1. EC930 Theory of Industrial Organisation Topic 4: Entry and entry deterrence
, spring term

2. Entry: some questions What market outcomes occur under “free entry”?
When is a market “contestable”?
What features (industry and institutional) form barriers to entry?
How can incumbent firms act strategically to deter entry?

3. Entry costs and market structure
Mankiw & Whinston (1986): Cournot with free entry
Assume
Unlimited number of potential entrants
Homogeneous good; identical marginal cost c
Fixed cost F per firm
Cournot competition
Demand: Q = (a – P) S
where S = total market size and Q = nq
I.e. inverse demand P = a – Q

4. Cournot equilibrium Output: per firm industry Market price
Profit per firm

5. Free entry equilibrium
n is such that
No inactive firm wishes to enter, and
No active firm wishes to quit
Thus  = 0  (ignoring integer constraints)
E.g.
Suppose a = 10, c = 3, S = 45, F = 5
Then = (10 – 3) 9 – 1 = 20
NB: what would happen if Bertrand not Cournot?

6. Mankiw & Whinston: Implications
How does market structure depend upon:
Scale economies: is decreasing in F
Doubling F reduces by approx 30%
Market size: increases with S and a
Relationship between and a is linear
Relationship between and S is approximately quadratic
Doubling S increases by approx 40%

7. Mankiw & Whinston: Evidence
Lyons & Matraves (1996) “Industrial concentration”
Find C4 ratio over a range of sectors to be
similar in France and Germany
higher in Belgium than France
France’s economy is roughly 5x size of Belgium’s

8. Welfare effects of entry
Does free market produce too much or too little entry?
Trade-off between
Competition
Duplication of fixed costs
Welfare: W = n + CS where CS = ½(a – p)Q
Choose n to max W
Substitute for , p, Q then differentiate w.r.t. n
Welfare-maximising

9. Compare free entry and welfare optimum
We know that
and, for x > 1,
Thus
Free entry generates excess entry
E.g. (parameters as before): = 20, n*  7

10. Intuition behind excess entry result
Two externalities from (further) entry
(1) Consumer surplus effect (+ve)
Increased competition reduces prices, increasing consumer surplus
(2) Business stealing effect (–ve)
Profits of incumbents are reduced
With homogeneous goods and symmetric firms, (2) dominates (1) and excessive entry occurs
True for general demand fns (not just linear)

11. Caveats to excess entry result
Differentiated goods (next lecture)
Variety generates consumer surplus
Cost asymmetries
Entry/exit process has a selection effect
 productive efficiency
Different behavioural assumptions
Entry barriers (and low n) may facilitate collusion
Asymmetric info: difficult for regulator to determine n*
Comparative info helps reduce agency problems
E.g. yardstick comparisons, stock market, labour market

12. Contestability (Baumol, Panzar & Willig 1982)
Model of ultra-free entry, which constrains even a monopoly incumbent
Assumptions
No sunk costs
No cost advantage to incumbent
Entry occurs quicker than incumbent can change its price
Outcome: incumbent is vulnerable to hit-and-run entry
Any price above cost attracts entry
Thus, excessive prices cannot be sustained

13. Outcome of contestability
(pI, qI) lies at intersection of demand and AC curves
Single firm operates: no duplication of F
P = AC: constrained efficient (in absence of subsidy)
Monopoly incumbent makes normal return only p
p = a – q pI
AC = F/q + c c q qI

14. Problems with contestability
Non-robust to changes in assumptions
What if there are sunk costs?
What if incumbent has a cost advantage?
What if incumbent can  price before entrant makes any sales?

15. Natural barriers to entry
Sunk costs as a barrier to entry (Stiglitz 1987)
Assumptions
(1) Two firms: incumbent (I) already operating
potential entrant (E) considering entry
(2) Homogeneous good
(3) Identical, constant marginal costs
(4) Price competition
(5) Small sunk entry cost 
Will entry occur?

16. Solving the entry game
Solve for SPE

17. Variations on entry game
Change assumptions
(2) Differentiated products
(4) Cournot competition
Either change has similar effect
E can gain some post-entry profits
For sufficiently small  entry will occur
But for sufficiently large  entry is prevented
Thus, sunk costs above a certain level still operate as a barrier to entry

18. Natural barriers to entry (Bain 1956)
Absolute cost advantage
Patent
Access to cheap inputs
Learning-by-doing
Economies of scale
Expensive to enter at small scale
Small residual market
Large, sunk capital expenditures
Product differentiation
Imperfect substitutes
Asymmetric info over quality: brand name important

19. Bain’s empirical findings
Identified industries with high entry barriers
High barriers  prices 10% above competitive level

20. Strategic entry deterrence
Bain defines 3 categories of entry conditions
Blockaded entry
Natural barriers protect incumbent from entry
Entry unprofitable even if incumbent produces monopoly Q
Deterred entry
Incumbent modifies its behaviour to prevent entry
E.g. capacity investment, limit pricing
Accommodated entry
Entry deterrence is too costly, entry will occur
Though incumbent may modify its behaviour to soften effects of entry

21. Models of strategic entry deterrence
Limit pricing: incredible threats
Sunk investment to deter entry
Capacity investment (Dixit 1980)
Asymmetric information
Repeated games: chain store paradox
Signalling: limit pricing revisited

22. Limit pricing [Bain (1956), Modigliani (1958), Sylos-Labini (1962)]
Idea: Incumbent reduces its price to the level where entry becomes (just) unprofitable
Model as a 2-stage game
Incumbent I chooses q
Entrant E observes q and decides whether or not to enter
I chooses level of q which is just low enough to keep E out, and sets its price accordingly  PL

23. Setting the limit price
Entrant faces residual demand D' (given I’s output)
Choose qL s.t. tangency between D' and AC  E = 0

24. Is limit pricing a SPE?

25. Making entry deterrence credible
To be credible, need intertemporal linkage between
Incumbent’s action at stage 1
Environment affecting entrant at stage 2
(i) Sunk cost/commitment affecting post-entry game
Capacity investment
Cost-reducing investment
Contracts or relationships with customers/suppliers
(ii) Actions which affect beliefs of entrant
Requires asymmetric information between I and E

26. Sunk investment as entry deterrence
[Spence (BJE 1977), Dixit (EJ 1980)]
Various investments can provide intertemporal linkage
e.g. spare capacity, marginal cost reduction
Commits incumbent to higher post-entry q
Investment must be sunk
If not, incumbent could (& would) reverse investment if this gave a higher payoff in the second (post-entry) stage
But by committing not to do this, it may deter entry and be better off overall

27. Capacity as entry deterrence (Dixit 1980)
Inverse demand p = a – bQ
Cost fn: Ci = F + wqi + rKi where qi  Ki
SRMC = w (capacity installed)
LRMC = w + r
2 stage game
Firm 1 (incumbent) chooses capacity K1
K1 can subsequently be increased but not reduced
Firm 2 (entrant) observes K1
Firms compete in quantities
Capacity can only be increased: K1'  K1

28. Solving the game Period 2 reaction functions
R2(q1) = (a – bq1 – w – r)/(2b)
R1(q2) = (a – bq2 – w)/(2b) up to K1
(a – bq2 – w – r)/(2b) above K1
Second period eqm is found from intersection of the two reaction functions
Position of eqm depends on firm 1’s first period capacity choice, K1

29. Reaction functions 2’s reaction fn is R2 (MC=w+r)
1’s reaction fn is R1 until K1 then moves down to R1'
Eqm at intersection, E
Eqm anywhere between A & B, depending on choice of K1
NB: A is Nash eqm without stage 1 capacity investment

30. Blockaded entry When is entry unprofitable for 2? (given fixed cost F)
Find Z on R2 where 2 = 0
To right of Z, 2 < 0: do not enter
Blockaded entry
1’s monopoly K1 = R1'(0): this is to right of Z
2 will not enter anyway

31. Strategic entry deterrence
Z is just to left of B
1’s monopoly K1 = R1'(0) is not sufficient to deter entry: 2 would enter
Increase K1 to D so that entry is just deterred
Incumbent (as monopolist) uses entire K1

32. Strategic entry accommodation
Accommodate entry
Z is to the right of B: entry cannot be deterred
1 chooses point on R2 that maximises 1
Choose capacity S (Stackelberg leader)

33. Dupont case study (Cabral ch 15)
Largest producer of titanium dioxide in 1970
Significant cost advantage over rivals (different ore)
Environmental regulation disadvantaged competitors
Strong financial position
Adopted strategy of expanding capacity
Satisfied all increases in demand
Deterred entry or expansion by its rivals
Market share: 1972: 30%; 1980: 56%
By 1985, 5 of the 6 rivals had exited

34. Asymmetric information
Entrant’s beliefs as basis for intertemporal linkage
Alternative to sunk investment models
2 models
Repeated games: Chain store paradox
Signalling: Limit pricing revisited

35. Chain store paradox (Selten 1987, KMRW 1982)
Incredible entry threat (no sunk investment)
Solve for SPE

36. Repeated game Infinite number of repetitions
No “final round”
Fight to maintain reputation (if  sufficiently high)
Entry is deterred
Finite number of repetitions
Final stage T is one-shot game: I will accommodate
No point fighting to maintain reputation in stage T–1
Or in stage T–2 …
Incumbent always accommodates
Entry occurs in stage 1

37. Incomplete information about I’s type
Entrant is unsure of incumbent’s type
RATIONAL: accommodates entry
THUG: always fights entry
Entrant’s beliefs (prior)
Small probability  > 0 that incumbent is a THUG
Updating of beliefs
Belief  is maintained while observes only fighting
If sees accommodation even once,   0
Outcome
Fighting is observed early on
Towards end, incumbent will accommodate

38. Limit pricing as cost signalling
Milgrom & Roberts (Ecta 1982): credible limit pricing
Entrant is unsure about incumbent’s costs, and makes an assessment based on observed price
Low price  low-cost incumbent  stay out
High price  high-cost incumbent  enter market
Incumbent may want to set a low price, to indicate that it has low cost, and deter entry

39. Signalling model (Tirole pp.368-371)
Incumbent I: marginal cost c, may be high or low
where cH > cL
I knows its type, but entrant E does not
Two-stage game
I chooses price p1 ; this is observed by E
E chooses stay out or enter  monopoly or duopoly
Discount factor 

40. Payoffs Incumbent’s monopoly profit
MH(p) : for high-cost incumbent charging price p
ML(p) : for low-cost incumbent charging price p
Duopoly profits (period 2, if entry occurs)
D1H ; D2H : for high-cost incumbent; entrant
D1L ; D2L : for low-cost incumbent; entrant
Suppose entry is profitable iff I is high-cost
i.e., D2H > 0 > D2L

41. Equilibrium (perfect Bayesian)
Incumbent would like to indicate low cost to deter entry
Does this indirectly by charging a low price in first period
Two types of equilibria
Separating eqm 
High- and low-cost types charge different period-1 prices
Type is revealed, entry does/does not occur accordingly
Pooling eqm
2 types set same period-1 price
No information revealed
No entry occurs

42. Separating eqm 2 necessary (& sufficient) conditions
(i) H-type does not want to pick L-type’s eqm price, pL
MH(pmH) + D1H  MH(pL) + M1H(pmH)
Note:
H-type’s period-1 price is static monopoly price, pmH: given entry occurs in period 2, H-type chooses price to maximise profit in period 1
Separating eqm may require L-type’s period 1 price to be below monopoly level: pL  pmL

43. Separating eqm (2) (ii) L-type maximises profit by choosing pL Note:
ML(pL) + M1L(pmL)  ML(pmL) + D1L
Note:
L-type would like pL as close to pmL as possible, given condition (i)
For separation to occur, charging a low price must be more costly to H-type than L-type

44. Separating eqm (3) Eqm strategy: in period 1
High-cost type chooses pmH
Low-cost type chooses pL
Beliefs of entrant must also be specified
Posterior belief (prob I is low-cost), having observed p1
Beliefs off eqm path
If H-type deviates, faces entry anyway: better to set p1 = pmH
If L-type deviates, faces entry: undesirable

45. Separating eqm (4) Outcome
Low-cost incumbent engages in limit pricing: must signal its type to distinguish from high-cost type and deter entry
Entrant learns incumbent’s cost; entry occurs exactly as in full information benchmark
Welfare is higher than under symmetric information
Period-2 welfare same (as entry unaffected)
Period-1 expected welfare higher, as L-type lowers price

46. Pooling eqm Pooling: both types choose same period-1 price, pP
No updating of entrant’s prior belief, x
2’s expected profit from entry given x
E = xD2L + (1x)D2H
If E > 0, entry is not deterred
Both types then prefer static monopoly prices in period 1
In which case, period-1 prices differ: not pooling eqm
Hence, existence of pooling eqm requires E < 0
Pooling price pP deters entry

47. Pooling eqm (2) Necessary conditions
Each type prefers pP to its monopoly price
ML(pP) + M1L(pmL)  ML(pmL) + D1L
MH(pP) + M1H(pmH)  MH(pmH) + D1H
Interval of possible eqm prices around pmL
Beliefs of entrant

48. Pooling eqm (3) Consider pooling eqm with p1 = pmL Outcome
High-cost incumbent engages in limit pricing: mimics low-cost type to deter entry
Entrant does not learn incumbent’s cost; less entry than in full information benchmark
Welfare effect of asymmetric information is ambiguous
Period-2 expected welfare lower (as no entry)
Period-1 expected welfare higher, as H-type lowers price