Oligopoly (Cournot + 3 Market Concentration measures) Flashcards
(19 cards)
Bertrand oligopoly
Same as Bertrand duopoly i.e if firms share the lowest MC, split sales
If one has lower MC than all, undercuts the 2nd most efficient supplier’s at price just below their MC.
Linear cournot oligopoly, with constant MC profit max problem. Let P = v -Σqj (i.e price depends output of all firms!)
Find BR₁(my own working pg8)
B) General best response for firm i)
C) what does firm i’s output depend on (important)
MaxΠ₁ = (V - Σqj - c₁)q₁ - f
Differentiate FOC with respect to q₁
V - 2q1 - sum of outputs not including q₁ since FOC removes it) - c1
Set = 0 and
Rearrange to get firm 1’s best response:
q₁ = 1/2 (v - c₁ - sum of outputs without q1)
B) Generally expressed as 1/2 (v - ci - [Q - qi])
C) So firm 1’s output depends on joint output of other n-1 firms!
What is final expression for qi (just remember key equation, don’t understand working)
b) intuition of final BR of general case (firm i)
b)
qi = v - ci + n(cbar - ci) / n+1
b)
If ci higher than cbar (firm i’s cost > average), will sell less
If ci less than cbar, will sell more
Price equation pg11 (just memorise not working)
B) result of cournot oligopoly using price equation
P = (v + Σcj) / n+1
v+ sum of firms costs / (n+1)
B) more firms = lower price since (n+1) is denominator
Findings of the general best response of firm i
(On quantity, price and cost)
Hint: use expressions
qi = v - ci + n(cbar - ci) / n+1
Q = (nv - Σcj) / (n+1)
P = (v + sum of firms costs) / (n+1)
Using the equations we find:
Quantity:
The more firms in the market, higher total output but each firms output lower! (Q higher, Qi lower)
Price is lower (use equation)
Cost: lower cost of an individual firm, the more it’ll produce (if ci lower than cbar)
This is asymmetric since we have cbar and ci
What is best response expression of firm i in a SYMMETRIC case (equal MC’s)
B) best response of all firms (Q)
C) price (P) in symmetric case
NEW: WHAT WOULD PROFIT BE FOR A FIRM (from mock exam q2a cournot oligopoly, or problem set 2 q1a!
With equal MC, cbar = ci so it cancels out in the expression so just left with
qi = v - c / n+1
B) Q = n(v-c) / n+1
C) P = v + nc / n+1
D) Profit is just q²!
qi = (v - c / n+1)²
So in the symmetric cases we just covered.
What can we notice when n=1 , vs a large value of n?
The answers we get when we let n=1 are prices and quantity under monopoly!!
e.g q₁ = v-c/n+1
so becomes q₁ = v-c/2 which is monopoly quantity!
Large value of n, will approach perfect competition quantity and prices!
Cournot oligopoly diagram pg 15 and 16 (best response diagram with Q-qi and qi)
Y axis Q-qi (output of everyone else)
X qi
At bottom of BRi line, firm i sells monopoly output, when Q-qi = 0 i.e other firms don’t sell, thus firm 1 monopolist
Upward sloping curve as if 2 firms in market, each firm sells same output so Q-i = qi
as we increase number of firms, curve Q-qi keeps getting steeper so equilibriium means qi keeps falling eventually till Qc perfect comp!
Partial equilibrium diagram pg 17
We just see P eventually = MC as no of firms increase
Key result:
cournot oligopoly approaches perfect competition as number of firms increases.
How can we find how quickly this happens though?
Compare welfare effects as n of firms changes
Use diagram i drew to work out welfare effects, answers on pg 19
Monopoly CS = 50: find area of CS triangle
As 22-12 = 10
10 x 10 /2 = 50
vs perfect comp is where P=MC, so CS
22-2 x 20 /2 = 200
Findings on pg 20/21
What do they tell us about our question on how quickly does perfect competition occur (i.e how many firms needed to reach Qc)
B) what about consumers
Quickly, lose DWL fast! Don’t need many firms to reach Qc/eliminate the welfare losses from monopoly. So we lose DWL quick!
B) although we lose deadweight loss quickly, consumer welfare changes slowly; consumer surplus is still a lot worse off even with 10 firms than they would be in perfect competition
This all assumes firms are symmetric though e.g increasing number of firms nears perfect competition, but it wouldn’t if there is one large firm and a number of small firms. still closer to monopoly not perfect comp
How can we measure market concentration (3)
Choose a number of firms, add up share of largest firms
Herfindahl index
Lerner index
Example of why summing up a number of firms’ market share
not informative
E.g choose to look at 4 largest firms in market
Consider the following two markets, with shares of the four largest firms given by:
• 0.3, 0.2, 0.2, 0.2
• 0.6, 0.1, 0.1, 0.1
They both give C₄ = 0.9 , but are they equally competitive?? no!
Herfindahl index
Uses squares of market shares, gives range between 0-1 (0=perfect comp 1= monopoly)
H = square each individual market shares and add them together
What would this mean for our previous examples (assume each industry has a fifth firm with share
0.1)
• 0.3, 0.2, 0.2, 0.2, 0.1: what is H index
• 0.6, 0.1, 0.1, 0.1, 0.1: what is H index
H=0.22
H=0.4
This appears to be better than C4 as it shows the
market with a dominant firm (bottom one) is less competitive
Lerner index
b) what is it weighted by then?
Weighted average of firms’ price-cost margins,
b) weighted by market shares
L = Σ(si x p-ci/p)
Si is market share of firm i
Intutition is if P a lot bigger than ci, large price cost margins, likely higher market share (since able to sell way above cost!
What does lerner index depend on
How firms compete (cournot vs bertrand), since use price-cost margins!
e.g Bertrand P=MC so L=0 (no market power - price takers)
but Cournot P>MC so L shows positive market power
Overall assessment of 3 method to assess market concenration
Herfindahl andn C4 only measure market concentration
Lerner index much better indicates market power, but hard to measure since requires knowledge of cost data for each firm to know price-cost margins
