to the entrant. If the offer is turned down, duopoly prevails as it is in the
limit pricing model; if the offer is accepted, the incumbent remains a monopoly. The entrant
learns the incumbent’s cost after turning down the merger offer and before waging the price
competition. Naturally, we assume that a monopoly makes more profit than a duopoly.
Lecture Notes: Industrial Organization
Joe Chen
140
Let’s also assume the following condition:
D2H > D2L > 0,
so that firm 2 (the entrant) would enter if it were not bought out.
© H H
ª
(pm , D2 ), (p∗1 , D2L ) , where p∗1 < pL
m , and is defined by:
M1H − M1H (p∗1 ) = δ(D2H − D2L ),
(*)
is a separating equilibrium. Why?
Note that in a separating equilibrium, the incumbent’s cost structure is revealed. Thus,
after observing pH
m , the entrant accepts being bought out if and only if the offer is no less
than D2H ; after observing p∗1 , it accepts offers no less than D2L . Hence, the benefit when
the high-cost type pretends that it were of the low-cost type is the difference in the merger
prices:
δ(D2H − D2L ),
while the cost of pretending is the loss of the first-period profit of:
M1H − M1H (p∗1 ).
Note also that if the low cost type charges pL
m , it gains in the first period by:
M1L − M1L (p∗1 ),
∗
while it also raises the merger price (observing pL
1 6= p1 , the entrant believes that the
incumbent is of the high-cost type) by :
δ(D2H − D2L ).
The single-crossing condition,
M1L − M1L (p∗1 ) < M1H − M1H (p∗1 ),
and equation (*) ensures that the low-cost type will not charge pL
m . Finally, note that the
low-cost type will not mimic the high-cost type by charging pH
m.
Lecture Notes: Industrial Organization
Joe Chen
141
What’s the welfare effect compared to the equilibrium of the complete information case,
ª
© H H
L
(pm , D2 ), (pL
m , D2 ) ? Again, it is possible that predatory (limit) pricing improves welfare.
However, this result is not robust.
9.6
The “Long Purse” Story
For all the models that we’ve discussed so far, the incumbent (predator) tries to convey
bad news to its rivals. Nevertheless, the predation does not affect the rival’s real prospects,
only the perception of these prospects. An alternative and popular theory of predatory
pricing states that a firm with substantial financial resources (has a “long purse” or a “deep
pocket”) can prey on a weaker rival. Because the strong or big firm can sustain losses for
a long period of time, it can drive the weak or small firm out of the market. Cutthroat
competition may affect the rivals’ real prospects, as the rivals cannot raise enough resources
to carry on.
However, it is not clear why the prey faces a financial constraint. It is in the interest of
the creditors not to impose financial constraints. Thus, people argue that some imperfection
in the capital market is essential to the “long purse” story. One needs to establish a link
between the equity (wealth) of a firm and its profit.
Consider a firm who seeks to finance an investment project of size K. Let E denote
the firm’s wealth (equity), E < K. The firm needs to borrow an amount D = K − E from
e ∈ [Π, Π], distributed as F (·) with
a bank. The investment yields a random profit of: Π
e < (1 + r)D, the firm
probability density function f (·). Let r be the rate of interest. So, if Π
goes bankrupt and retains nothing. Let the bankruptcy cost be B. The bank’s expected
profit is:
V (D, r) = [1 − F ((1 + r)D)] (1 + r)D +
Z
(1+r)D
Π
e − B)f (Π)d
e Π.
e
(Π
Suppose the banks are competitive so that the cost of their funds is r0 . Then the zero-profit
condition:
V (D, r) = (1 + r0 )D,
determines the the rate of interest: r(D, r0 ). Assume: dr/dD > 0.
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Joe Chen
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The firm invests in this project when its expected profit exceeds (1 + r0 )E, the opportunity cost of the wealth. Let W denote the net expected profit from the investment.
Then,
W≡
=
Z
Π
(1+r)D
Z
Π
(1+r)D
=
Z
Π
(1+r)D
h
i
e − (1 + r)D f (Π)d
e Π
e − (1 + r0 )E
Π
h
i
e − (1 + r)D f (Π)d
e Π
e − (1 + r0 )K + (1 + r0 )D
Π
h
i
e − (1 + r)D f (Π)d
e Π
e − (1 + r0 )K + V (D, r)
Π
e − (1 + r0 )K − F ((1 + r)D)B.
= E[Π]
Note that the first two terms equal the investment’s net value in a perfect financial world
and the third term represents the expected bankruptcy cost. It is clear that a higher
(lower) level of equity makes the investment more attractive (formidable): dW/dE > 0.
Mathematically, a higher equity lowers the probability of bankruptcy and therefore reduces
the expected bankruptcy cost. Intuitively, a higher equity lowers the amount that needs to
borrow. This lowers the interest rate r.
Now consider a 2 × 2 model. Firm 1 has no financial constraint. Firm 2 must finance
an investment K between the two periods if it wants to remain in the market. Firm 2’s
equity after the first period depends on its retained earnings after first-period competition.
By preying in the first period, firm 1 reduces first 2’s first-period retained earnings and
therefore reduces its second-period equity. Thus, firm 2 finds staying in the market less
attractive. Predation is successful if it drives E down enough so that W = 0.
The “long purse” story states that insufficient retained earnings, stemming in part from
the rival’s predatory behavior, may prevent young or financial constrained firms from expanding or from renewing their equipment. The story relies on the presumption that outside
financing is more costly than insider financing (retained earnings). It is actually the asymmetric information between the borrower and the lenders that matters.