# Lecture 1 Oligopoly, Entry Investment

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```					                        Motivation
Cournot competition
Free entry
Investment and strategic eﬀects
Conclusion

Lecture 1: Oligopoly, Entry & Investment
MFE Industrial Organization 2009

Charles Roddie

Nuﬃeld College, Oxford

30/4/2009

Charles Roddie    Lecture 1: Oligopoly, Entry & Investment
Motivation
Cournot competition
Free entry
Investment and strategic eﬀects
Conclusion

Cournot competition

n ﬁrms, costs Ci (qi ), market demand function D(p), inverse
demand function P(Q) = D −1 (Q).
Each ﬁrm chooses qi to maximize proﬁt π = qi P(Q) − Ci (qi ),
where Q = qj , given choices of other ﬁrms: Nash
Equilibrium.
First-order condition for maximum:
δπ
δqi = P(Q) + qi P (Q) − Ci (qi ) = 0.
Simultaneous solution of these equations is NE.

Charles Roddie    Lecture 1: Oligopoly, Entry & Investment
Constant returns to scale, identical ﬁrms

Cost c.q for producing q.
Linear demand D(p) = A − Bp
A−Q
Implies P(Q) =     B .
−1
FOCs: A−Q +
B      qi B −    c = 0 or Q + qi = A − B.c; assume
A − B.c > 0.
So qi s are identical, qi = Q and Q = nq, and
n
(n + 1)q = A − Bc; Q = n+1 (A − B.c) and
1   A
P(Q) = c + n+1 ( B − c) > c
Proﬁt per ﬁrm
1    A            1    1
π = q.(P(Q) − c) = q. n+1 ( B − c) =   (n+1)2 B
(A   − Bc)2
Eﬃciency measurement

One measurement of eﬃciency is “total surplus”, sum of:
producer surplus = proﬁts
consumer surplus=what market is worth to consumers
1 (A−BC )2
Competitive market maximizes surplus:              2    B       (see
graphs). Call this Smax .
all goes to consumer
n
Here producer surplus is n.π = 2 (n+1)2 Smax
Consumer surplus, since demand is linear, is
1    A             1 n                 n    A            n
2 Q( B   − P)] =   2 n+1 (A   − B.c)[ n+1 ( B − c)] = ( n+1 )2 Smax
1
(n+1)2 max
Graphs: A Monopolist’s Marginal Revenue
Marginal revenue of an extra unit:
Earn the price on the unit, but
depress price on existing sales
MR is below the demand curve, MR = P − Q.P (Q)
Graphs: An Oligopolist’s Marginal Revenue
Firm produces a share of output,
feels price depression on less,
Q.P (Q)
hence MR is higher, MR = P −            n    .
1
E.g., duopoly:   2   the price depression.
Surplus analysis
Surplus: numbers

Increasing entry reduces concentration, enhances performance.
Write performance as a percentage of maximum feasible value

No. of Firms       1      2      3      4      5   ...      ∞
Single Firm π   50.0   22.2   12.5    8.0    5.6   ...     0.0
Industry π      50.0   44.4   37.5   32.0   27.8   ...     0.0
Cons. Surplus   25.0   44.4   56.3   64.0   69.4   ...   100.0
Surplus         75.0   88.9   93.8   96.0   97.2   ...   100.0
DWL             25.0   11.1    6.2    4.0    2.8   ...     0.0

With 5+ ﬁrms, performance is close to perfect competition.
Discussion: What if costs are diﬀerent?

In a competitive setting
Only ﬁrm(s) with lowest cost produce; price=lowest cost
In an oligopoly setting
A range of ﬁrms still produce
lower cost ﬁrms produce a greater share, make greater proﬁts.
no production for ﬁrms above a certain cost
entry would help
Motivation
Cournot competition
Free entry
Investment and strategic eﬀects
Conclusion

What if there is free entry?

Firms decide simultaneously whether to enter market, how
much to produce
Just like oligopoly with inﬁnite number of ﬁrms:
competitive prices, total quantities; surplus maximization, all
going to consumers

Charles Roddie    Lecture 1: Oligopoly, Entry & Investment
Fixed costs and increasing returns to scale

Assume identical ﬁrms again
Analysis above extends to diminshing returns to scale without
major diﬀerences
more competition leads to eﬃciency, competitive equilibrium,
in a large market,
What if there are increasing returns to scale?
Fixed cost is special case (or limiting case)
What happens in competitive equilibrium? No equilibrium
exists!
If you could control actions of ﬁrms, what is most eﬃcient
outcome?
Discussion: examples of ﬁxed costs, increasing returns to scale
Fixed costs and free entry

Suppose ﬁrm has to pay ﬁxed cost F to enter market.
Model: ﬁrms decide to enter; once they enter, there is
Cournot competition equilibrium
Equilibrium number of ﬁrms entering:
Given by: if one more ﬁrm were to enter, proﬁts would be less
than zero
1   1               2
n of ﬁrms given by: (n+1)2 B (A − Bc)2 = (n+1)2 Smax ≥ F :
maximal n satisfying this
approximately n ≈ 2Smax /F − 1: does this ﬁt reality? (see
below)
Fixed costs and entry: total surplus analysis

Eﬀect of ﬁrm entering on total surplus:
Increase in total surplus when ﬁxed costs are ignored:
1
DWL is (n+1)2 Smax
2
Change is (take derivative): − (n+1)3 Smax : very small compared
to F
2
How do they compare?             S
(n+2)2 max
< F so
2                   2               2               (n+2)2
[ (n+1)3 Smax ]/F > [ (n+1)3 Smax ]/[ (n+2)2 Smax ] =   (n+1)3
<1
when n > 1
So if there is more than one ﬁrm, the last ﬁrm is decreasing
total surplus.
Calculation not very revealing; you don’t need to know it.
Excess entry

“Business-stealing” eﬀect: when a ﬁrm enters, it causes other
ﬁrms to reduce quantities - an eﬃciency loss. It doesn’t
internalize this: See Mankiw & Whinston (1986)
Causes “excess entry”: entry is more than eﬃcient level
Eﬃcient number of ﬁrms if you can control everything (ﬁrst
best): 1
Number of ﬁrms that actually enter:       2Smax /F − 1
Eﬃcient if you can control only the number of ﬁrms:
somewhere in between
Under the speciﬁc conditions that isolate this eﬀect
Application?

“Regulatory Reform” by Armstrong, Cowan, and Vickers:
“Does this result imply that partial liberalization—restricting the
number of entrants—is a better policy than total liberalization? For
a number of reasons we believe that it would be dangerous to draw
any such conclusion.”
1   Result may fail if the welfare measure puts more weight on
consumers.
2   Restricting entry may facilitate collusion.
3   Intervention to limit entry may encounter information
asymmetry.
4   Excess entry ignores ﬁrm asymmetries.
5   Equilibrium entry may be a result of entry-deterring behaviour.
6   “Product diversity eﬀect” of entry can reverse result.
Entry/exit in the automobile industry

1913: Ford Assembly line
High associated ﬁxed costs likely played role in short and long
terms.
Other factors such as technological exclusion
Industry examples: discussion

What caused rises and drops in ﬁrm numbers in automobile
and tyre industries?
How well would the theory (prediction about number of ﬁrms)
apply within industries today? Across industries?
Variables: capital costs and increasing/constant/decreasing
RTS, demand
Investment

Suppose the cost varies according to investment
Investing I leads to cost c(I).q, with c(I) decreasing in q
Suppose all decisions are taken simultaneously by all ﬁrms?
They decide investments and quantities and compete in
Cournot competition.
Eﬀective cost function C (q) = min(C (I).q + I)
Analysis same as before
What if investment is done ﬁrst?
Investment to inﬂuence expectations

Suppose investment decisions are made before quantity
production decisions
Think of building factories and actually using them to produce
products
How does this diﬀer from the simultaneous game?
If investment lowers costs of producing, what eﬀect does that
have on how the other player will behave?
In what direction does it diﬀer from equilibrium where
everything is simultaneous?
Do we get under/over-investment?
Strategic eﬀects: general principles

Eﬀects of investment on a ﬁrm’s proﬁts:
A direct eﬀect. For instance, investment may lower its
marginal cost.
An own-action eﬀect. It adjusts its output. But this is
second-order (doesn’t aﬀect FOC)
A “strategic eﬀect”. Competitors adjust their own actions.
In a Cournot competition, the strategic eﬀect of cost
reduction helps:
A ﬁrm’s expansion leads its competitors to contract their
output
which raises price and helps the investing ﬁrm.
In a price-setting Betrand competition, the strategic eﬀect of
cost reduction hinders:
A ﬁrm’s cost reduction leads it to lower its price
which prompts competitor price reductions, harming proﬁts.
Theory: commitment

Nash equilibrium with two players for simplicity:
∗          ∗    ∗         ∗
a1 = BR1 (a2 ), a2 = BR2 (a1 ), best responses to each other
That was simultaneous moves; suppose now one ﬁrm moves
ﬁrst
Now a1 maximizes u1 (a1 , BR2 (a1 ))
∗
Do at least as well because you can always play a1 and do as
well as before
∗         ∗           ∗    ∗
u1 (a1 , BR2 (a1 )) = u1 (a1 , a2 )
But generally do better because there are now new strategic
eﬀects, since own action changes other’s action.
Player 2 does better or worse depending on game.
Examples: want to commit to higher quantities, higher prices,
matching competitors prices, product quality, predatory pricing
Ways to eﬀectively commit, fully or partially

If you can’t move ﬁrst/make a binding commitment to, say, a
high quantity of production, what actions can you take to
inﬂuence expectations?
Quite a few:
Investment was one example: only partial so not as good as
full commitment, but it let other players know you can be
expected to produce more.
Repeatedly producing more (and building up a reputation):
this is the most standard explanation in economics
Appointing executives that want to increase market
share/using contracts that reward this?
Summary

Cournot competition: eﬀect of number of ﬁrms on prices,
proﬁts, quantities, eﬃciency.
The determinants of entry (and exit); possibility of excess
entry under ﬁxed costs/increasing RTS. Industry examples.
Various factors that can hinder entry.
Strategic eﬀects: the eﬀects beneﬁts of commitment; how to
achieve it. Inﬂuencing expectations via capital investment.

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