Market Foreclosure (Limit Pricing, Stackelberg Entry Deterrance (capacity), Fudenberg Investment (K1) Flashcards
3 key models for market foreclosures (where firms try to exclude existing/potential rivals)
Limit pricing
Entry deterrence in Stackelberg (capacity)
Fudenberg and Tirol entry deterrence (k1 and tough vs soft)
Limit pricing
Existing firm sets price below monopoly price to deter entry
When is limit pricing unlikely to happen
If full information (if both MC’s are known)
But with asymmetric information (if potential doesn’t know the incumbents MC) then it can happen
Limit pricing:
Firm 1 (existing) produces in period 1, firm 2 (potential) may enter in period 2.
With full information, what does the existing firm do
Just sets Pm. (Period 1 price is irrelevant to whether firm 2 enters or not)
So with full information existing sets Pm
Why?
Since costs are known:
If c2 > c1, firm 2 knows it can’t compete so not enter
If c2 ≤ c1, firm 2 will at least break even and will enter in period 2
This does not depend on p1 before the entry decision, so firm 1 should set the monopoly price
However with asymmetric information (firm 1’s MC is unknown) what happens?
B) how can they convince them?
Firm 1 can convince firm 2 c1<c2 to get firm 2 to not enter
B) It can convince them by setting a lower price today, below monopoly price!
Milgrom and roberts’ model of limit pricing
As we found in p1, firm 1 is a monopolist.
In p2, firm 2 chooses whether to enter, if enters pays a fixed cost
If firm 2 enters, firms choose outputs
Firm 1 has MC of cL or cH, unknown to firm 2 until they enter
Entry is profitable only if firm 1 has cH
2 equilibriums
Separating equilibrium - firm 1’s choice in period 1 reveals its type to firm 2
Pooling equilibrium - where firm 1 (with either cH or cL) chooses the same output in P1
When does firm 2 enter
Only in the separating equilibrium where firm 1 reveals its type, and has cH
(If reveals but cL firm 2 won’t enter)
Pooling equilibrium where firm 2 doesn’t enter - firm 1 (high or low cost) sets same output as in P1 (below monopoly)
Criteria for a pooling equilibrium to exist (2)
The gap between cL and cH can’t be too high
Firm 2 must have a belief of high probability that firm 1 has low cost (hence why do not enter)
2nd model:
Entry deterrence in Stackelberg
Firm 1 already produces, firm 2 considering. If enters, it is a stackelberg follower, and pays one-off cost of E.
Firm 1 chooses capacity, the amount produced after firm 2 enters.
We’ll see if firm 1 could/should deter
If firm 2 enters, what happens
Standard stackelberg equilibrium, they are stackelberg follower, but add one-off cost E subtracted from firm 2’s profit
When will firm 2 not enter (2)
If one off cost E too high
If firm 1deters entry by setting their capacity to a level where firm 2’s profit becomes negative
Case 1: firm 1 accommodates entry
Recall quantities, price, and profit of stackelberg leader and follower, now adding cost E for firm 2
Q1 (leader) = v-c/ 2
Q2 (follower) = v-c/ 4
P=v+3c/ 4
Then find profit (P-c)q1 or q2 and add -E to firm 2’s one
Case 2: firm 1 deters entry
How to find when firm 2 will not enter
Steps
Firm 2 will not enter if
E (one off cost too high) OR
If firm 1 deters entry by setting capacity to where firm 2’s profit negative. Do this by..
- Find firm 2’s profit max problem, then differentiate and rearrange to find best response function q2 = v-c-q1/ 2
- Them sub BR (q2) back into profit max problem, then rearrange to find E
Will not enter if
E > (v-c-q1)² / 4
Then rearrange to find q1: the minimum capacity firm 1 sets to make firm 2’s profits negative
So should entry be deterred (by increasing capacity) or accomodated: 3 cases of E
Firm 1 (leader) sets q₁m = v-c/2 = q₁s
For high E, expensive for firm 2 to enter, q1m>= qd1 , firm 1 quantity is enough to deter entry (needs q₁d), so doesnt need to add capacity
For low E, q1d is close to competitive output (thus low profit), cheap for firm 2 to enter so accept their entry (increasing capacity will drive price down to MC) - so let them enter and operate like standard stackelberg
For intermediate E, firm 1 should add capacity to deter entry
Final model: Fudenberg and Tirole
How does it differ from Stackelberg entry deterrance model
B) if firm 2 does enter, does this affect for firm 1
Previous model imcumbent choose capacity and produces that output.
This model, incumbent makes a first-stage investment decision, but not commited that output level e.g investing in R&D/advertising does not fix output levels
B) firm 2 entering affects how aggressively firm 1 over-invest or underinvests
Stage 1: firm 1 chooses investment level K1
Stage 2: Firm 2 chooses whether to enter. Firms make choices x1 and x2 (could be price or output)
Profit is a function of what…
A) If firm 2 doesnt enter
B) If firm 2 enters
A) firm 1 earns monopoly profits
π₁M (K1,x1)
(profit is a function of investment level and their price/output
B)
π1(K1,x1,x2) and
π2(K1,x1,x2)
(profit is a function of … and also the other firms price/output
We said in 2nd stage firms choose x1,x2 i.e which can either be price or output
Difference between competing in prices or output
Competing on output has downward sloping best responses - strategic substitutes i.e when firm 1 increase output, other reduces it
Competiting on prices has upward sloping best responses - strategic complements (when firm 1 raises price, so does the other) (
What does firm 2’s decision to enter depend on
Firm 1’s choice of K1 - whether it makes entry profitable
I.e enter if
π2(K1,x1,x2)> 0
What if increase K1 (firm 1 overinvests), what happens to π2
Can be positive or negative
Negative if firm 1’s investment is in cost-reducing R&D (bad for firm 2)
Positive if firm 1’s investment is in informative advertising expanding the market (good for firm 2)
So firm 1’s choice of K1 has direct and strategic effects:
Direct effect on firm 1’s profit (recall π1 is a function of k1 all the time)
Strategic effect: changing firm 2’s behaviour (enter if their π2>0 which is function of K1)
2 dimensions to the strategic effect of firm 1’s choice of K1 (changing firm 2’s behaviour)
Deters or accomodate entry
Change firm 2’s choice of price/output if it enters
So what does firm 1 consider in their choice of K1 (3)
Effect on their own profit ceteris paribus
Does it make firm 2 entry more likely or less likely
If firm 2 enters, does investment make competition more intense or less
this leads to different strategies they pursue (next)…
So with these 3 considerations, there are a number of strategies firm 1 can pursue in Fudenberg and Tirole
Top dog approach
Big/strong to look tough
Invest in cost-cutting tech (R&D to reduce prod costs) in stage one and cournot competition in stage 2
Overinvestment lowers costs increasing firm 1 output reducing firm 2’s output (recall downward sloping BR’s for output) and profit if they were to enter. Sufficient investment will make it unprofitable (as recall π2 function of k1 and x1)
overinvest regardless of whether they want to accomodate or prevent entry
Puppy dog approach, explain
over or underinvest
Be small/weak to look soft
Invest in cost-cutting technology but Bertrand in stage 2
Rather under-invest (to not intensify price comp) if it is going to accomodate entry to get/keep higher prices
Lean and hungry explain
over/under invest?
Small/weak to look tough
Invest in informative advertising and Bertrand in stage 2.
More advertising increases profits for both firms. So thus if firm 1 wants to deter entry, it should under-invest, to make the market seem unattractive
Fat cat explain it
b) over or underinvest
Be big/strong to look soft
Invest in informative advertsing, with price competition
They accomodate entry if they think profits with 2 in the market is larger (by sharing a large market) , so look soft to get firm 2 to enter.
Overinvest as informative advertising can increase market size and weaken price competition to accomdate entry
So 3 things to consider in firm 1’s strategy
Does it want to deter or accomodate (deter if profits larger as a monopolist, accomodate if profits larger in a larger market with the 2nd firm)
Does investment make it appear tough or soft
How will firms compete in stage 2 (cournot or bertrand)
Diagram for optimal strategy pg 30
