1.9.2 Oligopolistic Markets Flashcards
What are oligopolistic markets?
Markets dominated by small number of firms:
All models assume:
- Sellers have market power and behave strategically
- Buyers are price takers
- Significant barriers to entry, even in long run
What are cartels?
Firms collude by coordinating prices and quantities operating as a cartel, or they can compete with one another
Firms may be incentivised to form a cartel to increase profits
Best case for firms: behave as if they were a signle firm and set monopoly price, artificailly gaining monopoly power and so set monopoly prices
Forming cartels is profitable for any type of firm - even perfectly competitive ones - but much easier if there are fewer firms to begin with
How are cartels graphically presented
Page 25
(basically just supernormal profits)
In a market with n identical firms, if firms are the price takers, ec is equilibrium
However cartels set monopoly quantity qm, each firm sells qm = Qm/n at pm and gets higher profits than at ec
- lowers CS and raises PS for firms in cartel
Why dod we rarely see cartels?
Illegal - CMA/competition policy
Each cartel member incentive to produce more and increase own profit at expense of other cartel firms, creates incentive to cheat
Each firm has incentive to expand output.
At qm, MC <pm which is the firm’s effective MR
Competition policy:
- Cartels common until early 20th century
- All developed countries pass laws to forbid
- Firms caught breaking - UK milk cartel 2007, European vitamin cartel 2001
- Some activity undetected - done legally by simply folowing trends
- Some cartels operate beyond competition authorities
What would make cartels easier to form and what would make them easier to detect?
Form:
- Competition laws weak
- Cartel detect and punish cheating firms
Detect:
- Smaller uncertainty regarding collusion
- Easy to monitor rival output levels and prices
- High entry barriers (few firms)
- Production differentiation easier/harder - means lower profits from cheating, punishment through overall increased prodcution less effect, more complex agreements needed
What is a cournot oligopoly?
How oligopoly firms behave if they simultaneously choose how much two produce
Firms set their cost functions and quantities seperately - markets last one period, each firm choose quantity once
Example of a cournot oligopoly
e.g. estimated demand function Q = 339 - p, thus inverse is p = 339-Q
Q (total quantity) = qA + qB
Assume MC = 147
Simplest case: duopoly:
Firms set their quantities independently
- Market demand not met by other seller at any give n price
- Depends on competitiors choice
If B produces nothing then As demand curve is the market demand curve, so A optimal quantity is 96
If B produces qB = 64, A’s demand curve is market demand curve minus 64, so A optimal quantity is lowered to 64 (AR/MR shift inwards)
By determining A’s optimal output for all possible level of B’s output, we can find A’s best response function
A’s demand function:
P = 339 - (qA+qB)
How to calculate MR based on residual demand curve?
If B produce qB, A can act as a monopoly wrt people not using B
Given qB, if A chooses qA price it will be p = 339 - qA - qB
Revenue = 339A - qA^2 - qBqA
MR = DR/dqA = 339 - 2qA -qB
MR = MC
=> 339 - 2qA - qB = 147
qA = 96 - 0.5 qB
This is A’s best response function
With the same steps we can get qB = 96 - 0.5 qA
‘Note that this is the same as A’s best response with the subscripts reversed’
This is because MC are identical and both firms face same market demand function
You can then graph these i.e.
B best reponse:
qB= 96 - 0.5 qA
A best reponse:
qA = 96 - 0.5 qB
qB = 192 - 2qA
The intersect is the Cournot equilibrium by finding the intersection of the two beest response functions
What happens if there are 3 firms?
p = 339 - qA - qB - qC
Revenue calculated as before, multiply by qA
MR = dR/dqA
MR = MC = 147 (as previous example)
Use this to calculate A best reponse function
- B and C are the same with different subscripts
The Cournot equilibrium is a Nash equilibrium - all 3 firms best responding to their rival firms and so
qA = qB = qC = 48
- Firms output lower with more competitiors, but industry output increases to Q =144 and price falls to 195
With constant mraginal costs, as number of firms increases, the Cournot equilibrium gets closer to perfectly competitive equilibrium
What is the Bertrand Model?
- Argued Cournot assumption that firms choose quantity
- Instead firms choose price, consumers choose quantity
Analysed where firms compete in prices
- Derived each firms best response curve
Say there are 2 firms at p = 5, firm 2 charges p > 5
If firm 1 charges higher - sells nothing, no profit
If firm 1 matches - serve half the market
If firm 1 undercuts - captures entire market
- Best response to undercut by as little as possible
If firm 2 chooses p2 = 5, firm 1 should choose p1 = 5 - the only equilibrium where both firms play the best response
This is the Bertrand/Nash-Bertrand equilibrium
- Each firm optimal level given the choice of the other firm
- No firm incentive to deviate from original choice
Firms set p = MC and make 0 economic profits, so outcome very different from Cournot equilibrium
- Same as in perfect competition
- Does not depend on number of firms - will always be p = MC
What is the Bertrand paradox and how do we resolve it?
In reality many firms set prices not quantity - leads to unrealistic predictions
Resolving:
- Firms only set price, really set q
- Often long production lead times in such markets
- Once production plan made, output largely fixed
- Firm adjust price such that all quantity produced sold; but required price determined by earlier output decision
What are the features of most markets with differentiated products?
Cant capture entire market by lowering one’s price
Trade off between lower price and higher quantity
Price settting now leads to less extreme results, firm set p > MC
- Examples include almost all consumer goods market - explain why firms try so hard to differentiate
How does the Bertrand fare with differentiated products?
Demand functions 2 key features:
- Demand decreases in own prices, increases in competitors price - means no ‘jumps’ demand change smoothly with price changes - all products imperfect substitutes
What is an example of a Bertrand equilibrium in a differentiated product market
Example: Cola
Coke/Pepsi imperfect substitutes
Coke: qC = 58 - 4pC + 2pP
Pepsi: qP = 63.2 - 4pP + 1.6 pC
Both MC = 5, no fixed costs
- Similar approach to Cournot, prices as the choice variables
- πC = TR - TC = pcqc - 5qc (MC = change in TC / Q)
(so deltaTC = MCQ) - qC = 58 - 4pC +2pP (multiply into pCqC - 5qC)
πC = 58pC - 4pC^2 + 2pPpC - 290 + 20pC - 10pP - For given pP, optimum choice of pC when dπC/dpC = 0
=> 58 - 8pC +2pP + 20 = 0
Best response for Coke:
pC = 9.75 + 0.25pP
For Pepsi:
4. πP = TR - TC = pPqP - 5qP
- qP = 63.2 - 4pP + 1.6 pC
πP = 63.2pP - 4pP^2 + 1.6pCpP - 316 + 20pP - 8pC - dπP/dpP = 63.2 - 4pP + 1.6pC + 20 = 0
Best response for Pepsi:
pP = 10.4 + 0.2pC
- Plot Bertrand-Nash graph - upward sloping (never downward sloping)
pP = 10.4 + 0.2 (9.75 + 0.25pP)
pP = 13
pC = 13
qC = 58 - 4(13) + 2(13) = 32
qP = 63.2 - 4(13) + 1.6(13) = 32
Note price > MC for both firms!
